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Journal of automation, mobile robotics & intelligent systems

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Articles2

Interactive Programming of a Humanoid RobotMikołaj Wasielica, Marek Wąsik, Andrzej Kasiński DOI: 10.14313/JAMRIS_3-2014/21

WiFi-Guided Visual Loop Closure for Indoor Navigation Using Mobile DevicesMichał NowickiDOI: 10.14313/JAMRIS_3-2014/22

Application of the One-factor CIR Interest Rate Model to Catastrophe Bond Pricing under UncertaintyPiotr Nowak, Maciej RomaniukDOI: 10.14313/JAMRIS_3-2014/23

Boosting Support Vector Machines for RGB-D Based Terrain ClassificationJan Wietrzykowski, Dominik BelterDOI 10.14313/JAMRIS_3-2014/24

Power System State Estimation using Dispersed Particle FilterPiotr Kozierski, Marcin Lis, Dariusz HorlaDOI: 10.14313/JAMRIS_3-2014/25

Face Detection in Color Images using Skin SegmentationMohammadreza Hajiarbabi, Arvin AgahDOI: 10.14313/JAMRIS_3-2014/26

Computing with Words, Protoforms and Linguistic Data Summaries: Towards a Novel Natural Language Based Data Mining and Knowledge Discovery ToolsJanusz Kacprzyk, Sławomir ZadrożnyDOI: 10.14313/JAMRIS_3-2014/27

The Bi-partial Version of the p-median/p-center Facility Location Problem and Some Algorithmic Considerations Jan W. OwsinskiDOI: 10.14313/JAMRIS_3-2014/28

A Novel Generalized Net Model of the Executive Compensation DesignKrassimir T. Atanassov, Aleksander Kacprzyk, Evdokia SotirovaDOI: 10.14313/JAMRIS_3-2014/29

Journal of automation, mobile robotics & intelligent systems

Volume 8, n° 3, 2014 Doi: 10.14313/Jamris_3-2014

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contents

Journal of Automation, Mobile Robotics & Intelligent Systems VOLUME 8, N 3 2014

I P H RI P H RI P H RI P H R

Submi ed: 16th April 2014; accepted: 29th May 2014

Mikołaj Wasielica, Marek Wąsik, Andrzej Kasiński

DOI: 10.14313/JAMRIS_3-2014/22

Abstract:This paper presents a control system for a humanoidrobot based on human bodymovement tracking. The sys-tem uses the popular Kinect sensor to capture the mo-on of the operator and allows the small, low-cost, and

proprietary robot to mimic full body mo on in real me.Tracking controller is based on op miza on-free algo-rithms and uses a full set of data provided by Kinect SDK,in order tomakemovements feasible for the considerablydifferent kinema cs of the humanoid robot compared tothe human body kinema cs. To maintain robot stabilitywe implemented the balancing algorithmbased on a sim-ple geometrical model, which adjusts only the configura-on of the robot’s feet joints, maintaining an unchanged

imitated posture. Experimental results demonstrate thatthe system can successfully allow the robot to mimic cap-tured human mo on sequences.

Keywords: bipeds, control of robo c systems, humanoidrobots, legged robots, teleopera on

1. Introduc onProgramming humanoid robotmovements is a dif-

icult task. They are usually programmedwith numer-ical optimization techniques or manually, which re-quires a lot of knowledge and skills about kinemat-ics and dynamics of the robot. Whereas humanoidrobot movements should be natural and human-like,human motion capture systems appear to be the pre-ferred solution. However, differences between humanand robot kinematics and dynamics, as well as highcomputational cost cause dif iculties in the straight-forward solution of this problem.

In our previous work [13] we presented the small-size humanoid robot M-bot (Fig. 1) designed fromscratch as an alternative to robots built from commer-cially available kits [1] [2] [3]. As far as constructionis concerned the main assumption was the low costand relatively high number (23) of Degrees of Free-dom (DOF). In our recent work [12] we also presenteda manual programming method of the robot.

In this paper, we propose a simple, ef icient andlow-cost control system for our humanoid robot. Theinput device is Microsoft Kinect sensor [5], whichis relatively cheap compared to professional motioncapture (MoCap) systems and has an advantage inthat it does not require sophisticated MoCap suits towear. Kinect sensor and its included Microsoft KinectSoftware Development Kit (SDK) provide a 3D Carte-sian position of the joints of the observed person. We

use all available joints simultaneously to provide theclosest possible imitation of motion and static sta-bility of the robot. Our mimicking strategy is basedon optimization-free solutions and our balance con-troller uses a simple geometrical model. It should benoted that servomechanisms inM-bot have signi icantbacklash, no feedback, limited resolution and controlrate. Also construction of the robot was not preciselycalibrated. Experimental results demonstrate that thecontroller can track humanmotion capture data whilemaintaining balance of the robot.

After introducing related work in the next section,we brie ly summarize the overviewof the systemcom-ponents in section 3. Section 4 provides a detailed de-scription of the imitation strategy while a simple sta-bility controller is presented in section 5. Experimen-tal results are summarized in Section6. Thepaper con-cludes with Section 7.

Fig. 1. The robot (poses obtained from our mimickingsystem)

2. Related WorkMost of the available control frameworks for hu-

manoid robots require professional motion capturesystems, precise commercial robots, and sophisticatedalgorithms. For example, Yamane et al. [14] developeda system that allows a real force-controlled humanoidrobot tomaintain balancewhilemimicking a capturedmotion sequence. This system employs the model ofa simpli ied robot dynamics to control the balance, acontroller for joint feedback, and an optimization pro-cedure yielding joint torques that ensure simultane-ously balancing and tracking. However, this system

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does not allow tracking of motion sequences that in-clude contact state changes, like stepping. In [15] thisapproach is extended, but only on a simulated robot,by adding a procedure that keeps the center of pres-sure inside the polygon of support, which varies as therobot moves its feet.

Themotion-capture-based approaches to control ahumanoid robot mostly use pre-recorded motion se-quences. Only a few systems described in the liter-ature can interact with the human operator in real-time. Such a system, described in [11], uses the Kinectsensor and the Nao small humanoid. This system im-plements balance control and self-collision avoidanceby involving an inverse kinematics model and pos-ture optimization. The captured humanmotion is splitinto critical frames and represented by a list of opti-mized joint angles. The similarity of motion is evalu-ated by the con iguration of the corresponding linkson the actor and imitator in the torso coordinate sys-tem. This work is most similar to our approach, butit was demonstrated on a more complicated robotthat, unlike the M-bot, has reliable position feedbackin the joints. Moreover, the solution presented in [11]requires numerical optimization, while our approachyields a feasible robot con iguration in a single-step,using only geometric computations, and thus it is com-putationally ef icient.

3. System ComponentsOur control system scheme is presented in Fig. 2.

Input device of the system is Kinect sensor, which ob-tains a depthmapof the observed scene,where the hu-man being is located. Microsoft Kinect SDK beta 2 pro-cesses the cloud of points and returns a Cartesian po-sition of 20 skeletal joints [6]. This data is an input tothe trajectory forming algorithm, which converts the3D position of human joints to angular con igurationof the robot’s servomechanisms. Con iguration is thenmodi ied to provide static stability maintenance. Fi-nally corrected information of joints angles is trans-ferred to the robot.

Fig. 2. Kinect-based programming system overview

3.1. Mo on Capture System

Kinect is equipped with RGB camera (1280×1024pixels for 63×50 degrees FOV, 2.9 mm focal length,2.8μm pixel size), IR camera (1280×1024 pixels for57×45 degrees FOV, 6.1 mm focal length, 5.2μm pixelsize) [8], and IR pattern projector. Both IR cameraand IR projector are used to triangulate points posi-tion in space. Minimal depth sensor range is 800 mm

and maximal 4000 mm. However, the Kinect for Win-dows Hardware can be switched to Near Mode whichprovides range of 500 mm to 3000 mm. Resolution ofobtained depth map is 11-bit, which provides 2,048levels of sensitivity [7]. Highest possible frame rate is30 fps, which is available for depth and color stream in640×480 pixels resolution [4].

Fig. 3.Microso Kinect SDKMo onCapture process [10]

Microsoft Kinect SDK is able to track users pro-viding detailed information about twenty joints of theuser’s body in the camera ield of view. Fig. 3 shows anoverviewof this process. First, from single input depthimage human silhouettes are extracted (because ituses depth map it is no longer necessary to wear spe-cial MoCap suits). Then a per-pixel body part distri-bution is inferred. Each color indicates the most likelypart labels at each pixel. Finally local modes of eachpart distribution are estimated to give con idence-weighted proposal for the 3D location of body joints[10].

3.2. The robot

Our robot is a proprietary construction. It wasmade of scale model servomechanisms and hand-bended 1mm aluminium sheet (Fig. 1). The robotweights 1.8 kg and is 42 cm tall. Total number of DOFsis 23. It has 7 servos in each leg. Usually a robot leg has6 DOFs, but we added bended toes to improvewalkingpossibilities. Three DOFs are located in each arm, onein the trunk, and two in the head. Inside the robot islocated custom made printed circuit board equippedwith ATXMega microcontroller, 3-axial accelerometerand 3-axial gyroscope. All 23 servomechanism are di-rectly connected to motherboard. We added a blue-tooth module to enable wireless communication withthe host computer. This link is used to boost computa-tional capabilities of the microcontroller and to allowthe addition of external sensors like Kinect.

4. Mo on Imita on ProblemKinect sensorprovidesMoCapdata in3DCartesian

coordinates form, but our robot’s actuators are angu-lar position controlled. In this situation, since we op-erate in two different coordinate systems we have tode ine how to understand the adequacy of a human

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pose by the robot. We considered scaling the opera-tors joints position to compare it with the robot’s one,but we realized that our robot has different propor-tions to a human and also the operator will not al-ways be the same person. As a result we would haveto adjust the scale for each joint and for each operatorchange, which will not guarantee pose adequacy. Weobserved that humans learn new choreography by im-itating pose angular con iguration rather than Carte-sian position of joints, e.g. children learning some newposes from adults. Therefore we decided to representhuman posture as rotational joints con iguration andthen transfer it directly to the robot’s servomecha-nisms. Operating in multi-angular space guaranteesthe important con iguration-based scale invariance.

Fig. 4. Kinema c structure of the robot

We also wanted to avoid singular poses while stillachieving accurate pose imitation to avoid computa-tionally costly iterative calculus. In order to get thiswe assumed that the number of human DOFs and rel-ative orientation of the rotation of their axes are thesame as robot’s (Fig. 4). Distance between DOFs is un-restricted and depends on human proportions. As ori-gin of the Coordinate System (CS) we chose the inter-section of spine and shoulders axes. Our skeleton istreated as 5 independent kinematic chains (legs, armsand head). Then we provided structural reductionof DOFs. Namely, we consider a kinematic chain di-vided into several sections with maximum three DOFseach. Knowing the 3D position of 20 human jointsfrom Kinect we are able to obtain inverse kinemat-ics (IK) equations for each particular chain section.These IK equations are simple algebraic calculationsand thanks to this, we avoid much slower numericalcomputations. Because the position of each body partgivenbyKinect is used,weobtain exact representationof human body con iguration, avoiding singular posesat the same time. Moreover this solution is optimiza-tion free, because the obtained robot’s con igurationis practically close to the operator’s.4.1. Arms

According to the above assumption we consideredour upper limb as made of two sections. The shoul-der section-starts in origin of the CS with 2 DOFs and

arm section. We calculated particular sections con ig-uration with Eulerian rotation matrices representa-tion. However the arm of our robot has 3 DOFs, whilea human one has 4 DOFs, excluding the wrist. In thissituation we had to compensate for this disadvantageto a obtain visually acceptable con iguration. The ad-vantage of that robot construction is that the elbowcan be bended over the straight angle. Therefore weare able to minimize dead zones (Fig. 5). Also, whenservo reaches angular limit, con iguration for this jointchanges with hysteresis.

Fig. 5. Approxima ng human arm configura ons withthe limited number of DOFs in the robot

4.2. Head and TorsoMicrosoft Kinect SDK beta 2 do not provide human

head orientation, therefore we implemented a con-troller, which directs the robot’s ”eyes” to look on theoperators head. Knowing relative position of the robothead to the Kinect sensor and relative position of theoperator head, we were able to triangulate con igura-tion of 2 DOFs of the robot’s neck.

Single DOF of the robot torso enables it to tilt. Itsangular position is de ined as roll angle between ori-gin of CS and the hip CS of the operator.4.3. Legs

We divided the leg kinematic chain into two sec-tions: hip and knee.We do not consider the foot orien-tation, because information extracted from the Kinectdata is usually highly inaccurate (in section 5 we ex-plain how to obtain ankle joint con iguration). To de-ine hip joint con iguration, we took into account hipto heel vector orientation instead of thigh orientation.This results from the assumption that representationof the operator’s leg length is expressed as the pro-portional distance between hip and heel, which variesfrom 0 to 100% of the maximal leg length. Thereforeknee angular position is calculated with the law ofcosines. All of this is necessary to improve the balanc-ing algorithm of the robot. Since the hip joint has 3DOFs it is critical to de ine onemore vector, perpendic-ular to hip to heel vector, to obtain three Euler angles.To do this we de ined a vector, which is a cross prod-uct of the thigh and calf orientation. We used it, ratherthan feet orientation, because Kinect data for the calfand thigh area is much more accurate.4.4. Configura on Correc on

As result of the algorithm calculationswe obtainedcon iguration of all joints, a set of 23 elements. Some-times in this data outliers occur, caused by Kinectreading errors. To smooth the robot movements we

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average the last 6 measurements for each joint an-gle. Number of samples was manually adjusted (thegreater the number, the less dynamic movement). Wealso provided simple self-collision avoidance meth-ods. The algorithm limits the range of the angle of eachservomechanism, according to the eq. 1:

Θti =

Cimin if Θti ≤ Cimin ,

Θti if Cimax ≤ Θt

i ≤ Cimin ,Cimax if Θt

i ≥ Cimax ,(1)

where Cimin and Cimax are angular limits for ex-treme position of each servomechanism.4.5. Opera ng Modes

Additionally we implemented two operatingmodes: a show and face to face. In the irst modethe robot and the operator are turned in the samedirection i. e. to the audience. In this case con igura-tion of the operator can be directly transferred to therobot. But in second mode, where the robot faces theoperator, his con iguration has to be mirrored. Wechange location of con iguration in our data set of theleft side of the robot to the right and vice versa. If it isnecessary we change the angle sign.

5. Stability MaintenanceDescribed in section 4 robot con iguration does

not account for the different humanmass distributionand inertia. Because of Kinects signi icant measure-ment error of human feet position, the obtained an-kle con igurations are encumberedwith errors, whichis essential for pose stabilization. In this situation weneed to implement a separate balance algorithm in therobot. It is based on the static model and controls ac-tual COM position relatively to the robot’s supportingfeet. When a subsequent pose indicates loses of therobot static stability the control system adjusts COMposition by using only the robot feet joints.5.1. Center of Mass

To maintain stability of the robot, irst we con-sidered using a stabilizer based on the Zero MomentPoint (ZMP) [9]. Servomechanisms in our robot do notprovide any feedback information, even about angularposition. The robot does not have pressure sensors init’s feet too, therefore implementation of ZMPwas notpossible. To maintain the static stability we inally de-cided to implement a controller based on the positionof the Center of Mass (COM) projection on the groundplane.

We obtained themass and relative position of COMof each robot segment from CAD data. We calculatedabsolute COM position using con iguration data andthe relative COM position of each segment, respec-tively to the robot Coordinate System located in thetorso. Assuming that the robot consists of N rigid-body links in three dimensions, the absolute COM po-sition is given as

COMx,y,z =

∑Ni=1 mi[xi, yi, zi]

′∑Ni=1 mi

, (2)

where mi is a mass and [xi, yi, zi]′ is a position of

each robot segment.Because used servomechanisms have signi icant

backlash and positioning error of about ±1.5, we donot consider COM as point, but as a ball. We assumethat the ball represents punctual COMwith embeddedmeasurement uncertainty as its radius. This funda-mental assumption implicates that to maintain staticstability, projection of the COM to ground plane doesnot have to lie in the foot supporting area, but on theline segment connecting centers of the feet. Thereforespace of existing solutions was reduced from two toone dimension.5.2. Simple Stability Model

The main task of our system is to imitate theoperating person accurately, therefore any obtainedrobot’s con iguration modi ications are not recom-mended. Also the operator’s foot orientation readingsare of poor quality especially since the robot’s anklejoints are essential to balance. Combining these argu-ments we propose a simple solution.

Position of the robot’s COM is calculated before ex-ecuting each posture, 50 times per second. To adjustCOM position we use only feet orientation, rest of thebody joints are ixed. Changing feet orientation hasnegligibly small in luence to mass distribution, there-fore we can assume that the position of the robot’sCOM is constant according to the robot’s CS in currentframe. Thanks to that, the robots pose is same as theoperators. Also this solution is optimization free, be-cause no iterations are needed to estimate COM posi-tion for each con iguration change.

The only problem to solve is the calculation of ori-entation of the robots foot according to its CS. To dothiswepropose a simple geometricalmodel presentedin ig. 6. Firstweassumed that the groundonwhich therobot stands is lat, so the normal vector to the surfaceis parallel to gravity vector all over the place. Then wecan introduce vector V , which has to be parallel to thenormal of the support surface to maintain static sta-bility. Since the feet are robot’s support surface, withits centers in Pp and Pl points, the V should start inline segment PpPl and end in the COM. Also observingthat Pp and Pl should lie on the same surface, V has tobe perpendicular to thePpPl. Combining this assump-tions we obtained equation 3 to calculate V orienta-tion.

V =−−−→PLPP × (

−−−−−−→PLCOM ×−−−→

PLPP ) (3)

Knowing V orientation according to the robot’s CSwe can substitute it into inverse kinematics equations.Because the ankle joint has two DOFs, only a single3D vector is needed to de ine its orientation, and wecan easily calculate its con iguration using explicit al-gebraic transformations.5.3. Side fall preven on

Introduced ankle strategy guarantees stabilitymaintenance only when projection of COM to the linesegment will be inside this segment. In other words

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Fig. 6. Stability maintenance strategy: schema cs (A)and visualiza on on the robot (B)

we have to detect the possibility of exceeding outerboundary of the foot by COM and adjust con igurationto prevent against falling to one side. We decided todetect the possibility of falling bymeasuring the anglebetween two vectors (eq. 4):

(x, y) = arccos (x, y)

|x| · |y|. (4)

For each vectors pair angles are speci ied in eq. 5:

α = (−−−−−−→PPCOM, V ),

β = (−−−−−−→PLCOM, V ),

γ = (−−−−−−→PPCOM,

−−−−−−→PLCOM).

(5)

To ind out if next pose is stable we have to solveeq. 6:

Pose =

Stable if α+ β = γ ∧ α = 0 ∧ β = 0,Stability limit if α = 0 ∨ β = 0,Unstable if α+ β > γ.

(6)We simply calculatewhether vector V is inside our

modelled triangle (Fig. 6(A)). If it is inside the posewill be stable and no adjustments are needed. Con ig-uration can be directly transmitted to the robot. If itis on the stability boundary, con iguration also can betransmitted. In the third case we have to modify exist-ing con iguration to guarantee pose stability. Howeverdoing this we should as little as possible modify poseto maintain it’s similarity to the operator pose.

Fig. 7 presents scheme of adjusting pose. The aimis to transform the unstable con iguration (A) to a sta-ble one (D). First (A) we calculate the proper angle byusing eq. 5. This angle informs us about vertical devia-tion. Rotating our model by this angle (B), we can cal-culate the intersection point of ground and the edgeof the triangle. Knowing the position of this point andposition of vertex we are able to calculate the distancebetween them (C). We can simply shorten the appro-priate leg, as in amethod of adjusting leg length in sec-tion 4.3. Finally we obtain a stable pose (D), which canbe transferred to the robot, after updating the foot ori-entation.

Fig. 7. Illustra on of the side fall preven on strategy(from le to right)

5.4. Single Leg Standing and Correc on from IMUOur presented balance algorithm is also able to

provide stabilization on a single leg. It requires de in-ing vector V as V =

−−−−−−→PPCOM or V =

−−−−−−→PLCOM . Then

the balancing algorithm will be adjusting orientationof robot’s ankle so that the COM will be always overcenter of supporting feet.

By adding the inclination angles obtained from theIMU to the orientation of vector V we can also com-pensate to some degree the ground tilting.

This additional features have not been imple-mented, but theoretical considerations imply that theidea is correct.

6. Experimental Results6.1. Controller Implementa on

We implemented the controlling framework on astandard PC computer,which is connected to the robotby bluetooth. Each robot actuator is controlled by theinternal position feedback loop running at 50 Hz forposition control. Therefore our implementation of theposture controller runs at this rate. Our control systemuses a con iguration extracted from Kinect data twicebecause the Kinect provides skeletal data at about 25Hz. Also it should be noted, that information abouteach actuator position is not visible for our main con-troller. This results from the lack of any feedback in-formation from the low-cost servomechanisms used.

The robot mass distribution is obtained from aCAD model. Similarly the angular position of gears isevaluated by eye, so it approximates only con igura-tion based on the appearance of the robot. Also thesupport platform is not levelled. All these factors causethe inconsistency with the real data. To compensatefor this, while the robot is in initial pose, we manuallyadjust the foot joints until the robot is able to standup-right on its own. Thenwe add these constant offsets tothe reference joint angles in order to match the initialreference robot pose with the actual initial pose.

6.2. Control of the SystemThe control framework is designed to be user-

friendly. Because the systemwas presentedwith audi-ence participation, we implemented an operator cho-sen algorithm. From humans in the Kinect ield ofview, the person who raises their hand will take con-trol of the robot (Fig. 8 A). From this moment the af-fection is ixed on that person.

Controlling the robot utilises the whole operatorsbody, so it is not possible for him to manage the con-

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trol application in a traditional way by using a mouseor keyboard. Therefore we implemented voice com-mands in the robots control system. Thus it is possi-ble to establish a connection to stop or to turn off therobot. Mainly this mode is used to switch a controllingperson.

6.3. Tracking Human Mo on Data

In our experiment the operator presents simpleand the hardest poses for the robot involving bothupper-body and legs. Snapshots from the trial1 areshown in ig. 8. Each pose is presented in frontal view,to minimize occluding of body parts, which result inKinect readouts errors. If the error occurs as a signif-icantly fast joints position step, which is faster thanpeople are able to perform, the robot trying to followsuch amovement in some cases can fall down, becauseof the high value of dynamic forces.

Fig. 8. Snapshots from the experimental valida on: tak-ing the control (A), various postures achieved by therobot (B,C,D)

Analysing captured video frame by frame we ob-served insigni icant lag when mimicking motion us-ing Kinect. This lag is mainly caused by the Kinect SDKcalculations time. However, the robot movements stayas dynamic as the operator. Both feet and hands ofthe robot have the same maximum speed, which doesnot signi icantly affect the robots stability, thanks tothe robust stability controller. This is an original prop-erty of the robot compared to other solutions [15][11]. Sometimeswhen the robot joint reaches its angu-lar limit, it performs additional correctivemovements,which are not performed by the operator. Such move-ments help the robot to avoid singular con igurationsand improve robot-human pose similarity limitation.Finally, the overall motion sequence is very similar tothe reference motion performed by the operator.

7. ConclusionIn this paper we have proposed a straight-forward

method to build a real time full body human imitationsystem on the proprietary humanoid robot. First wesuggest to rely on the angular representation of a hu-man pose as it is independent of human size, uses afull set of available joints data, and needs no optimiza-tion. We also propose a straight-forward balance con-trol strategy based on ankle joints control and have

proved it to be ef icient. Experimental results demon-strate that our implementation successfully controls ahumanoid robot so that it tracks human motion cap-ture data while maintaining the balance.

ACKNOWLEDGEMENTSThis research was funded by the Faculty of ElectricalEngineering, Poznan University of Technology grant,according to the decision 04/45/DSMK/0126.

Notes1A supplemental video is available at:

http://lrm.cie.put.poznan.pl/ROBHUM.mp4

AUTHORSMikołaj Wasielica∗ – Poznan University ofTechnology, Institute of Control and Informa-tion Engineering, ul. Piotrowo 3A, 60-965 Poz-nan, e-mail: [email protected], www:http://www.cie.put.poznan.pl/.Marek Wąsik – Poznan University of Tech-nology, Institute of Control and Informa-tion Engineering, ul. Piotrowo 3A, 60-965Poznan, e-mail: [email protected], www:http://www.cie.put.poznan.pl/.Andrzej Kasiński – Poznan University of Tech-nology, Institute of Control and InformationEngineering, ul. Piotrowo 3A, 60-965 Poznan,e-mail: [email protected], www:http://www.cie.put.poznan.pl/.∗Corresponding author

REFERENCES[1] Aldebaran Robotics, 2012 (online product spec-

i ication, link: www.aldebaran-robotics.com).[2] I. Ha, Y. Tamura and H. Asama, “Development of

open humanoid platformDARwin-OP”, AdvancedRobotics, vol. 27, 2013, no. 3, pages 223–232,DOI:10.1080/01691864.2012.754079.

[3] Kondo Kagaku Co., Ltd, 2012 (online productspeci ication, link: www.kondo-robot.com).

[4] Microsoft, “Kinect for Windows Sensor Compo-nents and Speci ications”, 2012 (online docu-mentation, link:http://msdn.microsoft.com/en-us/library/jj131033.aspx).

[5] Microsoft, “Kinect for X-BOX 360”, 2010 (onlineproduct speci ication, link: http://www.xbox.com/en-US/kinect).

[6] Microsoft Kinect SDK, “Getting Started with theKinect forWindows SDKBeta fromMicrosoft Re-search”, 2011, pages 19–20, (online document,link: http://www.microsoft.com/en-us/kinectforwindowsdev/Downloads.aspx).

[7] Microsoft, “Kinect Sensor”, 2012 (online docu-mentation, link:http://msdn.microsoft.com/en-us/library/hh438998.aspx).

8

http://lrm.cie.put.poznan.pl/ROBHUM.mp4

www.aldebaran-robotics.com

www.kondo-robot.com

http://msdn.microsoft.com/en-us/library/jj131033.aspx

http://msdn.microsoft.com/en-us/library/jj131033.aspx

http://www.xbox.com/en-US/kinect

http://www.xbox.com/en-US/kinect

http://www.microsoft.com/en-us/kinectforwindowsdev/Downloads.aspx

http://www.microsoft.com/en-us/kinectforwindowsdev/Downloads.aspx

http://msdn.microsoft.com/en-us/library/hh438998.aspx

http://msdn.microsoft.com/en-us/library/hh438998.aspx


[8] OpenKinect, “Protocol Documentation”, 2012(online document, link: http://openkinect.org/wiki/Protocol/_Documentation/#Control/_Commands;a=summary).

[9] P. Sardain and G. Bessonnet, “Forces acting on abiped robot. Center of Pressure – Zero MomentPoint”, IEEETrans. Systems,Man, and Cybernetics,Part A, vol. 34, 2004, no. 5, pages 630–637.

[10] J. Shotton, A. Fitzgibbon, M. Cook, T. Sharp,M. Finocchio, R. Moore, A. Kipman and A.Blake, “Real-time human pose recognition inparts from single depth images”, Proc. IEEEConf. on Computer Vision and Pattern Recogni-tion, Providence, USA (2011), pages 1297–1304,DOI:10.1109/CVPR.2011.5995316.

[11] F. Wang, C. Tang, Y. Ou and Y. Xu, “A real-time human imitation system”, Proc. 10th WorldCongress on Intelligent Control and Automa-tion, Beijing, China (2012), pages 3692–3697,DOI:10.1109/WCICA.2012.6359088.

[12] M. Wasielica, M. Wasik, A. Kasinski and P.Skrzypczynski, “Interactive Programming of aMechatronic System: A Small Humanoid RobotExample”, IEEE/ASME International Conferenceon Advanced Intelligent Mechatronics (AIM)Wollongong, Australia (2013), pages 459–464,DOI:10.1109/AIM.2013.6584134.

[13] M. Wasielica, M. Wasik and P. Skrzypczynski,“Design and applications of a miniature anthro-pomorphic robot”, Pomiary Automatyka Robo-tyka, vol. 2, 2013, pages 294–299.

[14] K. Yamane, S. Anderson and J. Hodgins, “Con-trolling humanoid robots with human mo-tion data: Experimental validation”, Proc.IEEE/RSJ, Int. Conf. on Humanoid Robots,Nashville, USA (2010), pages 504–510,DOI:10.1109/ICHR.2010.5686312.

[15] K. Yamane and J. Hodgins, “Control-awaremapping of human motion data with step-ping for humanoid robots”, Proc. IEEE/RSJ,Int. Conf. on Intelligent Robots and Sys-tems, Taipei, China (2010), pages 726–733,DOI:10.1109/IROS.2010.5652781.

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http://openkinect.org/wiki/Protocol/_Documentation/#Control/_Commands;a=summary




W - V L C I LM D

W - V L C I LM D

W - V L C I LM D

W - V L C I LM D

Submi ed: 3th June 2014; accepted: 11th June 2014

Michał Nowicki

DOI: 10.14313/JAMRIS_3-2014/23

Abstract:Mobile, personal devices are ge ng more capable ev-ery year. Equipped with advanced sensors, mobile de-vices can use them as a viable pla orm to implementand test more complex algorithms. This paper presentsan energy-efficient person localiza on system allowingto detect already visited places. The presented approachcombines two independent informa on sources: wirelessWiFi adapter and camera. The resul ng system achieveshigher recogni on rates than either of the separate ap-proaches used alone. The evalua on of presented systemis performed on three datasets recorded in buildings ofdifferent structure using a modern Android device.

Keywords:mobile devices, localiza on, sensor fusion

1. Introduc onMobile devices, like tablets or smartphones, are

nowadays equippedwithmore sensors than few yearsago. Those sensors combinedwith increasing process-ing capabilities allow to develop more complex, real-time algorithms that can be used for personal naviga-tion or detection of potentially dangerous situations.Those algorithms have not only academic, but alsocommercial signi icance due to the popularity of per-sonal mobile devices in the modern world.

One of the sensors available in every, recent An-droid device is a WiFi adapter. Most users use thisadapter to connect towirelessAccess Points (APs), butit can be used as a sensor that measures the strengthof surroundingwireless networks. The researched ap-proaches utilizing WiFi scans can be divided into twogroups:WiFi triangulation orWiFi ingerprinting. TheWiFi triangulation uses three or more APs that arevisible in line-of-sight and triangulates the user po-sition based on the measured signal strength of eachnetwork [1]. This approach is effective if the local-ization is performed in open-space areas. In a typi-cal building with cluttered environment that is richin corridors and additional rooms, WiFi triangulationis still applicable, but the number of APs needed toperform successful localization is higher. Therefore,if there exists an additional prerequisite to use onlythe already existing APs infrastructure, WiFi triangu-lation can providemisleading localization as the num-ber of signal re lections negatively impacts the mea-sured signal strength. In structured environment, theWiFi information can be used to determine the mea-sured position based on the list of available wire-less networks in a single scan. This technique, called

WiFi ingerprinting, determines the similarity of cur-rent scan to previous scans or to the entries in arecorded database of WiFi scans. The ef icient, work-ing solutions utilizing WiFi ingerprinting were pre-sented in [3], [4] and [12]. Other researches focus onusing sensors that are equivalent to the equipmentpresent in typical mobile devices, but do not performthe experiments on actual mobile devices [3], [19].

This information might be used to provide an esti-mate of the user’s localization, but the precision of sig-nal measurement depends greatly on the orientationof the measurement with respect to the APs. Holdingthe mobile device in different way or shadowing thesignal with the person’s body affects the obtained re-sults and can have a negative impact on the repeata-bility of themeasurements. Therefore, to alleviate thisin luence, it is bene icial to incorporate informationfrom additional sensors, e.g., an inertial sensor. Mod-ern mobile devices are in most cases equipped witha 3-axis accelerometer, a 3-axis gyroscope, and a 3-axis magnetometer. The information from these sen-sors can be used to create a system estimating the ori-entation of a smartphone [10]. The orientation esti-mate can be later effectively used to enhance the WiFimeasurement.

Another sensor that is a standard inmobile devicesis a camera. The sight plays signi icant role in the local-ization strategy of human beings and therefore imageprocessing is researched in robotics and computer vi-sion communities. Methods estimating the total mo-tion based on consecutive image-image estimates arecalled Visual Odometry and are especially importantfor mobile robots [14]. Typically, those methods inda sparse set of features that are matched/trackedin consecutive images. The positions of features incompared images are used to estimate the trans-formation. Due to the frame-frame estimation, thosemethods suffer from an estimation drift arising dueto error summation over time. This approach pro-vides a continuous estimate of motion, but is alsocomputation-demanding and thus energy-consuming.Energy-ef iciency is especially important for small,portable devices, and from user’s point of view shouldnot have a signi icant, negative impact on the batterylifetime.

The WiFi and vision based approaches to indoorlocalization are usually researched separately, ne-glecting the possible synergies of both informationsources and gains due to data fusion. The knownworks approaching the problem of multi-sensor fu-sion for indoor localization on mobile devices are

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dominated by the continuous data fusion paradigm,employing a ilter-based framework [8]. The resultsbeing presented are often achieved with custom ex-perimental setups [19], not actual mobile devices.Thus, these works avoid confronting the problems oflimited computing power and energy. Some other ap-proaches focus on enhancing the WiFi-based localiza-tion with data from inertial sensors, but do not usecameras [11], [18].

This paper presents a prototype system that de-termines on demand the position of a person insidea building using data from the WiFi and camera of amobile device (smartphone). The acquired WiFi scanis used to determine the best ingerprint match tothe WiFi scans recorded previously and stored in adatabaseof known locations. Then, theWiFi-basedpo-sition estimate is con irmed and re ined by matchinga compact representation of the location’s visual ap-pearance to the image-based description of the knownlocations, also stored in a database. Thus, the pro-posed system combines data from both sources of lo-calization information available in a typicalmobile de-vice, achieving higher recognition rates than eithor ofsubsystems and is less prone to failures caused by thepeculiarities of a particular environment. Moreover,the system is energy-ef icient as the loop closure de-tection procedure is triggered only when needed, as adiscrete event. To the best knowledge of the author, asimilar idea has not been yet presented in the litera-ture.

In section 2, the structure of the proposed systemis presented, as well as the details of the WiFi-basedand image-based subsystems. The next section 3 fo-cuses on the experimental evaluation of each sub-system and the integrated solution. Moreover, it de-scribes three datasets recorded in different environ-ments and used for evaluation. The last section 4 con-cludes the paper and mentions future work.

2. System Structure2.1. WiFi Fingerprin ng

The WiFi ingerprinting approach was irstly de-scribed in [1]. As the WiFi ingerprint allows only tolocalize in a known environment, the system based onWiFi ingerprint operates in two stages:- data acquisition stage,- localization stage.In the data acquisition stage, certain positions are cho-sen as references, where available WiFi signals arescanned and stored in a database. These positions canbe randomly chosen, uniformly chosen or based on thestructure of the building. Due to the energy consider-ations, the proposed system scans only the positionsthat are important for user navigation, .e.g., doors thathave to be crossed, beginning of the long corridor orthe entrance to a newpart of the building. Due to theselimitations, it is assumed that the user is capable ofperforming local navigation whereas system providesglobal position information that the user can applyto plan his/her movement. The WiFi ingerprint ap-

proach assumes that each position can be uniquely de-ined by the combination of access points’ MAC ad-dresses and RSSI signal strength values. An exemplarysituation is represented in Fig. 1,where theusermove-ment is represented by dashed lines, whereas the dis-crete events, when WiFi scanning is performed, aredrawn using circles. Each WiFi found in a single posi-tion is marked using a line connecting the AP and userposition. The list of WiFi networks available in eachposition is the list of lines that are pointing towardsuser’s position.

Assuming that the WiFi database of a loor is cre-ated, it is essential to ef iciently compare the list ofscanned WiFis X to the WiFi scans stored in thedatabaseD. The comparison has to be performed us-ing a function that evaluates the difference of twoscans: new scan X and one of the scans Y in thedatabase D. Typically, the WiFi scans are comparedusing the Euclidean norm [1]:

d(X ,Y) =1

N

√√√√ N∑i=1

(Xi − Yi)2, (1)

where Xi and Yi represent the strengths of i-th net-work found in both scans, X and Y . Number N is thecount of networks found in both scans.

Finding the best correspondence in the databasecan be written as inding a record, which distancefunction to current scan is minimal:

Ymin = argminY∈D

d(X ,Y) (2)

The Euclidean distance is usually applied as it allowsto precisely position user based on themeasured RSSIvalues. But in the case of sparse position set it is moreimportant to rely on the unique set of found networksthan on the strength of these networks. Therefore anevaluation of various distance/similarity functions isperformed in section 3.

Moreover, as the system operates, it gathers newdata that might be stored as the scans that have beencorrectly matched to some WiFi ingerprint from thedatabase, or as unclassi ied cases. Thisway the systemmight gather new information, which can be used todetect, when user revisits position previously addedto the database. The information about new positionscan be also used to provide user with the databasecontaining positions important for particular user,which due to the personal importance might be revis-ited in the future.

2.2. Visual Loop Closure

Visual loop closure is a technique that tries to de-termine if the currently observed scene had been pre-viously encountered based on the captured images.

Computer vision algorithms usually try to processonly a subset of available image information in orderto reduce the processing time. This observation is alsovalid for visual loop closure, for which the detection ofa sparse set of salient features is performed. In most

11


Fig. 1. InWiFi fingerprin ng approach, user’s posi on is recognized based on the combina on of scannedWiFi networks

Fig. 2. The processing steps of the Visual Bag of Wordsapproach

cases the SURF [2] detector and descriptor is used. An-other possible approachmay utilize the HoG [7] infor-mation. Each feature is then described by the set ofvalues representing its local neighbourhood. Descrip-tors for all salient features are then compressed into asingle image descriptor called a word. This approachis known as the Bag-of-Words approach [6]. To com-press the information into an image’s word, the Bag-of-Words approach irstly determines the k clustersof descriptor types using the k-means algorithm andthen labels each image descriptor with the number ofcluster it has been assigned to. The numbers of de-scriptors assigned to each cluster is used to create ahistogram representing an image in further computa-tions. The process results in reducing the representa-tion of a single image into one vector of loating pointvalues. The processing low of Bag-of-Words is repre-

sented in Fig. 2.In practical applications, the vision-based loop clo-

sure is hard to detect robustly. Even a small differ-ence in the observation’s orientation can in luence theobserved feature set and therefore prevent the sys-tem from correctly recognizing that the placewas pre-viously visited. What is more, the database of imagewords takes a lot of memory and may grow with thesystem’s running time, therefore the correspondingimage’s are not stored.2.3. WiFi-guided Visual Loop Closure

The main contribution of this paper is the combi-nation of the already known algorithms in creation ofa robust, data integrating system. The idea behind theproposed algorithm is simple: try tomatchWiFi infor-mation giving global estimate than can be a good ini-tial estimate for further con irmation from the vision-based loop closure subsystem.

The system starts with gathering WiFi and imageinformation into database during the preparation taskto allow further loop closures. Due to the WiFi mech-anism, WiFi scanning time takes one to ive seconddepending on the used WiFi adapter drivers. These,relatively long scanning times make WiFi ingerprint-ing useless in case of a dynamic motion, e.g., per-son running through a building. What is important,dynamic motion also negatively impacts the vision-based loop closure as the images would contain sig-ni icant amount of motion blur. Therefore, in the pro-posed system, dynamic motion is detected using thecombination of gyroscope and accelerometer and inthat situation new information is not inserted into thedatabase. Assuming that the motion speed is belowthe chosen threshold, WiFi scan, image and orienta-tion from the Android-based orientation estimationsystem are stored. Between the starting and endingtime of the WiFi scanning, 20–40 images can be cap-

12


tured. From those images, the images with most dis-tinct orientations are chosen to best represent differ-ent points of view. For each scan, the image taken ap-proximately in the half of WiFi scan duration is cho-sen and will be referred to as the mid-scan image. Ifthere are images with orientation signi icantly differ-ent than the mid-scan image, those images are con-sidered to be used for visual loop closure. Maximally,mid-scan image and two additional images with high-est orientation difference are processed per scan inthe visual loop closure approach. For each image, it’ssalient features are detected and described using de-scriptors. The descriptors are then used to forman im-age’s word using Bag-of-Words approach. The createdword is a shorter representation of the image and al-lows ef icient comparison between images.

The processing of the localizationmode of the pro-posed system is presented in Fig. 3. The system gath-ers the WiFi and image information. From the image,Bag-of-Words technique creates a word representingobserved location. Then the WiFi scan is compared tothe database entries and in case of successfulWiFi in-gerprints match, the comparison of words represent-ing the images is performed. If the WiFi match is con-irmed by the image match, the mobile device is be-lieved to have been successfully localized. If the posi-tion is not recognized, the image and theWiFi scan arestored in the database as a new position used in therecognition process.

Fig. 3. Processing steps of the proposed loop closure ap-proach

2.4. Implementa on RemarksThe proposed approach is application-orientated,

therefore it has been tested on the Samsung GalaxyNote3,whichuses theAndroid4.4 as anoperating sys-tem. The information about the WiFi signal strengthwas captured using Android-available functionality inthe Java API. The time of a single WiFi scan time de-pends on the wireless adapter driver installed on themobile device and on the Samsung Galaxy Note 3 ittakes approx. 4 seconds.

The image processing was done using the com-monly used OpenCV library (2.4.8) [5], which is avail-

able for x86/x64 andAndroid platforms [16]. The pro-posed application consists of a Java-part used for GUIand less demanding computations, and C++ NDK li-braries for more demanding taska, e.g., image pro-cessing. The structure was proved to be a good trade-off between programming complexity and process-ing time and has been already proven to work wellin another Android-based experiments [15]. A similarproject structure is also used in [13].

3. Experimental Evalua on3.1. Recorded Datasets

The experiments were performed on the datasetrecorded in two buildings of the Poznan University ofTechnology (building of Mechatronics, Biomechanicsand Nanoengineering (PUT CM) and the Lecture Cen-ter (PUT CW) and a shopping mall located in Poznan(SM). The user equipped with a smartphone was mov-ing around thebuildings gatheringWiFi scans and cor-responding images in places that seemed importantfor user localization due to the building structure, e.g.short corridor connecting two parts of the building orunique objects in sight. The dataset PUT CM contains14 places of possible loop closures, where the datasetPUT CW contains 20 places of possible loop closures.The shopping mall dataset SM contains also 20 placesof possible loop closure. For each place, several WiFiscans and several images were recorded. For each ofthose positions, one recording was assumed to be in-serted into the database created prior to localization.The remaining samples were used in a testing phase.More information about the datasets is presented inTable 1. Exemplary images from the datasets are pre-sented in Fig. 4.

Tab. 1. Short descrip on of recorded datasets

dataset name PUT CM PUT CW SMnum. of positions 14 20 20num. of records 140 100 100avg. num. of WiFis 14.21 39.21 20.22in the scanavg. RSSI of 5 -75.045 -41.642 -32.143strongest WiFisBuilding corridors open- shoppingstructure space mall

3.2. Tes ng the Nature of WiFi SignalThe evaluation starts with an assessing the re-

peatability of WiFi scans. In a perfect environmentwith APs in line-of-sight, the measurement should beperfectly the same. In a cluttered environment withpossible, multiple re lections and additional distur-bances due to moving people, the scans informationmight be noisy. What is also essential to propose a dis-tance function measuring the similarity of two scansis the probability distribution of measurements. Thisexperiment consist of performing 1439 consecutivescans in a single spot using the SamsungGalaxyNote 3.

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Fig. 4. Exemplary images presen ng different buildingstructures for PUT CM (row a), PUT CW (row b) and SM (rowc) datasets

In the experiment the averageRSSI signal ismeasured,while looking for the standard deviation of the mea-surement. Also the repeatability was measured to de-termine if there is a clear correspondence to the mea-sured signal strength. The results of the experimentare presented in Tab. 2.

Tab. 2. WiFi signal floa ng example for 1439 measure-ments taken in a single spot

WiFi id avg(RSSI) std(RSSI) Network detectionpercent

1 -49.12 5.51 100.00%2 -74.24 3.05 100.00%3 -74.57 2.99 100.00%4 -83.49 3.42 56.12%5 -83.99 1.83 94.02%6 -84.15 2.69 82.82%7 -86.08 3.33 94.65%8 -86.64 1.78 94.65%9 -87.45 1.21 95.76%10 -87.57 1.47 67.39%

The presented results show that in most cases thestronger the signal, the higher is the standard devia-tion of these measurements. Moreover, with an excep-tion for network 4, the stronger networks are detectedwith higher repeatability percentage and thus they area good indicator if the user is in a vicinity of a previ-ously storedWiFi scan. Also, in Fig. 5 the histogram ofvalues for two WiFi networks with the greatest aver-age signal strength is presented. Due to the clutteredenvironment, the achieved probability distributionsare not Gaussian in all cases (like for WiFi with id=1).This observation indicates that when possible, it isbetter to relymoreon the combinationof detectednet-works than trust the measured signal strength, whichcan differ up to 20 dBm in a single spot.

−90 −80 −70 −60 −50 −40 −300

5

10

15

20

25

30

35

RSSI

Per

cent

of t

otal

Histogram of measured RSSI values

WiFi id=1WiFi id=2

Fig. 5. Experimental distribu on of RSSI for series ofmeasurements in a single spot

3.3. Tes ng the Distance Func ons used for WiFi ScansComparison

The WiFi ingerprinting in the proposed approachis used to localize in the discrete set of positions.Therefore, the WiFi ingerprinting returns informa-tionabout themost similar pose stored in thedatabaseor information about the unsuccessful match. Due tothese assumptions, the comparison of WiFi scans us-ing the standard Euclidean distance might not be thebest choice as the combination of detected WiFi net-works inmost cases is suf icient to determine inwhichposition the scan was performed. To determine thecorrectness of this statement, several de initions ofdistance/similarity functions are proposed and eval-uated on the recorded datasets. For each position, onescan was treated as the database entry, whereas otherscanswere compared to all available database entries.The results are presented in Tab. 3.

Tab. 3. Comparing WiFi fingerprin ng distance func-ons on the recorded datasets

Used function PUT CM PUT CW SMSimple similarity 72.86% 67% 75%Euclidean norm 61.43% 53% 94%Euclidean norm II 61.43% 53% 94%Gaussian with σ = 2 82.14% 99% 94%Gaussian with σ = 3 84.29% 99% 96%Gaussian with σ = 5 86.43% 100% 97%Gaussian with σ = 10 85.71% 100% 95%Gaussian with σ = 15 83.57% 98% 89%Gaussian with σ = 20 83.57% 96% 84%

The irst tested function was a simple similarityfunction, which for both scans represents the num-ber of WiFi networks that are detected in both scans.This function does not use the RSSI information, buthas been chosen as the baseline approach, that can bea reference point for other approaches. This methodachieved position recognition rates of 72.86%, 67%

14


and 75% for PUT CM, PUT CW and SM datasets respectively.The high recognition rates of this simple approach arebelieved to be task speci ic. In the performed tests, asparse set of WiFi measurements is taken in locationsthat are separated by several meters. As the localiza-tion positions are not placed closely to each other, inmany cases the combination of network names is suf-icient to correctly determine the user’s location. Thesecond tested function is the Euclidean distance de-ined as in the state-of-the-art works [1]. Surprisingly,the Euclidean norm results in lower regonition ratefor PUT CM and PUT CW datasets, which is in contrastto better recognition rate for SM. The author believesthat those results are caused by different structures ofthe building. In case of PUT buildings, the APs are usu-ally placed inside rooms and regardless of the corri-dor type, theWiFi information that reaches themobiledevice was probably de lected several times. In caseof the shopping mall, the open-spaces result in a WiFisignal propagating directly to the user, thus resultingin lesser number of de lections. Another tested func-tions was an Euclidean norm with an additional sub-tracted discount for each correctly matched network(called Euclidean norm II). This approach was basedon an observation, that WiFi scans with higher num-ber of matched networks are intuitively more likelyto be the same. This modi ication didn’t have any sig-ni icant impact and resulted in values similar to theEuclidean distance approach. Due to the low recogni-tion rate achieved with the Euclidean distance propo-sitions, the simple similarity idea was expanded to in-corporate RSSI values. For simplicity, the RSSI of thesame networks are assumed to have Gaussian distri-bution. Then the similarity of networks found in twoscans is de ined by Gaussian membership values. Thesimilarity between two scans X and Y is measured asa sumof Gaussianmembership values for all networksavailable in both scans. Formally, it can be written as:

SGauss(X ,Y, σ) =N∑i=1

exp− (Xi − Yi)2

−2σ2, (3)

where, N is the number of common networks foundin bothX andY scans. The σ is the standard deviationof the measurement used to de ine the shape of Gaus-sianmembership function. The choice ofσ is arbitrary,but from the experiment measuring the WiFi scans ina single spot, it was assumed that best results shouldbe achieved for a value in the range of 2 to 7. To con-irm this assumption, differentσ valueshavebeen cho-sen. As expected, the best results were obtained for σequal to 5. The results usingmodi ied similarity valuesturned up to be better when compared to previous ap-proaches. For PUT CM the recognition rate increased to86.43%, for PUT CW to 100%, for SM to 97%. In case of PUTCW, theWiFi information is suf icient to precisely local-ize the mobile device. In the remaining cases, the us-age of image informationmay be useful in inding loopclosures in scenarios, where WiFi matching failed.

3.4. Tes ng the Vision-based Loop ClosureThe next tests concern the recognition rate of the

vision-based loop closure subsystem. Similarly to theWiFi evaluation, for each distinct position one im-age was chosen as a reference. The remaining imageswere then compared against all of the images in thedatabase in order to ind a positive match.

The images taken with the Samsung Galaxy Note 3have amaximum resolution of 1920×1080 pixels (FullHD). Due to themobile platformprocessing power, theresolution of 640 × 480 pixels (VGA) is chosen as theimage of reduced size have 7 times less pixels to pro-cess. This results in obvious processing speed up. Adetailed comparison with VGA and FullHD images ispresented in Tab. 4.

The most time consuming part of any system us-ing the SURF detector/descriptor is the detection ofkeypoints that takes almost 1s on the Samung GalaxyNote 3. The obvious reduction of needed time can beachieved by lowering the number of keypoints used bysystem and thus described by the descriptor. Unfor-tunately, the minimal number of keypoints needed toachieve a robust system is application dependent andin the proposed tests 500 strongest keypoints werechosen. Another time reduction strategy is to use dif-ferent detector/descriptor pairs [15], but tests con-cerning the choice of detector/descriptor pairs are nota part of presented research.

Fig. 6. Similar corridors with corresponding imagewords observed in two distant localiza on posi ons inPUT CM dataset

When the detection and description parts are in-ished, a k-dimensional word creation is initiated. Theprocess start with the classi ication of descriptors ofkeypoints found in the image. Thedescriptors are clas-si ied into clusters, for which the minimal error tothe centroid is obtained. The centroids are computedprior to the localization. The centroids are found byperforming a k-means algorithm computation on adataset consisting of every descriptor found in all ref-erence images. After the classi ication, each image isdescribed by a histogram of length k with number ofdescriptors classi ied into each cluster. The construc-tion of the image word inishes with a normalizationprocedure of the histogram. The exemplary computedwords for images from PUT CM dataset are presented

15


Tab. 4. Processing me of the proposed visual loop closure subsystem

System part S. Galaxy Note 3 VGA S. Galaxy Note 3 Full HD Nexus 7 VGA Nexus 7 Full HDImage resizing 18.86 ms - 34.0 ms -Keypoints detection 460.53 ms 2376.32 ms 443.57 ms 2516.21 msKeypoints description 486.73 ms 720.86 ms 431.21 ms 648.57 msWord creation (K=5) 30.71 ms 30.14 ms 34.00 ms 33.64 msWord creation (K=20) 127.21 ms 126.78 ms 116.79 ms 116.07 msWord creation (K=50) 351.21 ms 349.43 ms 374.00 ms 300.43 msWord creation (K=200) 1417.36 ms 1378.71 ms 1303.36 ms 1133.71 msEstimated total time 1093 ms 3224 ms 1026 ms 3281 msper word creation (K=20)

in Fig. 6. After the normalization, k-dimensional wordfor an image is successfully computed, the subsystemdetermines the correct match to the reference framesstored in the database by comparing current image toall entries in the database. In the proposed subsystemthe comparison of words is done using the Euclideandistance. If the smallest distance between matches ishigher than a preset threshold, the match is consid-ered to be correct.

Fig. 7. The recogni on rate and me taken for word cre-a on for different number of centroids evaluated at PUTCW

To determine, what number of classes k used bythe k-means algorithm results in the highest recogni-tion rate, different number of k values were evaluated.The results are presented in Fig. 7. For the proposeddatasets, higher number of classes for the k-means al-gorithm results in higher recognition ratee. But, in thepresented vision-based loop closure approach, eachdescriptor is assigned tooneofk clusters. If thek valueis higher, the total time needed to classify descriptorsis higher. Therefore, it is necessary to ind a k valuethat results in high recognition rate within reasonabletime. From Fig. 7, the value of k equal to 200 is chosenas the best choice and used in described subsystem.

The results obtainedby theproposed approach arealso presented in Tab. 5. The visual loop closure hasthe highest recognition rate of visited places in caseof PUT CM dataset, which is equal to 97.86% for cho-sen k equal to 200. The small number of distinct ob-

Tab. 5. Accuracy of the proposed visual loop closure ap-proach

PUT CM PUT CW SMk = 5 70.71% 48% 64%k = 20 91.43% 72% 84%k = 50 95% 78% 86%k = 200 97.86% 88% 92%k = 500 98.57% 90% 97%k = 1500 98.57% 92% 98%

jects poses a great challenge for the visual system asthe detected features are in most cases similar for allof the positions in the sequence. The problem of sim-ilar places also arises for PUT CW, for which the lowestperformance is achieved. The recognition rate of 92%for the SM dataset inmost cases is a result of situations,when passing pedestrians are present in a signi icantpart of the image and thus make images from trainingand testing sets look different.

3.5. Results – Tes ng WiFi Guided Vision Loop Closure

The system that combines information from bothsubsystems is expected to outperform either of them.In Tab. 6 the best results obtained from both sub-systems are presented. The comparison shows, thatWiFi ingerprinting provides more reliable estimatefor the PUT CW or SM datasets, whereas visual loop clo-sure works better for the PUT CM dataset. In case of ap-plication tailored for a speci ic building, the systemde-signer may decide to use only one source of informa-tion. If the single-source solution is inef icient, thereexists a need for a system integrating data from bothsubsystems.

In case of an unknown building structure, it is es-sential to correctly weight information from both sub-systems. In the presented research, threemethods areproposed and tested:1) method I – rank-based,2) method II – normalize and sum,3) method III – normalize and multiply.

Method I, called rank-based, for each position toevaluate assigns the ranks based on the similarity ofWiFi scans and distance functions for vision-basedloop closure to positions stored in the database. For

16


each position to classify, the most probable estimatesfrom both subsystems are provided. Then, separatelyfor each subsystem, the most probable estimate is as-signed rank 1, the second most probable is assignedrank 2 and so forth. At this point of processing, eachposition to process contains two ranks representingthe estimates from both subsystems. Then, for eachreference position, a summation of assigned ranks isperformed. The position in the database with a lowestsumof ranks is chosen as a combined systemestimate.

Method II, normalize and sum, tries to incorporatealso information about the distances between posi-tion in the estimates of separate subsystems. To in-clude this information into the proposed system, sub-systems estimatesmust have a similar range of values.Therefore, for each position a vector of distances toall database entries is created and then normalized inL2 norm. The normalized vector of estimates for WiFiingerprinting is denoted by w. The equivalent, nor-malized vector for vision loop closure is denoted by v.As the WiFi subsystem operates using similarities be-tween classes, whereas vision-based loop closure usesdistances, the inal estimation is computed as differ-ence of estimates (w−v). The inally inferred positionis based on inding an index of maximal element in aw − v vector:

estimatedIDII = argmaxi

w(i)− v(i), (4)

Method III, normalize and multiple, uses a simi-lar strategy to previously presented method II. In thiscase, the distances fromvision loop closure are recom-puted to represent similarities by exchanging eachvalue x in a vector v with 1 − x. The resulting vec-tor is againnormalized. Thebest position estimatedbythe integrated system corresponds to an index ofmax-imal value after elementwise multiplication of vectorsv and w:

estimatedIDIII = argmaxi

(1− v(i)). ∗ w(i), (5)

The proposed system is evaluated in the samewayas shown for the subsystems. The results are pre-sented in Tab. 6. It is shown that when concernedabout the PUT CM building, all of different functionsfor the system using WiFi data performed worse thanvision-based loop closure. In other cases, the pro-posed system performs the same or better than ei-ther of the subsystems. The best results are obtainedfor method II and it is the recommended method ifthe structure of the building is unknown or if thesystem must operate in changing conditions regard-ing the uniqueness of images and number of avail-able WiFi networks. In case of a system created forspeci ic building it is recommended to record a train-ing and testing set and perform experiments to cor-rectly weight the input of each subsystem. In somecases it might be also necessary to detect same po-sitions based solely on WiFi, whereas in other com-pletely rely on gathered images. These mentioned re-marks are application-speci ic and cannot be appliedto universal system. In case of the proposed system

operating in three different buildings, the recognitionratewas equal or greater than 90%in each, tested casewithout usage of additional subsystem weights.

Tab. 6. Localiza on recogni on rate of subsystems anddifferent approaches to the system combining informa-on fromWiFi and Vision subsystems

PUT CM PUT CW SMWiFi ingerprinting 86.43% 100% 97%Visual loop closure 97.86% 88% 92%Method I (rank-based) 92.14% 97% 97%Method II (sum) 90% 100% 98%Method III (product) 88.57% 100% 98%

4. ConclusionThe proposed event-based, WiFi-guided visual

loop closure approach presents a new approach todata integration of mobile platforms’ sensor informa-tion that results in a system than outperforms each in-dividual approach. The information from camera usu-ally helps in localization in areaswith small number ofWiFis, e.g., corridors or staircases. What is surprising,the systemperformedwell in the case of corridors thatseemed alike. The system works with lesser recogni-tion rate in case of a shopping mall, where suddenpedestrian’s occlusions negatively affect the visual lo-calization. Moreover, the achieved results suggest thatWiFi and vision information complement each otherand provide a data needed to create a more robust lo-calization system.

Contrary to proposed event-based localization, thefurther workswill focus on providing a continuous es-timate at the user by estimating the motion throughthe vision-based monocular visual odometry with ad-ditional incorporation of WiFi information.

ACKNOWLEDGEMENTSThe author would like to thank Piotr Skrzypczynskifor numerous discussions regarding the presented lo-calization system.

This work is inanced by the Polish Ministry of Sci-ence and Higher Education in years 2013-2015 underthe grant DI2012 004142.

AUTHORMichał Nowicki∗ – Institute of Control andInformation Engineering, Poznan Univer-sity of Technology, Poznan, Poland, e-mail:[email protected].∗Corresponding author

REFERENCES[1] P. Bahl, V. N. Padmanabhan, “RADAR: An In-

Building RF-Based User Location and TrackingSystem.” In: 19th Annual Joint Conf. of the IEEE

17


Computer and Communications Societies (INFO-COM), 2000, pp. 775–784. DOI: http://dx.doi.org/10.1109/INFCOM.2000.832252.

[2] H. Bay, A. Ess, T. Tuytelaars, L. Van Gool, “SURF:Speeded up robust features”, Comp. Vis. and Im-age Underst., vol. 110, no. 3, 2008, pp. 346–359.DOI: http://dx.doi.org/10.1016/j.cviu.2007.09.014.

[3] J. Biswas, M. Veloso, “WiFi localization and nav-igation for autonomous indoor mobile robots.”In: 10 IEEE Int. Conf. on Robotics and Automation(ICRA), 20, 2010, pp. 4379–4384. DOI: http://dx.doi.org/10.1109/ROBOT.2010.5509842.

[4] S. Boonsriwai, A. Apavatjrut, “Indoor WIFI local-izationonmobile devices.” In:201310th Int. Conf.on Electrical Engineering/Electronics, Computer,Telecommunications and Information Technology(ECTI-CON), 2013, pp. 1–5. DOI: http://dx.doi.org/10.1109/ECTICon.2013.6559592.

[5] G. Bradski, “The OpenCV library”, Dr. Dobb’sJournal of Software Tools, opencv.org, 2000.

[6] G. Csurka et al., “Visual categorization with bagsof keypoints.” In: Workshop on Statistical Learn-ing in Computer Vision, ECCV, 2004, pp. 1–22.

[7] N. Dalal, B. Triggs, “Histograms of oriented gradi-ents for human detection.” In: IEEE Computer So-ciety Conf. on Computer Vision and Pattern Recog-nition (CVPR), 2005, vol. 1, pp. 886–893. DOI:10.1109/CVPR.2005.177.

[8] T. Gallagher et al., “Indoor positioning systembased on sensor fusion for the Blind and Visu-ally Impaired.” In: Int. Conf. Inndoor Positioningand IndoorNavigation (IPIN), 2012, pp. 1–9. DOI:10.1109/IPIN.2012.6418882.

[9] A. Glover et al., “OpenFABMAP: An Open SourceToolbox for Appearance-based Loop Closure De-tection.” In: IEEE Int. Conf. on Robotics and Au-tomation, St Paul, Minnesota, 2011.

[10] J. Goslinski, M. Nowicki, “Performance Compari-son of EKF-based Algorithms for Orientation Es-timation on Android Platform.”

[11] M. Holcik, “Indoor Navigation for Android,” M.S.thesis, Faculy of Informatics, Masaryk Univ.,Brno, 2012.

[12] H. Liu et al., “Accurate WiFi Based Localizationfor Smartphones Using Peer Assistance,” IEEETransactions on Mobile Computing, vol. PP, no.99, 2013, pp. 1. DOI: 10.1109/TMC.2013.140.

[13] K. Muzzammil bin Saipullah, A. Anuar, N. A. bintiIsmail, Y. Soo, “Real-time video processing us-ing native programming on Android platform.”In: Proc. IEEE 8th Int. Col. on Signal Proc. and itsApp., 2012, pp. 276–281.

[14] M. Nowicki, P. Skrzypczynski, “Combining pho-tometric and depth data for lightweight and ro-bust visual odometry.” In: European Conferenceon Mobile Robots (ECMR), 2013, pp. 125–130.DOI: 10.1109/ECMR.2013.6698831.

[15] M. Nowicki, P. Skrzypczynski, “PerformanceComparison of Point Feature Detectors and De-scriptors for Visual Navigation on Android Plat-form,” Int. Wireless Communications and MobileComputing Conference (IWCMC), 2014.

[16] K. Pulli et al., “Real-time Computer Vision withOpenCV,” Commun. ACM, 2012, vol. 55, no. 6,pp. 61–69. DOI: 0.1145/2184319.2184337.

[17] N. Ravi, P. Shankar, A. Frankel, A. Elgammal,L. Iftode, “Indoor localization using cameraphones,” Proc. 7th IEEE Work. on Mobile Comp.Sys. and App., 2006, pp. 1–7.

[18] U. Shala, A. Rodriguez, “Indoor Positioning us-ing Sensor-fusion in Android Devices,” M.S. the-sis, Dept. Computer Science, Kristianstad Univ.,Kristianstad, 2011. http://hkr.diva-portal.org/smash/record.jsf?pid=diva2:475619

[19] M. Quigley, D. Stavens, A. Coates, S. Thrun,“Sub-meter indoor localization in un-modi ied environments with inexpen-sive sensors.” Proc. IEEE/RSJ Int. Conf. onIROS, Taipei, 2010, pp. 2039–2046. DOI:10.1109/IROS.2010.5651783.

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http://dx.doi.org/10.1109/INFCOM.2000.832252

http://dx.doi.org/10.1109/INFCOM.2000.832252

http://dx.doi.org/10.1016/j.cviu.2007.09.014

http://dx.doi.org/10.1016/j.cviu.2007.09.014

http://dx.doi.org/10.1109/ROBOT.2010.5509842


http://dx.doi.org/10.1109/ECTICon.2013.6559592

http://dx.doi.org/10.1109/ECTICon.2013.6559592

opencv.org

10.1109/CVPR.2005.177

10.1109/IPIN.2012.6418882

10.1109/TMC.2013.140

10.1109/ECMR.2013.6698831

0.1145/2184319.2184337

http://hkr.diva-portal.org/smash/record.jsf?pid=diva2:475619

http://hkr.diva-portal.org/smash/record.jsf?pid=diva2:475619

10.1109/IROS.2010.5651783


A O - CIR I R M CB P U




Submi ed: 10th June 2014; accepted: 27th June 2014

Piotr Nowak, Maciej Romaniuk

DOI: 10.14313/JAMRIS_4-2013/23

Abstract:The number and amount of losses caused by naturalcatastrophes are important problems for insurance in-dustry. New financial instruments were introduce totransfer risks from insurance to financial market. In thispaper we consider the problem of pricing such instru-ments, called the catastrophe bonds (CAT bonds). Wederive valua on formulas using stochas c analysis andfuzzy sets theory. As model of short interest rate we ap-ply the one-factor Cox–Ingersoll–Ross (CIR) model. In thispaper we treat the vola lity of the interest rate as a fuzzynumber to describe uncertainty of the market. We alsoapply the Monte Carlo approach to analyze the obtainedcat bond fuzzy prices.

Keywords: asset pricing, catastrophe bonds, CIR model,stochas c analysis, Monte Carlo simula ons, fuzzy num-bers

1. Introduc onNowadays, natural catastrophes are important

source of serious problems for insurers and rein-surers. Even single catastrophic event could resultsin damages worth of billions of dollars – e.g. thelosses from Hurricane Katrina in 2005 are estimatedat $40–60 billion (see [26]). The insurance industry isnot prepared for such extreme damages. The classicalinsurance approach is based on assumption of inde-pendent and small (in comparison of the value of thewhole insurance portfolio) losses (see, e.g. [3]). Thisassumption is not adequate in the case of outcomesof natural catastrophes, like hurricanes, loods, earth-quakes etc. Therefore, after such catastrophic event,there are bankruptcies of the insurers, problems withliquidity of their reserves or increases of reinsurancepremiums. For example, afterHurricaneAndrewmorethan 60 insurance companies fell into insolvency (see[26]).

Then new kind of inancial instruments were in-troduced. The main aim of such inancial derivativesis to transfer risks from insurance markets into inan-cial markets, which is know as securitization (see, e.g.,[10,15,28]). Catastrophebond, knownalso as cat bondor Act-of-God bond (see, e.g., [8, 14,17,31,33,38,40])is an example of such new approach.

The payment function of the catastrophe bond isconnected with additional random variable, i.e. trig-gering point. This triggering point (indemnity trigger,parametric trigger or index trigger) depends on oc-currence of speci ied catastrophe (like hurricane) in

given region and ixed time interval or it is connectedwith the value of issuer’s actual losses from catas-trophic event (like lood), losses modeled by specialsoftware based on the real parameters of a catastro-phe, or other parameters of a catastrophe or value ofcatastrophic losses (see, e.g. [17,40,41]). Usually if thetriggering point occurs, the payments for the bond-holder are lowered or even set to zero. Otherwise, thebondholder receives full payment from the cat bond.

The cat bond pricing literature is not very rich. Aninteresting approach applying discrete time stochas-tic processes within the framework of representativeagent equilibrium was proposed in [9]. In [2] the au-thors applied compound Poisson processes to incor-porate various characteristics of the catastrophe pro-cess. The authors of [5] improved and extended themethod from [2]. In [1] the doubly stochastic com-pound Poisson process was used to model the claimindex, and QMC algorithms was applied. In [13] struc-tured cat bonds were valued with application of theindifference pricing method. Vaugirard in [40] usedthe arbitragemethod for pricing catastrophe bonds. Inhis approach a catastrophe bondholder was deemedto have a short position on an option based upon a riskindex. Similar approach was proposed in [25], wherethe Markov-modulated Poisson process was used fordescription of the arrival rate of natural catastrophes.In this paper we continue our earlier research con-cerningpricing cat bonds (see [33]).Weapply stochas-tic analysis and fuzzy arithmetic to obtain the catas-trophe bond valuation expression. In our approachthe risk-free spot interest rate r is described by theCox–Ingersoll–Ross model. For description of naturalcatastrophe losses we use compound Poisson processwith a deterministic intensity function. We also con-sider a complex form of catastrophe bond payoff func-tion, which is piecewise linear. Main assumptions inour approach are: (i) the absence of arbitrage on theinancial market, (ii) neutral attitude of investors tocatastrophe risk. Similar assumptions were made byother authors (see, e.g. [40]).

Applying fuzzy arithmetic, we take into accountdifferent sources of uncertainty, not only the stochas-tic one. In particular, the volatility parameter of thespot interest rate is determined by luctuating inan-cialmarket and inmany situations its uncertaintydoesnot have stochastic type. Therefore, in order to ob-tain the cat bond valuation formula we apply fuzzyvolatility parameter of the stochastic process r. As re-sult, price obtained by us has the form of a fuzzy num-ber. For a given α (e.g. α = 0.9) its α-level set can be

19


used for investment decision-making as the interval ofthe cat bond prices with an acceptable membershipdegree. Similar approach was applied to option pric-ing in [42] and [30, 34, 35], where Jacod-Grigelionischaracteristics of stochastic processes (see, e.g. [29,39]) were additionally used. In more general setting,so called soft approaches are applied in many otherields, see, e.g. [19–23].

This paper is organized as follows. Section 2 con-tains preliminaries on fuzzy and interval arithmetic.In Section 3 the catastrophe bond pricing formula incrisp case for the Cox–Ingersoll–Ross risk-free inter-est ratemodel is derived. Section 4 is devoted to catas-trophe bond pricing with fuzzy volatility parameter.Since the pricing formula is considered for arbitrarytimemoment beforematurity, fuzzy random variablesare additionally introduced. Apart from the fuzzy val-uation formula, the expressions describing the formsof α-level sets of the cat bond price are obtained. InSection 5 the introduced formulas are used to obtainthe fuzzy prices of catastrophe bonds. Based on fuzzyarithmetic and Monte Carlo approach, the behaviorof prices is analyzed for various settings close to thereal-life cases. Special attention is paid to the in luenceof selected parameters of the model of catastrophicevents on the evaluated fuzzy prices. Finally, Section6 contains conclusions.

2. Fuzzy Sets PreliminariesIn this section we present basic de initions and

facts concerning fuzzy and interval arithmetic, whichwill be used in the further part of the paper.

For a fuzzy subset Aof the set of real numbersRwedenote by µA its membership function µA : R → [0, 1]

and by Aα = x : µA (x) ≥ α the α-level set of A forα ∈ (0, 1]. Moreover, by A0 we denote the closure ofthe set x : µA (x) > 0.

A fuzzy number a is a fuzzy subset of R for whichµa is a normal, upper-semicontinuous, fuzzy convexfunction with a compact support. If a is a fuzzy num-ber, then for each α ∈ [0, 1] the α-level set aα isa closed interval of the form aα = [aLα, a

Uα ], where

aLα, aUα ∈ R and aLα ≤ aUα . We denote the set of fuzzy

numbers by F (R).Let us assume that⊙ is a fuzzy-number binary op-

erator⊕,⊖,⊗ or⊘, corresponding to its real-numbercounterpart :+,−,× or /, according to the ExtensionPrinciple.

Let ⊙int be a binary operator ⊕int, ⊖int, ⊗int or⊘int between twoclosed intervals [a, b] and [c, d]. Thenthe following equality holds:

[a, b]⊙int[c, d] = z ∈ R : z = xy, x ∈ [a, b], y ∈ [c, d],

where is the corresponding real-number binary op-erator +,−,× or /, under the assumption that 0 /∈[c, d] in the last case. Thus, if a, b are fuzzy numbers,then a ⊙ b is also a fuzzy number and the followingequalities are ful illed.

(a⊕ b)α = aα ⊕int bα = [aLα + bLα, aUα + bUα ] ,

(a⊖ b)α = aα ⊖int bα = [aLα − bUα , aUα − bLα] ,

(a⊗ b)α = aα ⊗int bα =

= [minaLα bLα, aLα bUα , aUα bLα, aUα bUα ,maxaLα bLα, aLα bUα , aUα bLα, aUα bUα ] ,

(a⊘ b)α = aα ⊘int bα =

= [minaLα/bLα, aLα/bUα , aUα/bLα, aUα /bUα ,maxaLα/bLα, aLα/bUα , aUα /bLα, aUα /bUα ] ,

if α-level set bα does not contain zero for all α ∈ [0, 1]in the case of⊘.

A fuzzy number a is called positive (a ≥ 0) ifµa (x) = 0 for x < 0 and it is called strictly positive(a > 0) if µa (x) = 0 for x ≤ 0.

A triangular fuzzy number a = (a1, a2, a3) is afuzzy number with the membership function of theform

µa (x) =

x−a1

a2−a1if a1 ≤ x ≤ a2

x−a3

a2−a3if a2 ≤ x ≤ a3

0 otherwise..

In our further considerationswewill use the followingproposition, proved in [42].Proposition 1. Let f : R → R be a function such thatf−1 (y) is a compact set for each y ∈ R. Then f in-duces a fuzzy-valued function f : F (R) → F (R) via theExtension Principle and for each Λ ∈ F (R) the α-levelset of f(Λ) has the form f(Λ)α = f(x) : x ∈ Λα.

We recall the notions of weighted interval-valuedand crisp possibilistic mean values of fuzzy numbers.For details we refer the reader to [16].

Let a ∈ F (R). A non-negative, monotone increas-ing function f : [0, 1] 7→ R such that

∫ 1

0f(α)dα = 1 is

said to be a weighting function. The lower and upperweighted possibilistic mean valuesM∗(a) andM∗(a)of a are de ined by the integrals:

M∗(a) =

∫ 1

0

aLαf(α)dα,

M∗(a) =

∫ 1

0

aUα f(α)dα.

Theweighted interval-valued possibilisticmeanM(a)and the crisp weighted possibilistic mean M(a) of thefuzzy number a have the following form:

M(a) = [M∗(a),M∗(a)],

M(a) =M∗(a) +M∗(a)

2.

Let B (R) be the Borel σ- ield of subsets of R and(Ω,F) be ameasurable space. A fuzzy-number-valuedmap X : Ω 7→ F (R) is called a fuzzy random variableif

(ω, x) : X (ω) (x) ≥ α∈ F × B (R)

for every α ∈ [0, 1] (see, e.g. [36]).

20


3. Catastrophe Bond Pricing in Crisp CaseAs it was previously noted, the triggering point

changes the structure of the payment function of thecat bond. Usually cat bonds are issued by insurers orreinsurers (see, e.g., [37]) via a special tailor-madefund, called a special purpose vehicle (SPV) or spe-cial purpose company (SPC) (see, e.g., [24, 40]). Thehedger (e.g. insurer or reinsurer) pays an insurancepremium in exchange for coverage in the case if trig-gering point occurs (see Figure 1). The investors pur-chase the catastrophe bonds for cash. The premiumand cash lows are directed to SPV, which purchasessafe securities and issues the catastrophe bonds. In-vestors hold these assets whose payments depend onoccurrence of the triggering point. If the pre-speci iedevent occurs during the ixed period (e.g. there is aspeci ied kind of natural catastrophe), the SPV com-pensates the insurer and the cash lows for investorsare changed. Usually these lows are lowered, i.e. thereis full or partial forgiveness of the payment. However,if the triggering point does not occur, the investorsusually receive the full payment (i.e. the face value ofthe bond).

Fig. 1. Payments related to issuing and termina ng ofthe cat bond

In the further part of this section we derive andpresent the pricing formula for catastrophe bonds incrisp case, assuming no arbitrage opportunity on themarket. At the beginning we introduce all necessaryde initions and assumptions.

We use stochastic processes with continuous timeto describe the dynamics of the spot risk-free interestrate and the cumulative catastrophe losses. The timehorizon has the form [0, T ′], where T ′ > 0. The date ofmaturity of catastrophe bonds T is not later than T ′,i.e. T ≤ T ′. We consider two probability measures: PandQ and denote the expected values with respect tothem by the symbolsEP andEQ.

We introduce standard Brownian motion(Wt)t∈[0,T ′] and Poisson process (Nt)t∈[0,T ′] witha deterministic intensity function ρ(t), t ∈ [0, T ′]. TheBrownian motion will be used for description of therisk-free interest rate.

We introduce a sequence (Ui)∞i=1 of independent,

identically distributed random variables with initesecondmoment. For each i the randomvariableUiwilldescribe the value of losses during i-th catastrophicevent.

We de ine compound Poisson process by the for-mula

Nt =

Nt∑i=1

Ui, t ∈ [0, T ′] .

for modeling the cumulative catastrophic losses tillmoment t.

All the introduced above processes and randomvariables are de ined on probability space (Ω,F , P ).We introduce the following iltrations:

(F0

t

)t∈[0,T ′]

,(F1

t

)t∈[0,T ′]

and (Ft)t∈[0,T ′].(F0

t

)t∈[0,T ′]

is generatedbyW ,

(F1

t

)t∈[0,T ′]

by N and (Ft)t∈[0,T ′] byW and N .Moreover, they are augmented to encompass P -nullsets from F0

T ′ , F1T ′ and F = FT ′ , respectively.

(Wt)t∈[0,T ′], (Nt)t∈[0,T ′] and (Ui)∞i=1 are in-

dependent and the iltered probability space(Ω,F , (Ft)t∈[0,T ′] , P

)satis ies usual assumptions:

σ-algebra F is P -complete, the iltration (Ft)t∈[0,T ′]

is right continuous and eachFt contains all the P -nullsets from F .

Let r = (rt)t∈[0,T ′] be the risk-free spot inter-est rate, i.e. short-term rate for risk-free borrowingor lending at time t over the in initesimal time inter-val [t, t+ dt]. We assume that r is an one-factor af inemodel. Formore details concerning af ine interest ratemodels we refer the reader to [11] and [12]. The Cox –Ingersoll – Ross model, considered in this paper, is ofthis type.

The risk-free spot interest rate (rt)t∈[0,T ′], belong-ing to the class of one-factor af ine models, is a diffu-sion process of the form

drt = α (rt) dt+ σ (rt) dWt, (1)

where

α (r) = φ− κr and σ2 (r) = δ1 + δ2r

for constants φ, κ, δ1, δ2 (see, e.g. [27]). We denote byS the set of all the valueswhich r can havewith strictlypositive probability. We require that δ1 + δ2r ≥ 0 forall values r ∈ S .

We assume that zero-coupon bonds are traded onthe market, investors have neutral attitude to catas-trophe risk and interest rate changes are replica-ble by other inancial instruments. Moreover, we as-sume that there is no arbitrage opportunity on themarket. Then the family of zero-coupon bonds pricesis arbitrage-free with respect to r for the probabil-ity measure Q equivalent to P , given by the Radon-Nikodym derivative

dQ

dP= exp

(−∫ T

0

λtdWt −1

2

∫ T

0

λ2tdt

), P − a.s.

(2)where λt = λ0σ (rt) is the market price of risk pro-cess, λ0 ∈ R. Under Q the process r is described by

drt = α (rt) dt+ σ (rt) dWQt , (3)

where

α (r) = φ− κr, φ = φ− λ0δ1, κ = κ+ λ0δ2 (4)

21


andWQt isQ - Brownian motion.

We ix n ≥ 1, T ∈ [0, T ′] and Fv > 0. LetK = (K0,K1, ...,Kn) be levels of catastrophic losses,where

0 ≤ K0 < K1 < K1 < ... < Kn.

Let w = (w1, w2, ..., wn) be a sequence of non-negative numbers such that their sum is not greaterto 1, i.e.∑n

i=1 wi ≤ 1.

De inition 1. By the symbol IB (T, Fv) we denotecatastrophebondwith the face valueFv, the date ofma-turity and payoff T and the payoff function of the form

νT,Fv = Fv

1−n−1∑j=0

NT ∧Kj+1 − NT ∧Kj

Kj+1 −Kjwj+1

.

For the considered type of catastrophe bond thepayoff function is a piecewise linear function of NT .If the catastrophe does not occur (i.e. NT < K0),the bondholder receives the payoff equal to its facevalue Fv. If NT ≥ Kn, the payoff is equal toFv (1−

∑ni=1 wi). If Kj ≤ NT ≤ Kj+1 for j =

0, 1, ..., n, the bondholder is paid

Fv

1−∑

0≤i<j

wi+1 −NT ∧Kj+1 − NT ∧Kj

Kj+1 −Kjwj+1

and in the interval [Kj ,Kj+1] the payoff de-creases linearly from Fv

(1−

∑0≤i<j wi+1

)to

Fv(1−

∑0≤i≤j wi+1

)as the function of NT .

We will use the following general theorem con-cerning catastrophebondpricing, provedbyus in [32].Theorem 1. Let (rt)t∈[0,T ′] be a risk-free spot interestrate given by the diffusion process (1) and such that, af-ter the change of probability measure described by theRadon –Nikodymderivative (2), it has the form (3)withthe coef icients given by equalities (4). Let IBT,Fv (t) bethe price at time t, 0 ≤ t ≤ T , of the catastrophe bondIB (T, Fv). Then

IBT,Fv (t) = η (t, T, rt, Fv) , 0 ≤ t ≤ T, (5)

where

(i)

η (t, T, r, Fv) =

= exp (−a (T − t)− b (T − t) r)EQ(νT,Fv|F1

t

);(6)

(ii) functions a (τ) and b (τ) satisfy the following sys-tem of differential equations:

1

2δ2b

2 (τ) + κb (τ) + b′ (τ)− 1 = 0, τ > 0,

(7)

a′ (τ)− φb (τ) +1

2δ1b

2 (τ) = 0 τ > 0

with a (0) = b (0) = 0.

In particular,

IBT,Fv (0) =η (0, T, r0, Fv)

= exp (−a (T )− b (T ) r0)EP νT,Fv. (8)

The interest rate process r, applied in this paper,is the Cox–Ingersoll–Ross model described by the fol-lowing stochastic equation

drt = κ (θ − rt) dt+ Γ√rtdWt (9)

for positive constants κ, θ and Γ. The CIR model isaf ine with parameters φ = κθ, δ1 = 0 and δ2 = Γ2.Generally, for the considered model, interest rate can-not become negative (i.e., S = [0,∞)), which is a ma-jor advantage relative to other models. Moreover, ifits parameters satisfy the inequality 2φ ≥ Γ2, thenS = (0,∞). The CIR model has the property of meanreversion around the long-term level θ. The parameterκ controls the size of the expected adjustment towardsθ and is called the speed of adjustment. The volatilityis the product Γ√rt and therefore the interest rate isless volatile for low values than for high values of theprocess rt.

The following theorem is a special case of Theorem1 for the spot interest rate dynamics described by theCox–Ingersoll–Ross model.

Theorem 2. Let the risk-free spot interest rate(rt)t∈[0,T ′] be described by the CIR model. Assume thatIBT,Fv (t) is the price of the bond IB (T, Fv) at mo-ment t ∈ [0, T ]. Then

IBT,Fv (t) = ea(T−t)−b(T−t)rtEQ(νT,Fv|F1

t

), (10)

whereb (τ) =

(eγτ − 1)(κ+γ)

2 (eγτ − 1) + γ, (11)

a (τ) =2φ

Γ2

[ln(

γ(κ+γ)

2 (eγτ − 1) + γ

)+

(κ+ γ) τ

2

],

(12)κ = κ+ λΓ, γ =

√κ2 + 2Γ2.

In Theorem 2 the constant λ is the product λ =λ0Γ. Since all the model parameters should be posi-tive after change of probability measure, we assumethat κ > 0. The equalities (11) and (12) are obtainedas the solution of the system of equations (7). One canalso ind them in inancial literature (see, e.g. [27]),since they are used in the zero-coupon bond pricingformula.

4. Catastrophe Bond Pricing in Fuzzy CaseUsually some parameters of the inancial market

are not precisely known. In particular, the volatilityparameter of the spot interest rate is determined byluctuating inancial market and very often its uncer-tainty does not have stochastic character. Therefore itis unreasonable to choose ixed values of parameters,which areobtained fromhistorical data, for later use in

22


pricing model, since they can luctuate in future (see,e.g. [42]).

To estimate values of uncertain parameters onecan use knowledge of experts, asking them for forecastof a parameter. The forecasts can be transferred intotriangular fuzzy numbers. Their average can be com-puted and used for estimation of the parameter. Suchan estimationmethodwasproposed in [4] and [18] forinancial applications.

In the reminder of this paperwe assumemore gen-erally that the volatility parameter is a strictly positivefuzzy number, which is not necessarily triangular. Wedenote the fuzzy volatility parameter by Γ.

In the following theorem we present catas-trophe bonds pricing formula for the one-factorCox–Ingersoll–Ross interest rate model.Theorem 3. Assume that IBT,Fv (t) is the price ofbond IB (T, Fv) at moment t ∈ [0, T ] for a strictly pos-itive fuzzy volatility parameter Γ. Then

IBT,Fv (t) = ea(T−t)⊖b(T−t)⊗rt ⊗ EQ(νT,Fv|F1

t

),

(13)where

a (τ) = ϕ⊗δ (τ) , b (τ) = α (τ)⊘ β (τ) ,

ϕ = (2φ)⊘(Γ⊗Γ

), κ = κ⊕ λ⊗Γ > 0,

γ =√κ⊗κ⊕ 2⊗Γ⊗Γ,

α (τ) = eγ⊗τ ⊖ 1, β (τ) =1

2⊗α (τ)⊗ (κ⊕ γ)⊕ γ

and

δ (τ) = ln(γ ⊘ β (τ)

)⊕ τ

2⊗ (κ⊕ γ) .

Moreover, for α ∈ [0, 1],

(IBT,Fv (t))α = (14)[EQ

(νT,Fv|F1

t

)e(a(T−t))Lα−(b(T−t))

U

α(rt)

Uα ,

EQ(νT,Fv|F1

t

)e(a(T−t))Uα−(b(T−t))

L

α(rt)

Lα

],

where

κα =

[λΓL

α + κ, λΓUα + κ

]for λ > 0,[

λΓUα + κ, λΓL

α + κ]

for λ < 0,

κ for λ = 0,

(15)

(κ⊗κ)α =

[(λΓL

α + κ)2

,(λΓU

α + κ)2]

for λ > 0,[(λΓU

α + κ)2

,(λΓL

α + κ)2]

for λ < 0,

κ2 for λ = 0,(16)

γα =

[√(κ⊗κ)

Lα + 2

(ΓLα

)2,

√(κ⊗κ)

Uα + 2

(ΓUα

)2],

(17)

(α (τ))α =[eγ

Lα τ − 1, eγ

Uα τ − 1

],

ϕα =

2φ(ΓUα

)2 , 2φ(ΓLα

)2 , (18)

(δ (τ)

)α=

[ln(

γLα

12 (α (τ))

Uα (κU

α + γUα ) + γU

α

)

+τ(κLα + γL

α

)2

, ln(

γUα

12 (α (τ))

Lα (κL

α + γLα ) + γL

α

)

+τ(κUα + γU

α

)2

], (19)

(b (τ)

)α=

[(α (τ))

Lα

12 (α (τ))

Uα (κU

α + γUα ) + γU

α

,

(α (τ))Uα

12 (α (τ))

Lα (κL

α + γLα ) + γL

α

](20)

and

(a (τ))α =

[(ϕα ⊗int

(δ (τ)

)α

)L,(

ϕα ⊗int

(δ (τ)

)α

)U]. (21)

Proof. We replace the crisp volatility parameter Γby its fuzzy counterpart Γ and arithmetic operators+,−, . by ⊕, ⊖, ⊗ in (10). As result we obtain the for-mula (13).

Let α ∈ [0, 1] and τ ≥ 0. For a given fuzzy num-ber F we denote by FL

α and FUα the lower and upper

bound of its α-level set.Since φ, κ > 0 and Γ > 0, the number κ⊗κ ⊕

2⊗Γ⊗Γ is also strictly positive. From direct calcula-tions it follows that (15) and (16) hold.

Function exp (x) for x ∈ R and functions √x andln (x) for x > 0 satisfy the assumptions of Proposition1 and they are increasing.Thus, γ > 0,

γα =

[√(κ⊗κ⊕ 2⊗Γ⊗Γ

)Lα,

√(κ⊗κ⊕ 2⊗Γ⊗Γ

)Uα

]

and (17) is satis ied. Fromdirect calculations it followsthat κ⊕ γ > 0, α (τ) ≥ 0, β (τ) > 0, b (τ) ≥ 0 and (20)is ful illed. Proposition 1 implies the equality

(ea(τ)⊖b(τ)⊗rt

)α=

[e(a(τ)⊖b(τ)⊗rt)

L

α ,

e(a(τ)⊖b(τ)⊗rt)U

α

], (22)

>From properties of the Cox–Ingersoll–Ross interestrate model it follows that the fuzzy random variablert is positive for t ∈ [0, T ] and, since b (T − t) ≥ 0,

23


that (14) holds. Applying Proposition 1 also gives theequality(

ln(γ ⊘ β (τ)

))α

=

[ln(

γLα

12 (α (τ))

Uα (κU

α + γUα ) + γU

α

),

ln(

γUα

12 (α (τ))

Lα (κL

α + γLα ) + γL

α

)],

Finally, the standard interval calculations give theforms of ϕα,

(δ (τ)

)αand (a (τ))α =

(ϕ⊗ δ (τ)

)αde-

scribed by (18), (19) and (21).

Applying the equality

µ ˜IBT,Fv(t)(c) = sup

0≤α≤1αI( ˜IBT,Fv(t))

α

(c)

one can obtain themembership function of ˜IBT,Fv (t).For a suf iciently high value of α (e.g. α = 0.95) theα-level set of ˜IBT,Fv (t) can be used for investmentdecision-making. A inancial analyst can choose anyvalue from the α-level set as the catastrophe bondprice with an acceptable membership degree.

5. Monte Carlo ApproachThe calculations required to ind the price of the

cat bond via the formulas introduced in Section 4could be very complex, especially if the payment func-tion or the model of losses are not straightforwardones. Then instead of directly inding an analytical for-mula for the price, other approaches may be used. Inthis paper we focus on Monte Carlo simulations andapplication of fuzzy arithmetic for α-cuts.

To model complex nature of the practical cases,the parameters similar to the ones based on the real-life data are applied. In [6] the parameters of the CIRmodel are estimated using Kalman ilter for monthlydata of the Treasury bond market. But these values,namely φ, κ,Γ, r0, are crisp ones (compare with Ta-ble 1). Because in Section 4 the cat bond pricing ap-proach for the CIR model with fuzzy number Γ wasestablished, then instead of crisp value Γ = 0.0754(as estimated in [6]), the fuzzy triangular number Γis applied (see Table 1). This fuzzy value is similar tothe crisp parameter obtained in [6], but with the in-troduced fuzzy volatility the future uncertainty of theinancial markets is modeled.

The other applied model, i.e. the process of losses,is also based in our approach on the real-life data. In[7] the information of catastrophe losses in the UnitedStates provided by the Property Claim Services (PCS)of the ISO (Insurance Service Of ice Inc.) and the rel-evant estimation procedure for this data are consid-ered. For each catastrophe, the PCS loss estimate rep-resents anticipated industrywide insurance paymentsfor different property lines of insurance covering. Anevent is noted as a catastrophe when claims are ex-pected to reach a certain dollar threshold.We focus onlognormal distribution of the value of the single loss

andNHPP (non-homogeneous Poisson process) as theprocess of the quantity of catastrophic events (see Ta-ble 1), but other random distributions and other pro-cesses could be directly applied using the approach in-troduced in this paper.

Asnoted in [7], becauseof annual seasonality of oc-currence of catastrophic events, the intensity functionof losses for NHPP is given by

ρNHPP(t) = a+ 2πb sin (2π(t− c)) . (23)

The triggering points in our considerations are re-lated to quantiles given by QNHPP-LN(x), i.e. the x-thquantile of the cumulated value of losses for the NHPPprocess (quantity of losses) and lognormal distribu-tion (value of each loss).

After conducting N = 1000000 Monte Carlo sim-ulations, the fuzzy value of the cat bond price was ob-tainedusing fuzzy arithmetic (see Figure2). This fuzzyprice is close to symmetry in the case of the param-eters from Table 1. Based on this fuzzy number, therelevant intervals of prices for various α may be alsofound. Because of practical purposes the analyst maybe also interested in crisp value of the cat bond price,then e.g. α = 1 can be set or the crisp possibilisticmean can be calculated (see [34, 35] for related ap-proach in analysis of European options pricing). Theobtained results in the considered case are enumer-ated in Table 2. For the crisp possibilistic mean the in-tuitive function f(α) = 2α is applied. The differencebetween both of the obtained crisp values is about0.091%.

0.80 0.85 0.90 0.95Price

0.2

0.4

0.6

0.8

1.0

alpha

Fig. 2. Fuzzy price of the cat bond (parameters of themodel from Table 1)

For other symmetric fuzzy values of the volatilityΓ considered in our analysis, the calculated fuzzy catbond prices have similar shapes (see Figure 3). Themembership function could be also evaluated in thecase of asymmetrical triangular fuzzy values of Γ (seeFigure 4).

The model of catastrophic events is usually basedonhistorical data as in the casediscussed in [7]. There-fore the estimators calculated from such data may benot completely adequate for future natural catastro-phes. Then the behavior of cat bond prices could beanalyzed if some of the important parameters of themodel are changed. For example, if the parameter µLNof lognormal distribution of the single loss becomes

24


Tab. 1. Parameters of Monte Carlo simula ons

ParametersCIR model (crisp) φ = 0.00270068, κ = 0.07223, r0 = 0.02

CIR model (fuzzy) Γ = (0.07, 0.075, 0.08)Intensity of NHPP a = 30.875, b = 1.684, c = 0.3396Lognormal distribution µLN = 17.357, σLN = 1.7643Triggering points K1 = QNHPP-LN(0.75),K2 = QNHPP-LN(0.85),

K3 = QNHPP-LN(0.95)Values of losses coef icients w1 = 0.4, w2 = 0.6

Tab. 2. Crisp prices for the cat bond (parameters of themodel from Table 1)

Method Priceα = 1 0.851857Crisp possibilistic mean 0.852631

0.75 0.80 0.85 0.90 0.95 1.00Prices

0.2

0.4

0.6

0.8

1.0

alpha

Fig. 3. Fuzzy price of the cat bond for variousfuzzy values of Γ ((0.072, 0.075, 0.078) – do ed line,(0.07, 0.075, 0.08) – dashed line, (0.068, 0.075, 0.082) –solid line)

0.80 0.82 0.84 0.86 0.88 0.90 0.92Prices

0.2

0.4

0.6

0.8

1.0

alpha

Fig. 4. Fuzzy price of the cat bond for variousfuzzy values of Γ ((0.07, 0.075, 0.077) – do ed line,(0.073, 0.075, 0.08) – dashed line)

higher and other parameters are the same as in Table1, then the relevant fuzzy prices of the cat bonds areshifted left-side (see Figure 5) and the crisp prices arelower (see Table 3). The same applies for the case ofvarious values of the parameter σLN (see Figure 6 andTable 4). As it may be seen from Figure 5 and Figure6, these parameters have important impact on the ob-

tained cat bond prices.

mu=17.2

mu

mu=17.4

mu=17.3

0.75 0.80 0.85 0.90 0.95 1.00Prices

0.2

0.4

0.6

0.8

1.0

alpha

Fig. 5. Fuzzy price of the cat bond for various values ofµLN

Tab. 3. Crisp prices for for various values of µLN

µLN 17.2 17.3 17.4Price for α = 1 0.893286 0.86935 0.83707Crisp possibilisticmean

0.894098 0.87014 0.837831

sigma=1.74

sigma=1.75

sigma=1.76

0.80 0.85 0.90 0.95Prices

0.2

0.4

0.6

0.8

1.0

alpha

Fig. 6. Fuzzy price of the cat bond for various values ofσLN

6. ConclusionsIn this paper the catastrophe bond pricing formula

in crisp case for the Cox–Ingersoll–Ross risk-free in-terest rate model is derived. Then on basis of this for-mula catastrophe bond valuation expression for fuzzy

25


Tab. 4. Crisp prices for for various values of σLN

σLN 1.74 1.75 1.76Price for α = 1 0.865891 0.858843 0.854912Crisp possibilisticmean

0.866678 0.859623 0.855689

volatility parameter is obtained. Since the pricing for-mula is considered for arbitrary time moment beforematurity, fuzzy random variables are introduced. Be-sides the fuzzy valuation formula, the forms of α-levelsets of the cat bond price are received. Therefore thisapproach can be applied for general forms of fuzzynumbers.

Also the Monte Carlo simulations are conducted inorder to directly analyze the fuzzy cat bond prices. Weapply fuzzy arithmetic and introduce triangular fuzzynumber for the value of the volatility in CIRmodel, butusing other fuzzy numbers (e.g. L-R numbers) is alsopossible in our setting. Then the in luence of the shapeof fuzzy numbers and other parameters of the modellike distribution of the single loss on the inal cat bondprice is considered.

AUTHORSPiotr Nowak∗ – Systems Research Institute Pol-ish Academy of Sciences, ul.Newelska 6, 01–447Warszawa, Poland, e-mail: [email protected] Romaniuk∗ – Systems Research Institute Pol-ish Academy of Sciences, The John Paul II Catholic Uni-versity of Lublin, ul. Newelska 6, 01–447 Warszawa,Poland, e-mail: [email protected].∗Corresponding author

REFERENCES[1] Albrecher H., Hartinger J., Tichy R.F., ”‘QMC tech-

niques for CAT bond pricing”,Monte Carlo Meth-ods Appl., vol. 10, no. 3–4, 2004, 197–211.

[2] Baryshnikov Y., Mayo A., Taylor D.R., Pricing CATBonds. Working paper, 1998).

[3] Borch, K., The Mathematical Theory of Insurance,Lexington Books, Lexington (1974)

[4] Buckley J.J., Eslami E., ”Pricing Stock Options Us-ing Fuzzy Sets”, Iranian Journal of Fuzzy Systems,vol. 4, no. 2, 2007, 1–14.

[5] Burnecki K., Kukla G., ”Pricing of Zero-Couponand Coupon CAT Bond”, Applied Mathematics,vol.30, 2003, 315–324.

[6] Chen R.-R., Scott L., ”Multi-factor Cox-Ingersoll-Ross Models of the Term Structure: Estimatesand Tests from a Kalman Filter Model”, Journal ofReal Estate Finance and Economics, vol. 27, no. 2,2003, 143–172.

[7] Chernobai A., Burnecki K., Rachev S.,Trueck S., Weron R., ”Modeling catastro-

phe claims with left-truncated severity dis-tributions”, Computational Statistics, vol.21, issue 3–4,2006, 537–555. DOI: http://dx.doi.org/10.1007/s00180-006-0011-2.

[8] Cox S.H., Fairchild J.R., Pedersen H.W., ”EconomicAspects of Securitization of Risk”, ASTIN Bulletin,vol. 30, no. 1, 2000, 157–193.

[9] Cox S.H., Pedersen H.W., ”Catastrophe RiskBonds”, North American Actuarial Journal , vol.4, issue 4, 2000, 56–82. DOI: http://dx.doi.org/10.1080/10920277.2000.10595938.

[10] Cummins J.D., Doherty N., Lo A., ”Can insurerspay for the ”big one”? Measuring the capacityof insurance market to respond to catastrophiclosses”, Journal of Banking and Finance , vol. 26,no. 2–3, 2002, p. 557. DOI:http://dx.doi.org/10.1016/S0378-4266(01)00234-5.

[11] Dai Q., Singleton K.J., ”Speci ication analysis ofaf ine term structuremodels”, Journal of Finance,vol. 55, no. 5, 2000, 1943– 1978. DOI: http://dx.doi.org/10.1111/0022-1082.00278.

[12] Duf ie D., Kan R., ”A yield-factor model of inter-est rates”, Mathematical Finance, vol. 6, no. 4,1996, 379–406. DOI: http://dx.doi.org/10.1111/j.1467-9965.1996.tb00123.x.

[13] Egami M., Young V.R.:, ”Indifference prices ofstructured catastrophe (CAT) bonds”, Insurance:Mathematics and Economics, vol. 42, no. 2, 2008,771–778. DOI: http://dx.doi.org/10.1016/j.insmatheco.2007.08.004.

[14] Ermolieva T., Romaniuk,. M., Fischer. G.,Makowski. M., ”Integratedmodel-based decisionsupport for management of weather-relatedagricultural losses”. In: Enviromental informaticsand systems research. Vol. 1: Plenary and sessionpapers - EnviroInfo 2007, ed. by Hryniewicz. O.,Studzinski J., Romaniuk M., Shaker Verlag 2007.

[15] Freeman P. K., Kunreuther H., Managing Envi-ronmental Risk Through Insurance. Kluwer Aca-demic Press, Boston 1997. DOI: http://dx.doi.org/10.1007/978-94-011-5360-7.

[16] Fuller R., Majlender P., ”On weighted possi-bilistic mean and variance of fuzzy numbers”,Fuzzy Sets and Systems, vol. 136, no. 3, 2003,363–274. DOI: http://dx.doi.org/10.1016/S0165-0114(02)00216-6.

[17] George J.B., ”Alternative reinsurance: Usingcatastrophe bonds and insurance derivativesas a mechanism for increasing capacity in theinsurance markets”, CPCU Journal, vol. 52, no. 1,1999, p. 50.

[18] Gil-Lafuente A. M., Fuzzy logic in inancial analy-sis, Springer, Berlin 2005.

[19] Kowalski P. A., Łukasik S., CharytanowiczM., Kul-czycki P., ”Data-Driven Fuzzy Modeling and Con-trol with Kernel Density Based Clustering Tech-nique”, Polish Journal of Environmental Studies,vol. 17, no. 4C, 2008, 83–87.

26

http://dx.doi.org/10.1007/s00180-006-0011-2

http://dx.doi.org/10.1007/s00180-006-0011-2

http://dx.doi.org/10.1080/10920277.2000.10595938

http://dx.doi.org/10.1080/10920277.2000.10595938

http://dx.doi.org/10.1016/S0378-4266(01)00234-5

http://dx.doi.org/10.1016/S0378-4266(01)00234-5

http://dx.doi.org/10.1111/0022-1082.00278

http://dx.doi.org/10.1111/0022-1082.00278

http://dx.doi.org/10.1111/j.1467-9965.1996.tb00123.x

http://dx.doi.org/10.1111/j.1467-9965.1996.tb00123.x

http://dx.doi.org/10.1016/j.insmatheco.2007.08.004


http://dx.doi.org/10.1007/978-94-011-5360-7

http://dx.doi.org/10.1007/978-94-011-5360-7

http://dx.doi.org/10.1016/S0165-0114(02)00216-6

http://dx.doi.org/10.1016/S0165-0114(02)00216-6


[20] Kulczycki P., Charytanowicz M., ”Bayes sharpen-ing of imprecise information”, International Jour-nal of Applied Mathematics and Computer Sci-ence, vol. 15, no. 3, 2005, 393–404.

[21] Kulczycki P., Charytanowicz M., ”AsymmetricalConditional Bayes Parameter Identi ication forControl Engineering”, Cybernetics and Systems,vol. 39, no. 3, 2008, 229–243.

[22] Kulczycki, P., Charytanowicz, M., ”A CompleteGradient Clustering Algorithm Formedwith Ker-nel Estimators”, International Journal of AppliedMathematics and Computer Science, vol. 20, no. 1,2010, 123–134. DOI: http://dx.doi.org/10.2478/v10006-010-0009-3.

[23] Kulczycki P., Charytanowicz M., ”ConditionalParameter Identi ication with Different Lossesof Under- and Overestimation”, Applied Math-ematical Modelling, vol. 37, no. 4, 2013, 2166– 2177. DOI: http://dx.doi.org/10.1016/j.apm.2012.05.007.

[24] Lee J. P., Yu M. T., ”Valuation of catastrophereinsurance with catastrophe bonds”, Insurance:Mathematics and Economics, vo. 41, no. 2, 2007,264–278. DOI: http://dx.doi.org/10.1016/j.insmatheco.2006.11.003.

[25] Lin S. K., Shyu D., Chang C. C., ”Pricing Catastro-phe Insurance Products in Markov Jump Diffu-sionModels”, Journal of Financial Studies, vol. 16,no. 2, 2008, 1–33.

[26] Muermann A., ”Market Price of Insurance RiskImplied by Catastrophe Derivatives”, NorthAmerican Actuarial Journal, vol. 12, no. 3, 2008,221–227. DOI: http://dx.doi.org/10.1080/10920277.2008.10597518.

[27] Munk C., Fixed Income Modelling, Oxford Univer-sity Press 2011. DOI: http://dx.doi.org/10.1093/acprof:oso/9780199575084.001.0001.

[28] Nowak P., ”Analysis of applications of some ex-ante instruments for the transfer of catastrophicrisks”. In: IIASA Interim Report I IR-99-075,1999.

[29] Nowak P., ”On Jacod-Grigelionis characteris-tics for Hilbert space valued semimartingales”,Stochastic Analysis and Applications, vol. 20, no.5, 2002, 963–998. DOI: http://dx.doi.org/10.1081/SAP-120014551.

[30] Nowak P., Romaniuk M., ”Computing optionprice for Levy process with fuzzy parameters”,European Journal of Operational Research, vol.201, no. 1, 2010, 206–210. DOI: http://dx.doi.org/10.1016/j.ejor.2009.02.009.

[31] Nowak P., Romaniuk M., Ermolieva T., ”Evalua-tion of Portfolio of Financial and Insurance In-struments: Simulation of Uncertainty”. In: Man-aging Safety of Heterogeneous Systems: Decisionsunder Uncertainties and Risks, ed. by ErmolievY., Makowski M., Marti K., Springer-Verlag BerlinHeidelberg 2012.

[32] Nowak P., Romaniuk M., Application of the one-factor af ine interest rate models to catastrophebonds pricing. Research Report, RB/1/2013, SRIPAS, Warsaw 2013.

[33] Nowak P., Romaniuk M., ”Pricing and simula-tions of catastrophe bonds”, Insurance: Math-ematics and Economics, vol. 52, no. 1, 2013,18–28. DOI: http://dx.doi.org/10.1016/j.insmatheco.2012.10.006.

[34] Nowak P., Romaniuk M., ”A fuzzy approach tooption pricing in a Levy process setting”, Int. J.Appl. Math. Comput. Sci., vol. 23, no. 3, 2013,613–622. DOI: http://dx.doi.org/10.2478/amcs-2013-0046.

[35] Nowak P., Romaniuk M.:, ”Application of Levyprocesses and Esscher transformed martingalemeasures for option pricing in fuzzy framework”,Journal of Computational and Applied Mathemat-ics, vol. 263, 2014, 129–151. DOI: http://dx.doi.org/10.1016/j.cam.2013.11.031.

[36] Puri M.L., Ralescu D.A., ”Fuzzy randomvariables”, Journal of Mathematical Analy-sis and Applications, vol. 114, no. 2, 1986,409–422. DOI: http://dx.doi.org/10.1016/0022-247X(86)90093-4.

[37] Ripples IntoWaves: The Catastrophe Bond Marketat Year-End 2006. Guy Carpenter& Company, Inc.and MMC Security Corporation 2007.

[38] Romaniuk M., Ermolieva T., ”Application EDGEsoftware and simulations for integrated catas-trophe management”, International Journal ofKnowledge and Systems Sciences, vol. 2, no. 2,2005, 1–9.

[39] Shiryaev A.N., Essentials of stochastic i-nance, Facts, Models, Theory, World Scienti ic1999. DOI: http://dx.doi.org/10.1142/9789812385192.

[40] Vaugirard V.E., ”Pricing catastrophe bonds byan arbitrage approach”, The Quarterly Reviewof Economics and Finance, vol. 43, no. 1, 2003,119– 132. DOI: http://dx.doi.org/10.1016/S1062-9769(02)00158-8.

[41] Walker G., ”Current Developments in Catastro-phe Modelling”. In: Financial Risks Managementfor Natural Catastrophes, ed. by Britton, N. R.,Olliver, J. Brisbane, Grif ith University, Australia1997.

[42] Wu H.-Ch., ”Pricing European options based onthe fuzzy pattern of Black-Scholes formula”, Com-puters & Operations Research, vol. 31, no. 7,2004, 1069–1081. DOI: http://dx.doi.org/10.1016/S0305-0548(03)00065-0.

27

http://dx.doi.org/10.2478/v10006-010-0009-3

http://dx.doi.org/10.2478/v10006-010-0009-3

http://dx.doi.org/10.1016/j.apm.2012.05.007

http://dx.doi.org/10.1016/j.apm.2012.05.007



http://dx.doi.org/10.1080/10920277.2008.10597518

http://dx.doi.org/10.1080/10920277.2008.10597518

http://dx.doi.org/10.1093/acprof:oso/9780199575084.001.0001

http://dx.doi.org/10.1093/acprof:oso/9780199575084.001.0001

http://dx.doi.org/10.1081/SAP-120014551

http://dx.doi.org/10.1081/SAP-120014551

http://dx.doi.org/10.1016/j.ejor.2009.02.009

http://dx.doi.org/10.1016/j.ejor.2009.02.009



http://dx.doi.org/10.2478/amcs-2013-0046

http://dx.doi.org/10.2478/amcs-2013-0046

http://dx.doi.org/10.1016/j.cam.2013.11.031

http://dx.doi.org/10.1016/j.cam.2013.11.031

http://dx.doi.org/10.1016/0022-247X(86)90093-4

http://dx.doi.org/10.1016/0022-247X(86)90093-4

http://dx.doi.org/10.1142/9789812385192

http://dx.doi.org/10.1142/9789812385192

http://dx.doi.org/10.1016/S1062-9769(02)00158-8

http://dx.doi.org/10.1016/S1062-9769(02)00158-8

http://dx.doi.org/10.1016/S0305-0548(03)00065-0

http://dx.doi.org/10.1016/S0305-0548(03)00065-0


B S V MRGB-D B T C

B S V MRGB-D B T C

B S V MRGB-D B T C

B S V MRGB-D B T C

Submi ed: 6th June 2014; accepted: 15th July 2014

Jan Wietrzykowski, Dominik Belter

DOI: 10.14313/JAMRIS_3-2014/24

Abstract:This paper deals with the terrain classifica on problemfor an autonomous mobile robot. The robot is designedto operate in an outdoor environment. The classifier in-tegrates data from RGB camera and 2D laser scanner.The camera provides informa on about visual appear-ance of the objects in front of the robot. The laser scan-ner provides data about distance to the objects and theirability to reflect infrared beam. In this paper we presentthe method which create terrain segments and classifiesthem using joint applica on of Support Vector Machine(SVM) classifier and AdaBoost algorithm. The classifica-on results of the experimental verifica on are provided

in the paper.

Keywords: Terrain classifica on, mobile robot, RGB-D

1. Introduc onAutonomous navigation in urban environment is

a challenge for mobile robots. The robot which oper-ates in urban space should localize itself, ind the pathto the goal position and avoid obstacles. Moreover, itshould obey rules which are designed for humans. Itis obvious that autonomous car-like robot should fol-low the road. Access to the pavement is prohibited.The robot which is designed as short distance couriershould use pavement for locomotion and avoid roadas possibly dangerous area. The access to the lawnshould also be prohibited. In this case it isn’t danger-ous for the robot, but such a behavior is against prin-ciples of community life. To obey all rules the robotshould recognize various terrain types.

The autonomous operation in urban environmentdiffers to operation in off-road natural environment.The irst difference is related to traversability assess-ment methods. Outdoor and and off-road locomotiontakes into accountmainly the shape of the terrain. Theterrain type does not play an important role. Grass aswell as asphalt is considered as traversable. Such situ-ation is not acceptable in urban environment. More-over, in off-road environment the borders betweenvarious regions are dif icult do distinguish (e.g. thegrass can be also found on the ield track). In man-made environment most of objects and terrain typeshave standard size, color and location. On the otherhand robot which operates in urban-like environmenthas to distinguish between very similar areas like roadand pavement.

1.1. Problem statementOur goal is to create the robot which can navigate

in urban environment. The paper is focused on terrainclassi icationwhich is important part of the navigationsystem of a mobile robot. We are interested in roboticcompetitions for delivery or search and rescue. Thescenario of such challenges include autonomous navi-gation on paved park roads (Robotour) or inding andfetching an object (e.g. 1 kilo ”bag of gold” in RobotsIntellect competition).

The robot which navigates in urban environ-ment can’t use only depth sensors to create environ-ment model. Some obstacles, however lat, are nottraversable (e.g. lawn). Other places like pedestriancrossing should be recognized to apply special strat-egy for traversing. This can be done by visual camera.Using monocular RGB camera only the robot wouldhaveproblems to distinguish between asphalt and lat,vertical and gray wall. It is much easier to classify ter-rain using two complementary sensors.

In the paper we present way to classify terrain us-ing data from RGB-D sensors (in our case laser scan-ner and visual camera). We are interested in segmen-tation of an image and labeling detected areas. To thisend, we applied classi ication strategy which utilizesSVM classi ication and AdaBoosting. We present re-sults from indoor and outdoor experiments. The ob-tained results are compared with other approaches toshow ef iciency of the proposed method.

1.2. Related work and research contribu onMost of the existing terrain classi ication methods

employ RGB cameras for features extraction [5,13]. Inour work we increase the robustness of the classi i-cation procedure by incorporation information aboutdepth of the scene. Laible et al. presented that the clas-si ication accuracy can be increased by the analysisof the whole scene and taking into account neighbor-ing regions [15]. The decision about terrain type can’tbe taken using local terrain properties only. Context,neighboring terrain types and location of the consid-ered image segment play important role in the classi i-cation procedure. To join information fromweak clas-si iers Laible et al. proposed the application of Condi-tional Random Fields [15].

The joint application of 2D laser scanner and RGBcamera to terrain classi ication is not new. Dahlkampet al. proposed to use data from range inder to su-pervise learning algorithm [6]. The surface model ob-tained from depth data is used to ind a traversablearea (road). Then, the visual data from a camera

28


is used by a learning algorithm. The classi icationmethod uses mixture of Gaussians in RGB space toclassify the terrain. The model is updated whenevernew learning dataset is provided by self-supervisingprocedure. The re-learning procedure allows the sys-tem to adapt even when the road changes from grayasphalt to green grass. In our case this situation isnot desirable. The classi ier should determine not onlythe traversability, but also the terrain type. The grass(however lat) should be also considered as an obsta-cle for our robot. In contrast to method presented byDahlkamp et al. we use RGB and depth data duringclassi ication stage.

A reliable terrain classi ication can be also ob-tained using visual features and SVM classi ication [9].In the method proposed by Filitchkin and Byl SURFfeatures are used. To deal with various surfaces, whichdifferwith number of visual features, the optimizationon Hessian threshold detection is proposed. However,the feature-based classi ication is sensitive to motionblurring problem. Thus, we decided to use few inde-pendent sources of information.

Most reliable classi ication methods suffer fromhigh computational cost. Angelova et al. proposeda cascade of classi iers instead of single, multi-dimensional classi ication to obtain high speed andpreserve high classi ication accuracy [1]. They takeadvantage of the fact that some terrain types mightbe easily separated from the others. This observationcan be used to create decision tree. The classi icationstarts from the fastest classi ication sub-procedure.The most computationally expensive procedures areperformed at the end an only for regionswhich are dif-icult to distinguish.

Additional classi ication capabilities are availablefor legged robots. Such robots can use force/torquesensors as an additional source of information to clas-si ication procedure [12,19]. Also wheeled robots canuse properties of the contact with the ground to sup-port classi ication procedure (e.g. vibrations whichpropagate through suspension structure [11]).

2. Percep on and data acquisi onThe environment perception is based on two sen-

sor: a generic USB camera (Microsoft LifeCam Stu-dio) and laser range inder. The robot acquires VGA(640×480) images. VGA resolution is suf icient forclassi ication and allows to decrease the computationtime of the procedure. The Hokuyo UTM-30LX laserinder used in this research can operate outdoor. Therange of the sensor is up to 30 m. The angular reso-lution is 0.25 and each scan takes 25 ms. Single scancontains information about terrain pro ile. When therobot moves forward or rotates it acquires 3D shapeof the environment. Both sensors are tilted down toacquire terrain properties.

To create map of the environment the robot has todetermine the position of the sensors in global coor-dinate system OG at each scan of range inder. Therobot uses GPS, encoders and Inertial MeasurementUnit (IMU) to localize itself. Data from all sensors are

Fig. 1. Configura on of the sensors a ached to therobot’s pla orm

integrated using Kalman Filter. The robot is equippedwith IMU CHR-UM6 sensor on board. It allows tomea-sure properly the shape of the environment on roughterrain. The robot can take into account the inclina-tion of the platformduring integration of themeasure-ments. In our researchweuse twovariousmobile plat-forms. However, the presented classi ication methodis platform independent.

The con iguration of sensors is presented in Fig. 1.The coordinate systems OK , OI and OL are attachedto the camera, IMU and laser range inder, respec-tively. To integrate data from all sensors the corre-spondence between each pixel of the camera imageand points of the laser scan has to be known. To thisend, the pose of each sensor has to be determined bythe calibration procedure. The calibration procedurealso determines intrinsic parameters of the camera.We applied Camera Calibration Toolbox for Matlab byJean-Yves Bouguet [4] to ind focal length and locationof the principal point.

To ind relation between camera and laser rangeinder a plane-to-line itting method was applied [20].We can use checkerboard marker from intrinsiccalibration to determine a plane which representsmarker. From the laser scan we can ind an equationof the line located on on this plane. From the mea-surements set we can compute transformation be-tween camera and laser scanner coordinate system. Topresent calibration results between camera and laserscannerwedraw single scan on the camera image. Theresult is presented in Fig. 2.

Moreover, we should ind orientation between ex-teroceptive sensors (camera and LRF) and IMU unit.To this end, we used the method proposed by Lobo

29


Fig. 2. Calibra on results of the camera and the laserrange finder

SegmentationInput image

and

LRF data

Labeled

image

Cascade of

classi ers

+1 T

Cascade of

classi ers

+1 T

Fig. 3. Structure of the terrain classifica on procedurewhich uses RGB-D input data and returns labeled image

et al. [16]. In this case we use checkerboard markerwhich is perpendicular to gravity vector. Taking intoaccount orientation measured by the camera we canind orientation offset of the IMU unit.

Finally to computepose of eachmeasuredpointPL

in global coordinate systemOG we apply (1):

PG = GAI · IAK · KAL · PL, (1)

where KAL is a transformation from the cameracoordinate system to the laser coordinate system, IAK

is a transformation from IMU unit to the camera co-ordinate system and GAI is the IMU unit pose in theglobal coordinate system obtained from the localiza-tion system.

3. Terrain classifica onThe input to our system is data from RGB camera

andHokuyo laser scanner. The architecture of the clas-si ication procedure is presented in Fig. 3. At the be-ginning the segmentation is performed using RGB im-age. For each segment we compute k visual and depthfeatures (f1, ..., fk). A set of features is then used forclassi ication. We decided to use combination of SVMweak classi iers and boosting technique to join results(Fig. 4). It was shown that this approach has betterperformance in training time [10]. We also show thatclassi ication results are better. To use boosting tech-nique we should use weak classi iers (which perform

RGB Depth

f1 f2 f3 fk

c1 c2 cn

C

SVM

AdaBoost

Fig. 4. Classifica on scheme with SVM weak classifiersand AdaBoost

better than random classi ier, e.g. Decision Stump). In-stead we can use strong classi iers e.g. SVM or NeuralNetworkwhich are appropriatelyweakened [7]. In ourmethod nweak SVM classi iers (c1,...,cn) are used. TheoutputC from the classi ier is the terrain category rec-ognized by the system.

3.1. Segmenta on

In our method we perform image segmentationand then classi ication for each RGB-D segment. Weavoid classi ication for each pixel separately becausewe don’t always have corresponding depth for eachpixel. Moreover, single pixel does not contain all infor-mation about the terrain properties like roughness ob-tained from depth data or variance of color. We alsoavoid dividing the image into regular mesh [14, 17].Constant and rectangular regionmay contain two sep-arate terrains and such a cell should be classi ied astwo separate classes. Instead, we perform image seg-mentation and thenwe classify each region separately.

Weuse amethodproposedbyPedroFenzenszwalband Daniel Huttenlocher for image segmentation [8].The segmentation method used in our system dividesan image into components. The behavior of the seg-mentation method is speci ied only by two parame-ters. First parameter kc is responsible for preferredcomponent size. Second parameter Smin representsthe minimal size of components.

Before segmentation the image is smoothed byGaussian ilter with σ = 0.8. At the beginning of thesegmentation the algorithm creates initial graph G(Fig. 5). Each edge E of the graph connects two ver-tices, representing single neighboring pixels of the im-age. The weight w of an edge is computed using dif-ference in pixel color values [r,g,b] with an Euclideandistance. Then, edges of the graph are sorted in an as-cending order with respect to weights w. A set of seg-ments is initialized – each vertex of the graph repre-sent separate segment. Next, for each edge which be-longs to separate components weightwq is computed.The computed weight wq is compared with threshold

30


Init set of

components S0, q=0

Create Initial

Graph G(V,E)

q<size(E)

?

Compute weight wq

and threshold wt

wq<wt

?

merge two components

connected by edge eq,

q=q+1

Start

Merge components

smaller than Smin

Finish

Fig. 5. Segmenta on procedure used for image par -oning

a b

Fig. 6. Segmenta on results – original image (a) andoutput components (b)

weight wt:

wt = min(INT (vi)+kc

Size(vi), INT (vj)+

kcSize(vj)

),

(2)where vi is the considered vertex, vj is the neigh-

boring vertex, Size(v) is the size of component repre-sented by vertex v and INT (v) is the maximal weightbetween vertices which create the whole component.If wq is smaller or equal wt vertices are merged intosingle component S. In an opposite case, the con ig-uration of segments does not change. Finally, the al-gorithm removes components which are smaller thanthreshold Smin. Components which are too small aremerged with neighboring components. The algorithmreturns a set of components S.

The results of the segmentation procedure are pre-sented in Fig. 6.3.2. Classifica on

For classi ication purpose we use Support VectorMachine supervised learning algorithm [3]. We de-cided to use SVM because it works well with multi-dimensional input vector. The output from the classi-ier is the value of assignment to each category of ter-rains. We created ive weak classi iers. The input foreach classi ier is de ined as follows:1) two dimensional histogram of values in Hue-

Saturation color space (4 × 4 bins) converted to

a b

Fig. 7. Intensity values obtained from Hokuyo laserrange finder – observed scene (a) and registered inten-sity values (b)

one-dimensional vector,2) 8 bin histogram of Value in HSV space,3) meanand covariancematrix for pixels inHSVspace

converted to a 1× 12 vector,4) mean and covariance matrix for values of depth

and intensity from Hokuyo laser scanner con-verted to a 1× 6 vector,

5) 25 bin histogram of intensity values from Hokuyolaser scanner.First three classi iers use color image feature as

an input for classi ication. The next two classi iers usedata from depth sensor. We use depth data directlyas well as intensity values which are provided by theHokuyo driver. The intensity value depends on thecolor and texture of the surface. Thus, intensity valueprovides important information about observed sur-face [15]. Example intensity values for the various ter-rain types are presented in Fig. 7. Using intensity val-ueswe can easily distinguish between various types ofterrain without direct information about color of thesurface.

For boosting we use improved version of Ad-aBoost algorithm [18] basedonMultiBoost implemen-tation [2] which deals with multi-class weak-learning.

4. ResultsFirst experiments were performed indoor. Our

goal was to avoid problems with uncertainty of the lo-calization systemwhich introducesmapping error.Wecreated mockup with various terrain types like arti i-cial grass, elastic gum, timber and tile loor (Fig. 7a).

For training classi iers we used 33 manuallymarked scenes. Next 35 scenes were used for testing.For segmentation we set k = 50 which allows to ob-tain 3000 training samples. For testingweuse k = 200which allows to obtain segments which represent big-ger area. Thus, we avoid situations when grass is di-vided into green patches representing grass and smallblack patches representing soil. We are interested inclassi ication of the whole region with heterogeneoustexture.

Example classi ication results are presented inFig. 8. Colors in Fig. 8b represent various type of ter-rain: green – grass, brown – timber loor, blue – as-phalt, yellow – rocky terrain. Only some small areasare classi ied improperly. The component of the tim-ber loor is classi ied as a rocky terrain. Also small re-

31


a b

Fig. 8. Results – the example scene (a) and classifica onresults

gion between the grass and the loor is classi ied im-properly as an asphalt (mainly because of black colorof this part).

Tab. 1. Confusion matrix for indoor experiment

terrain type grass timber rocks asphaltgrass 94% 5% 1% 0%timber 0% 90% 10% 0%rocks 0% 3% 96% 1%asphalt 0% 1% 2% 96%

We also performed statistical analysis for thewhole testing set. The results are presented in Tab. 1.Each row in the table represent the terrain typemarked by the expert. Each column represent outputfrom proposed classi ication method. The classi ica-tion results pc1,c2 presented in Tab. 1 are computed asfollows:

pc1,c2 =Nc1

Nc2

· 100%, (3)

where Nc1 is the number of pixels classi ied as classc1 and Nc2 is the number of pixels marked by expertas class c2. It means that 94% of pixels which belongto grass are classi ied properly as a grass, 5% of pixelsare classi ied as timber and 1% as rocks.

Tab. 2. Comparison between various configura ons ofthe proposed classifier and input features

classi icatory typeterrain type Cc Cl MON Cone Ckl

grass 43% 95% 86% 95% 94%timber 94% 16% 75% 71% 90%rocks 39% 85% 98% 98% 96%asphalt 64% 97% 96% 89% 96%average 60% 75% 86% 89% 94%

We also compared various con igurations of clas-si iers and input features. We compared six con igura-tions:1) Cc – SVMclassi icationwithAdaBoost and features

computed using RGB image only2) Cl – SVM classi icationwith AdaBoost and features

computed using depth data only3) MON – SVM classi ication without AdaBoost us-

ing single vector of features computed using RGBand depth data

4) Cone – SVM classi ication with AdaBoost and sin-gle features vector computed using RGB and depthdata

5) Ckl – SVM classi ication with AdaBoost and fea-tures computed using RGB and depth data (solu-tion proposed in the paper)The results of the comparison experiment are pre-

sented in Tab. 2. The best performance is obtained byclassi icator proposed in the paper. The average clas-si ication accuracy is 94% while the performance forstandard SVM classi icator is 86%.

Tab. 3. Computa on me

task time [s]segmentation sorting 0,699

segmentation 0,414merging 0,274

features extraction pre-processing 0,122computation 0,022

classi ication computation 0,260total 1,791

We also checked the computation time of each ele-ment of the proposed procedure. The results are pre-sented in Tab. 3. The most consuming part is the seg-mentation procedure. Sorting of edges takes 0.7 s, seg-mentation 0.4 s and removing segments smaller thanthreshold takes almost 0.3 s. Features extraction isfaster and takes only 0.144 s including preparationof depth and color data and features computation.The classi ication takes0.26 s. Thewhole classi icationprocedure takes 1.791 s. It is fast enough to implementthe method on the real robot because the robot needsat least 2 s to acquire information about new terrain.4.1. Outdoor experiment

We also performed outdoor experiment on therobot with the inal setup of sensors. The robot classi-ies grass, asphalt and two types of pavements (pave1and pave2 in Tab. 4). The color and the geometricalproperties of the pavements and the asphalt are simi-lar. Thus we added a new set of features which allowsto distinguish between similar terrain types. The newinputs of the classi ier are related to shape of the seg-mented regions. For each region we detect line seg-ments using RANSAC. The line segments are used tocompute additional input features. The input valuesare as follows:1) regularity coef icient which is computed as a sum

of line segments lengths divided by the total num-ber of pixels which belong to border of the region,

2) mean of line segments lengths,3) variance of line segments lengths,4) number of line segments,5) 10 bin histogram of line segments orientations.

The classi ication results are presented in Tab. 4.The average classi ication precision is 82%. It is signif-icantly smaller in comparison to results of the experi-ments performed indoor. The outdoor experiments on

32


Tab. 4. Confusion matrix for an outdoor experiment

terrain type grass pave1 pave2 asphaltgrass 99% 1% 1% 0%pave1 18% 81% 2% 0%pave2 4% 25% 68% 3%asphalt 0% 3% 37% 60%

1a 1b 1c

2a 2b 2c

3a 3b 3c

4a 4b 4c

5a 5b 5c

Fig. 9. Results of the outdoor experiment – the examplescene (a) segmenta on (b) and classifica on (c) results.

the real robot aremore challenging. The irst dif icultyis connected to similarity between classi ied regions.The other dif iculties are caused by imprecise localiza-tion system (odometry and IMU). The robot moves inirregular terrain. Thus, the imprecise measurementsof the inclination of the robot’s platform causes in-correct location of the 3D points obtained from rangemeasurements.

The example classi ication results are presented inFig. 9. Colors in Fig. 9c represent various type of ter-rain: green – grass, yellow – pavement 1, red – pave-ment 2, blue – asphalt. The classi ication results areaccurate enough to use the proposed method on thereal robot dedicated to robotic competition.

5. Conclusions and future workIn thepaperwepresented the terrain classi ication

method for themobile robot.We show that the perfor-mance of the classi ication can be increased by usingboosting technique to combine output fromweak SVMclassi iers. The results for SVM and AdaBoost classi-ier arebetter than for single SVMclassi ierwithmulti-dimensional features vector. SVM algorithm works ef-iciently with multi-dimensional problems. By usingourmethodwe reduce the dimensionality of the prob-

lem. The performance of the classi ication increases asa result.

To show performance and advantages of ourmethod we performed experiments indoor on terrainmockup and outdoor in real environment. We carriedout the analysis of classi ication results. We comparedvarious combinations of classi ication input and con-igurations of the classi ier. We conclude that the clas-si ication results are better when depth data are used.The advantages of the method which uses the datafrom LRF are mainly due to the intensity values. Theyprovide information about properties of the object’ssurface which is well utilized by the classi ier.

We also show the computation time of each ele-ment of the procedure. Themost expensive part is seg-mentation. It takes more than 1 s to divide the imageinto segments. From the application point of view weare going to replace existing procedure by the fasterone. On the other hand our goal is to increase per-formance of the segmentation procedure. To this end,we are going to use methods which take into accountdepth and color data simultaneously during segmen-tation.

In future we are going to add next layer to classi-ication method. Our goal is to take into account clas-si ication results of neighboring segments as well asdepth and color of the considered segment.Webelievethat context-aware segmentation will bring better ef-iciency of the classi ication procedure.

AUTHORSJan Wietrzykowski – Poznan University of Technol-ogy, Institute of Control and Information Engineer-ing, ul. Piotrowo 3A, 60-965 Poznan, Poland, e-mail:[email protected] Belter∗ – Poznan University of Technol-ogy, Institute of Control and Information Engineering,ul. Piotrowo 3A, 60-965 Poznan, Poland, e-mail: [email protected].∗Corresponding author

REFERENCES[1] A. Angelowa, L. Matthies, D. Helmick, and

P. Perona, “Fast terrain classi ication usingvariable-length representation for autonomousnavigation”. In: Proceedings of the conferenceon Computer Vision and Pattern Recogni-tion, Minneapolis, USA, 2007, pp. 1–8, doi:10.1109/CVPR.2007.383024.

[2] D. Benbouzid, R. Busa-Fekete, N. Casagrande,F.-D. Collin, and B. Kegl, “Multiboost: a multi-purpose boosting package”, Journal of MachineLearning Research, vol. 13, 2012, pp. 549–553.

[3] C. Bishop, Pattern Recognition and MachineLearning, Springer, 2006.

[4] J.-Y. Bouguet. “Camera calibra-tion toolbox for matlab”, 2014,www.vision.caltech.edu/bouguetj/calib_doc.

33

http://dx.doi.org/10.1109/CVPR.2007.383024

http://dx.doi.org/10.1109/CVPR.2007.383024


[5] J. Chetan, M. Krishna, and C. Jawahar, “Fastand spatially-smooth terrain classi ication usingmonocular camera”. In: Proceedings of 2010 20thInternational Conference on Pattern Recognition,Istanbul, Turkey, 2010, pp. 4060–4063.

[6] H. Dahlkamp, A. Kaehler, D. Stavens, S. Thrun,and G. Bradski, “Self-supervised monocular roaddetection in desert terrain”. In: Proceedings ofRobotics: Science and Systems, Philadelphia, USA,2006.

[7] T. Dietterich, “An experimental comparison ofthreemethods for constructing ensembles of de-cision trees: Bagging, boosting, and randomiza-tion”, Machine Learning, vol. 40, no. 2, 2000, pp.139–157.

[8] P. Felzenszwalb and D. Huttenlocher, “Ef-icient graph-based image segmentation”,International Journal of Computer Vision,vol. 59, no. 2, 2004, pp. 167–181, doi:10.1023/B:VISI.0000022288.19776.77.

[9] P. Filitchkin and K. Byl, “Feature-based terrainclassi ication for littledog”. In: Proceedings ofIEEE/RSJ Int. Conf. on Intelligent Robots and Sys-tems, Vilamoura, Portugal, 2012, pp. 1387–1392,doi: 10.1109/IROS.2012.6386042.

[10] E. Garcıa and F. Lozano, “Boosting support vectormachines”. In: Proceedings of 5th InternationalConference onMachine Learning andDataMiningin Pattern Recognition, Leipzig, Germany, 2007,pp. 153–167.

[11] I. Halatci, C. Brooks, and K. Iagnemma, “Terrainclassi ication and classi ier fusion for planetaryexploration rovers”. In: Proceedings of 2007 IEEEAerospace Conference, Big Sky, USA, 2007, pp.1–11, doi: 10.1109/AERO.2007.352692.

[12] M. Hoep linger, C. Remy, M. Hutter, L. Spinello,and R. Siegwart, “Haptic terrain classi i-cation for legged robots”. In: Proceed-ings of 2010 IEEE International Conferenceon Robotics and Automation (ICRA), An-chorage, USA, 2010, pp. 2828–2833, doi:10.1109/ROBOT.2010.5509309.

[13] R. Karlsen and G. Witus, “Terrain understandingfor robot navigation”. In: Proceedings of 2010IEEE/RSJ International Conference on IntelligentRobots and Systems (IROS), San Diego, USA, 2007,pp. 895–900, doi: 10.1109/IROS.2007.4399223.

[14] Y. Khan, P. Komma, and A. Zell, “High resolutionvisual terrain classi ication for outdoor robots”.In: Proceedings of IEEE International Confer-ence on Computer Vision Workshops (ICCV Work-shops), Barcelona, Spain, 2011, pp. 1014–1021,doi: 10.1109/ICCVW.2011.6130362.

[15] S. Laible, Y. Khan, and A. Zell, “Terrain clas-si ication with conditional random ields onfused 3d lidar and camera data”. In: Proceed-ings of European Conference on Mobile Robots,Barcelona, Spain, 2013, pp. 172–177, doi:10.1109/ECMR.2013.6698838.

[16] J. Lobo and J. Dias, “Relative pose calibra-tion between visual and inertial sensors”,International Journal of Robotics Research,vol. 26, no. 6, 2004, pp. 561–575, doi:10.1177/0278364907079276.

[17] D. Maier, C. Stachniss, and M. Bennewitz,“Vision-based humanoid navigation using self-supervised obstacle detection”, InternationalJournal of Humanoid Robotics, vol. 10, no. 2,2013, doi: 10.1142/S0219843613500163.

[18] R. Schapire and Y. Singer, “Improved boostingalgorithms using con idence-rated predictions”,Machine Learning, vol. 37, 1999, pp. 297–336,doi: 10.1145/279943.279960.

[19] K. Walas, A. Schmidt, M. Kraft, and M. Fularz,“Hardware implementation of ground classi ica-tion for a walking robot”. In: Proceedings of the9th International Workshop on Robot Motion andControl, Wąsowo, Poland, 2013, pp. 110–115,doi: 10.1109/RoMoCo.2013.6614594.

[20] Q. Zhang and R. Pless, “Extrinsic calibration of acamera and laser range inder”. In:Proceedings ofthe IEEE/RSJ International Conference on Intelli-gent Robots and Systems, Sendai, Japan, 2004, pp.2301–2306, doi: 10.1016/j.proeng.2012.01.669.

34

http://dx.doi.org/10.1023/B:VISI.0000022288.19776.77

http://dx.doi.org/10.1023/B:VISI.0000022288.19776.77

http://dx.doi.org/10.1109/IROS.2012.6386042

http://dx.doi.org/10.1109/AERO.2007.352692



http://dx.doi.org/10.1109/IROS.2007.4399223

http://dx.doi.org/10.1109/ICCVW.2011.6130362

http://dx.doi.org/10.1109/ECMR.2013.6698838

http://dx.doi.org/10.1109/ECMR.2013.6698838

http://dx.doi.org/10.1177/0278364907079276

http://dx.doi.org/10.1177/0278364907079276

http://dx.doi.org/10.1142/S0219843613500163

http://dx.doi.org/10.1145/279943.279960

http://dx.doi.org/10.1109/RoMoCo.2013.6614594

http://dx.doi.org/10.1016/j.proeng.2012.01.669


P S S E D P FP S S E D P FP S S E D P FP S S E D P F

Submi ed: 30th June 2014; accepted: 10th July 2014

Piotr Kozierski, Marcin Lis, Dariusz Horla

DOI: 10.14313/JAMRIS_4-2013/25

Abstract:The paper presents a new approach to par cle filtering,i.e. Dispersed Par cle Filter. This algorithm has been ap-plied to the power system, but it can also be used in othertransmission networks. In this approach, the whole net-work must be divided into smaller parts. As it has beenshown, use of Dispersed Par cle Filter improves the qual-ity of the state es ma on, compared to a simple par clefilter. It has been also checked that communica on be-tween subsystems improves the obtained results. It hasbeen checked by means of simula on based on model,which has been created on the basis of knowledge aboutprac cally func oning power systems.

Keywords: par cle filter, power system, state observer,state es ma on, dispersed es ma on

1. Introduc onThe Power System State Estimation (PSSE) prob-

lem is relatively old, because it has over 40 years, andthe irst idea of state estimation in power system hasbeen proposed by Fred Schweppe in 1970 [21]. ButPSSE is still used also in more advanced calculations,such as Optimal Power Flow (OPF). In this case, cor-rect state vector estimation directly affects inal solu-tion.

PSSE is also important in terms of energy security,to prevent so-called “blackouts” – this is the highestdegree of failure of the power system, in which manyvillages and towns can be without access to electricpower. To prevent such accidents, current control ofthe results obtained in thePSSE calculations is needed.

A lot of different algorithms have been created sofar in order to solve the problem of PSSE, such asWeighted Least Squares (WLS), varieties of KalmanFilter (Extended Kalman Filter (EKF) [11], UnscentedKalman Filter (UKF) [24]). In [23] authors presentedthe use of a different estimator than typically used inthe WLS method, and apart from the typical Newtonmethod they suggested the use of Primal-dual InteriorPoint Method (PDIPM). In [4], authors proposed thevariety of Particle Filter (PF) as a state observer in rel-atively small power system.

In this article a new algorithm, i.e. Dispersed Par-ticle Filter (DPF) has been proposed. It involves theuse not just one, but several different PF instances torun in parallel for different parts of the power system(each instance can be carried out in another compu-tational unit, which can be placed in another area ofpower system). This approach is consistent with indi-

Fig. 1. Branch in network between i-th and j-th buses

cated in [10] needof PSSEbasedondata fromdifferentcontrol centres.

The second Section is devoted to the power sys-tem and is followed by Section presenting basic infor-mation about particle ilter, while the fourth Sectiondescribes simulations that have been carried out, pre-senting results and the conclusions. Section no. 5 sum-marizes the entire article.

2. Power SystemPower system has been selected as object. Net-

work is composed ofB buses (nodes) and L branches(lines) that connect speci ied buses. Branch schemehas been shown in Fig. 1, where y′

ij/2 is a half total

line charging susceptance [25], whereas yij

is a lineadmittance, which can be expressed by the equation

yij=

1

Zij

=1

Rij + jXij. (1)

Based on yijand y′

ij/2 admittancematrix Y can be

created accordingly to equations

Y ij = −yij

i = j , (2)

Y ii =B∑

j=1j =i

(y′ij

2+ y

ij

). (3)

Set of all voltages U and angles δ at the buses un-ambiguously describe state of the power system

x = [x1 x2 . . . x2B−1]T

= [U1 . . . UB δ2 . . . δB ]T

, (4)

because based on them it is possible to calculate all theother values in power system. But there is a problemwith the angles, because the only thing that can be cal-culated is the difference between them. Therefore, one

35


reference node must be chosen, in which angle is al-ways equal to 0 (in expression (4) irst node has beenchosen as reference, hence δ1 is always equal to 0, andthis angle is not included in the state vector). Accord-ingly, the state vector is limited to 2B − 1 variables.

The measured values in the network are powerinjections in the nodes, power lows through thebranches and voltage values in the buses. The last typeof measurement (voltage magnitude) is special, be-cause it is directly state variable. In other cases, themeasured values can be expressed by the equations

Pi(U, δ) = Pi =

=B∑

j=1

UiUjYij cos (δi − δj − µij) , (5)

Qi(U, δ) = Qi =

=

B∑j=1

UiUjYij sin (δi − δj − µij) , (6)

Pij(U, δ) =Pij = U2i Yij cos (−µij)

− UiUjYij cos (δi − δj − µij) , (7)

Qij(U, δ) = Qij = U2i Yij sin (−µij)

− UiUjYij sin (δi − δj − µij) + U2i

y′ij2

, (8)

where (5-6) are the power injections (active and re-active), while (7-8) are the power lows. It should benoted that the Pij and Pji are two different powerlows (as well asQij andQji), and irst index speci iesthe node where the measurement is made. Yij and µij

values are given in admittance matrix based on

Y ij = Yij · exp (jµij) . (9)

Formore information about the power system, ref-erences [1,18,25] are recommended.

3. Par cle FilterThe principle of operation is based on Bayesian il-

tering, and the PF is one of possible implementation ofthe Bayes ilter [3]

posterior︷︸︸︷p(x(k)|Y(k)

)=

=

likelihood︷︸︸︷p(y(k)|x(k)

)·

prior︷︸︸︷p(x(k)|Y(k−1)

)p(y(k)|Y(k−1)

)︸︷︷︸

evidence

, (10)

where x(k) is vector of state variables in k-th time step,y(k) is vector ofmeasurements, whereasY(k) is a set ofoutput vectors from the beginning of simulation to k-th time step.

Posterior probability density function (PDF) isrepresented by the set of particles in PF, where eachparticle is composed of the value xi (vector of statevariables) and the weight qi. Therefore it can be writ-ten that the set of particles corresponds to the poste-rior PDF. With higher number of particles N , this ap-proximation is more accurate

p(x(k)|Y(k)

)N→∞= p

(x(k)|Y(k)

)=

=N∑i=1

qi,(k)δ(x(k) − xi,(k)

), (11)

where δ(·) is a Dirac delta.In [12] the authors point out that the prior should

be chosen so that as many particles as possible weredrawn in the areawhere likelihood has signi icant val-ues. Prior can be written as [2]

p(x(k)|Y(k−1)

)=

∫p(x(k)|x(k−1)

)p(x(k−1)|Y(k−1)

)dx(k−1) , (12)

where p(x(k)|x(k−1)) is a transition model andp(x(k−1)|Y(k−1)) is posterior from previous time step.

First who suggest something what today can beconsidered as a particle ilterwasNorbertWiener, andit was as early as in irst half of the twentieth century[22]. However, only a few decades later, the power ofcomputers made it possible to implement these algo-rithms. Algorithmproposed in [9] byGordon, Salmondand Smith, named by them Bootstrap Filter (BF), isconsidered as the irst PF. The operation principle ofthe algorithm is presented below.

Algorithm 1 (Bootstrap Filter)

1) Initialization. Draw N initial particle values fromthe PDF p(x(0)). Set iteration number k = 1.

2) Prediction. DrawN new particles based on transi-tion model: xi,(k) ∼ p(x(k)|xi,(k−1)).

3) Actualization. Calculate weights of particles basedon equation qi,(k) = p(y(k)|xi,(k)).

4) Normalization. Normalize particle weights so thattheir sum be equal to 1

qi,(k) =qi,(k)∑Nj=1 q

j,(k). (13)

5) Resampling. Draw N new particles based on pos-terior PDF obtained in steps 2–4.

6) End of iteration. Calculate estimated vector value,increase number of iteration k = k + 1, go tostep 2.BF algorithm belongs to a class of Sequential Im-

portance Resampling (SIR) algorithms and is one ofits simpler implementation. Of course, alsomore com-plicated algorithms are proposed in the literature, forexample Auxiliary PF [20], Rao-Blackwellised PF [8]or the Gaussian PF [13]. However, for purpose of this

36


article, BF algorithm and its modi ications were used– results which have been obtained in previous stud-ies [14, 16] are satisfactory. In addition, the simplic-ity of implementation with such a complex problem,which is the PSSE, led to the choice of algorithm pro-posed in [9].

Resampling (5 step in Algorithm 1) also can bemade in several different ways. In algorithm the strat-i ied resampling has been used. In order to learnmoreabout the resampling, see [6,17,19].

To ind more information about particle ilter, ref-erences [2,7,15] are recommended.

3.1. Dispersed Par cle Filter

Network composed of 16 buses has been pro-posed, as shown in Fig. 2, so there are 2B − 1 = 31state variables. To use DPF the whole power systemhas been divided into 3 parts – PS1, PS2 and PS3. Thisdivision is one of many possible, as well as the num-ber of subsystems in this example. The main purposein this article was to show how the division of the sys-tem into smaller parts affects on obtained results.

For the DPF implementation the assumption hasbeen made that only measurements inside the subnetare available. However, for a good modeling, borderlines and nodes at their ends are also required. Forexample, in the irst subsystem there are 9 modelednodes (1, 2, 3, 4, 5, 6 and additionally 7, 8 and 13) andthe number of state variables in PS1 is 17 (in the othertwo subsystems there are 8 nodes, and 15 state vari-ables – reference node must exist in each subnet).

As one can see, the number of state variables ineach subsystem has been decreased and this shouldhas positive in luence on estimation quality.

4. Simula ons16-nodal system has been proposed for simula-

tions (see Fig. 2). The numbers in circles indicate num-bers of the nodes and values of R,X and y′/2 are, re-spectively, line resistance, line reactance and half ofthe total line charging susceptance. The double circlesrepresent the location of the generators, single cir-cles are the loads. There are also locations and typesof measurements – the gray squares mark measure-ments of the power lows, while the grey circles markthemeasurements of power injections andvoltage val-ues.

One simulation, which consists of 100 time stepshas been prepared and has been used for all calcula-tions.

Simulation computations for all subsystems havebeenmade not in parallel, but sequentially one by one.

4.1. Simula on Results

The irst simulations have been performed for thesimple PF algorithm. The results have been shown inFig. 3. The simulation for each number of particles Nhas been repeated 100 times with different values ofthe seed of random number generator. The value D,which is shown in the graph, was calculated based on

mean square errors (MSE) of each of the state vari-ables (there are 31 state variables inwhole power sys-tem). This can be written as

D = 106 ·31∑i=1

(MSEi)2. (14)

Thanks to this, estimation quality of whole system canbe represented by one coef icient.

Next the another approach has been proposed, inwhich simultaneously three different particle iltersoperate, each in a different subsystem, thus creatingDispersed Particle Filter. The assumption has beenmade that the individual subnets does not communi-cate with each other and does not exchange any infor-mation. Values of the state variables in each nodewereobtained based on the estimated values in the subnets.The simulation results have been shown in Fig. 4.

As before, the graph shows the averaged results ofD, based on 100 different simulations for each valueofN . Signi icant improvement is visible, both in termsof the mean and standard deviation.

In the third approach the exchange of data be-tween subnets has been implemented. For the borderbranch information about the power lowswas passedto another subsystem, and was taken as additionalmeasurements. For example, in PS3 one of such borderbranch is the line (1,13). Information, which was sentfrom PS1 to PS3, was the estimated values of P1,13 andQ1,13. Both of these valueswere regarded in PS3 as an-other measurements. Similar information was trans-ferred from the PS3 to the PS1, but this time the valuesP13,1 andQ13,1. The results have been shown in Fig. 5.

In the last approach the impact of the additionalmeasurement (transferred as in the previous case) –voltage magnitude in bus – has been checked. The re-sults have been shown in Fig. 6.

All results (excluding the standard deviation) havebeen shown in Fig. 7, for comparison.

Based on obtained results, one can see that the useof DPF signi icantly improves the quality of estima-tion, in comparison to the standard PF algorithm. As itcan be seen, performance improves even for the DPFwithout any communication between subnets. Thiscan be explained by the fact that in the case of stan-dard PF particles have to move in a 31-dimensionalspace (the number of state variables). In the case ofDPF number of particles was smaller, but the numberof dimensions of the state vector was also decreased –to 17 (for the PS1) and15 (for the PS2 andPS3). Similarconclusions can be found in [5] (case without commu-nication).

The results obtained for DPF with additional mea-surements of power lows and voltage are very simi-lar to those in which the voltage measurement is notpassed. This is understandable, because in the valuesof the power lows are already contained informationabout state variables in this node.

5. SummaryThe article presents a new approach to particle

iltering in the problem of Power System State Esti-

37


Fig. 2. Power system used in simula ons composed of 16 buses, with marked measurements

Fig. 3. MeanD values for standard PF

Fig. 4. MeanD values for DPF without any communica-on between subsystems.

mation – Dispersed Particle Filter. In each con igura-tion of communication, results obtained by the DPFwere better than for the standard PF. This is becausepower systemdivision causes reductionof state vectorlength, and improvement of estimation quality is ob-

Fig. 5. Mean simula on results for DPF with addi onalmeasurements of power flows

Fig. 6. Mean simula on results for DPF with addi onalmeasurements of power flows and voltages

served with decrease of object order. The best resultshave beenobtained for caseswith additionalmeasure-ments.

Further studies on the DPF are being planned, in-

38


Fig. 7. Simula on results for different algorithms.

cluding the impact of the number of subsystems onsimulation results. For a smaller number of state vari-ables into subsystem simulation results should be bet-ter, hence the best division will be probably one sub-system for every bus.

There are also plans for FPGA algorithm imple-mentation and veri ication of the proposed algorithmperformance of parallel computing for several compu-tational units.

AUTHORSPiotr Kozierski∗ – Poznan University of Technol-ogy, Institute of Control and Information Engineering,ul. Piotrowo 3a, 60-965 Poznan, Poland, e-mail: [email protected] Lis – Poznan University of Technology, In-stitute of Electrical Engineering and Electronics,ul. Piotrowo 3a, 60-965 Poznan, Poland, e-mail:[email protected] Horla – Poznan University of Technology,Institute of Control and Information Engineering,ul. Piotrowo 3a, 60-965 Poznan, Poland, e-mail: [email protected].∗Corresponding author

REFERENCES[1] Abur A., Exposito A.G., “Power System State

Estimation: Theory and Implementation”,Marcel Dekker, Inc., 2004, pp. 17–49. DOI:10.1201/9780203913673.

[2] Arulampalam S., Maskell S., Gordon N., Clapp T.,“A Tutorial on Particle Filters for On-line Non-linear/Non-Gaussian Bayesian Tracking”, IEEEProceedings on Signal Processing, vol. 50, no. 2,2002, pp. 174–188.

[3] Candy J.V., “Bayesian Signal Processing”,WILEY, New Jersey, 2009, pp. 36–44. DOI:10.1002/9780470430583.

[4] Chen H., Liu X., She C., Yao C., “Power System Dy-namic State Estimation Based on a New ParticleFilter”, Procedia Environmental Sciences, vol. 11,Part B, 2011, pp. 655–661.

[5] Djuric P. M., Lu T., Bugallo M. F., “Mul-tiple particle iltering”, In: 32nd IEEEICASSP, April 2007, III pp. 1181–1184. DOI:10.1109/ICASSP.2007.367053.

[6] Douc R., Cappe O., Moulines E., “Comparisonof Resampling Schemes for Particle Filtering”,In: Proceedings of the 4th International Sym-posium on Image and Signal Processing andAnalysis, September 2005, pp. 64–69. DOI:10.1109/ISPA.2005.195385.

[7] Doucet A., Freitas N., Gordon N., “SequentialMonte Carlo Methods in Practice”, Springer-Verlag, New York, pp. 225–246 (2001). DOI:10.1007/978-1-4757-3437-9.

[8] Doucet A., Freitas N., Murphy K., Russell S., “Rao-Blackwellised Particle Filtering for DynamicBayesian Networks”, In: Proceedings of the Six-teenth conference on Uncertainty in arti icial in-telligence, 2000, pp. 176–183.

[9] Gordon N.J., Salmond D.J., Smith A.F.M., “NovelApproach to Nonlinear/Non-Gaussian BayesianState Estimation”, IEE Proceedings-F, vol. 140,no. 2, 1993, pp. 107–113. DOI: 10.1049/ip-f-2.1993.0015.

[10] Horowitz S., Phadke A., Renz B., “The Future ofPower Transmission”, IEEE Power and EnergyMagazine, vol. 8, no. 2, 2010, pp. 34–40. DOI:10.1109/MPE.2009.935554.

[11] Huang Z., Schneider K., Nieplocha J., “Feasibil-ity Studies of Applying Kalman Filter Techniquesto Power System Dynamic State Estimation”, In:Power Engineering Conference, IPEC 2007, De-cember 2007, pp. 376–382.

39


[12] Imtiaz S.A., Roy K., Huang B., Shah S.L., Jam-pana P., “Estimation of States of Nonlinear Sys-tems using a Particle Filter”, In: IEEE Inter-national Conference on Industrial Technology,ICIT 2006, December 2006, pp. 2432–2437. DOI:10.1109/ICIT.2006.372687.

[13] Kotecha J.H., Djuri P.M., “Gaussian Parti-cle Filtering”, IEEE Trans Signal Processing,vol. 51, no. 10, 2003, pp. 2592–2601. DOI:10.1109/TSP.2003.816758.

[14] Kozierski P., Lis M., “Auxiliary and Rao-Blackwellised Particle Filters Comparison”,Poznan University of Technology Academic Jour-nals: Electrical Engineering, Issue 76, 2013,pp. 79–88.

[15] Kozierski P., Lis M., “Filtr Czasteczkowy w Prob-lemie Sledzenia – Wprowadzenie”, Studia z Au-tomatyki i Informatyki, vol. 37, 2012, pp. 79–94.

[16] Kozierski P., Lis M., Krolikowski A., Gulczynski A.,“Resampling – Essence of Particle Filter”, CRE-ATIVETIME, Krakow, vol. 1, 2013, pp. 174–185.

[17] Kozierski P., Lis M., Zietkiewicz A., “Resamplingin Particle Filtering – Comparison”, Studia z Au-tomatyki i Informatyki, vol. 38, 2013, pp. 35–64.

[18] Kremens Z., Sobierajski M., “Analiza Syste-mow Elektroenergetycznych”, WydawnictwaNaukowo-Techniczne, Warszawa, 1996,pp. 39–191.

[19] Murray L., Lee A., Jacob P., “Rethinking Resam-pling in theParticle Filter onGraphicsProcessingUnits”, arXiv preprint, arXiv:1301.4019, 2013.

[20] Pitt M., Shephard N., “Filtering via Simu-lation: Auxiliary Particle Filters”, Journalof the American Statistical association,vol. 94, no. 446, 1999, pp. 590–599. DOI:10.1080/01621459.1999.10474153.

[21] Schweppe F.C., Rom D.B., “Power System Static-State Estimation, Part II: Approximate Model”,IEEE Transactions on Power Apparatus and Sys-tems, vol. 89, no. 1, January 1970, pp. 125–130.DOI: 10.1109/TPAS.1970.292679.

[22] Simon D., “Optimal State Estimation”, WI-LEY–INTERSCIENCE, New Jersey, 2006,pp. 461–484. DOI: 10.1002/0470045345.

[23] Singh R., Pal B.C., Jabr R.A., “Choice of Estima-tor for Distribution SystemState Estimation”, IETGeneration, Transmission & Distribution, vol. 3,Iss. 7, 2009, pp. 666–678. DOI: 10.1049/iet-gtd.2008.0485.

[24] Valverde G., Terzija V., “Unscented Kalman Fil-ter for Power System Dynamic State Estima-tion”, IET Generation, Transmission & Distri-bution, vol. 5, Iss. 1, 2011, pp. 29–37. DOI:10.1049/iet-gtd.2010.0210.

[25] Wood, A.J., Wollenberg B., “Power Generation,Operation and Control”, John Wiley & Sons Inc.,1996, pp. 91–130, 453–513.

40

Journal of Automation, Mobile Robotics & Intelligent Systems VOLUME 8, N° 3 2014

41

Face Detection in Color Images Using Skin Segmentation

Mohammadreza Hajiarbabi, Arvin Agah

Submitted: 6th July 2014; accepted: 15th July 2014

DOI: 10.14313/JAMRIS_3-2014/26

Abstract:Face detection which is a challenging problem in com-puter vision, can be used as a major step in face recog-nition. The challenges of face detection in color images include illumination differences, various cameras char-acteristics, different ethnicities, and other distinctions. In order to detect faces in color images, skin detection can be applied to the image. Numerous methods have been utilized for human skin color detection, including Gaussian model, rule-based methods, and artificial neu-ral networks. In this paper, we present a novel neural network-based technique for skin detection, introducing a skin segmentation process for finding the faces in color images. Keywords: skin detection, neural networks, face detection, skin segmentation, and image processing

1. IntroductionFace recognition is an active area of research in

image processing and computer vision. Face recog-nition in color images consists of three main phases. First is skin detection, in which the human skin is de-tected in the image. Second is face detection in which the skin components found in the first phase are de-termined to be part of human face or not. The third phase is to recognize the detected faces. This paper focuses on skin detection and face detection phases.

Face detection is an important step not only in face recognition systems, but also in many other computer vision systems, such as video surveillance, human-computer interaction (HCI), and face image retrieval systems. Face detection is the initial step in any of these systems. The main challenges in face detection are face pose and scale, face orientation, facial expres-sion, ethnicity and skin color. Other challenges such as occlusion, complex backgrounds, inconsistent illu-mination conditions, and quality of the image further complicate face detection in images. The skin color detection is also an important part in many computer vision applications such as gesture recognition, hand tracking, and others. Thus, skin detection is also chal-lenging due to different illumination between images, dissimilar cameras and lenses characteristics, and the ranges of human skin colors due to ethnicity. One important issue in this field is the pixels’ color values which are common between human skin and other entities such as soil and other common items [2].

There are a number of color spaces that can be used for skin detection. The most common color spac-es are RGB, YCbCr, and HSV. Each of these color spaces has its own characteristics.

The RGB color space consists of red, green and blue colors from which other colors can be generated. Although this model is simple, it is not suitable for all applications [16]. In the YCbCr color space, Y is the il-lumination (Luma component), and Cb and Cr are the Chroma components. In skin detection, the Y compo-nent can be discarded because illumination can affect the skin. The equations for converting RGB to YCbCr are as follows:

Y = 0.299R+0.587G+0.114B Cb = B – YCr = R – Y

The HSV color space has three components, name-ly, H (Hue), S (Saturation), and V (Value). Because V specifies the brightness information, it can be elimi-nated in skin detection. The equations for converting RGB to HSV are as follows:

=255

=255

=255

Cmax = max (R', ', B'), Cmin = min (R', G', B'), x = Cmax – Cmin

for x not being zero other wise S = 0

V = Cmax

2. Skin Color DetectionThree skin detection methods of Gaussian,

rule-based, and neural networks are discussed in this section.


Articles42

2.1. Gaussian MethodsThis technique which was proposed in [20], uses

the Gaussian model in order to find the human skin in an image. The RGB image is transformed to the YCbCr color space. The density function for Gaussian vari-able X = (Cb Cr)T∈ R2 is:

=1

| |

1

2

Where

and the parameters are:

The parameters are calculated using sets of train-ing images. For each pixel value, the density func-tion is calculated; however, only the (Cb Cr) value is used because the Y component has the illumination information which is not related to skin color. The probability value of more than a specified threshold is considered as skin. The final output is a binary im-age where the non-skin pixels are shown by black and human skin by white. It is worth to mention that the amount for parameters µ and C are calculated using a specified training samples and can be varied by us-ing other training samples.

2.2. Rule-Based MethodsSkin detection based on rule-based methods has

been used in several research efforts as the first step in face detection. Chen et al. analyzed the statistics of different colors [5]. They used 100 images for train-ing, consisting of skin and non-skin in order to cal-culate the conditional probability density function of skin and non-skin colors.

After applying Bayesian classification, they determined the rules and constraints for the human skin color segmentation. The rules are:

r(i)>α, β1< r(i) – g(i)) < β2, γ1 < r(i) – b(i)) < γ2σ1< (g(i) – b(i)) < σ2

With α = 100, β1 = 10, β2 = 70, γ1 = 24, γ2 = 112, σ1 = 0

and σ2 = 70

Although this method works on some images per-fectly, the results are not reliable on images with com-plex background or uneven illumination.

Kovac et al. introduced two sets of rules for images taken indoor or outdoor [11]. These rules are in RGB space, where each pixel that belongs to human skin must satisfy certain relations.For indoor images:

R>95 ,G>40 ,B>20, max R, G, B – min R, G, B > 15,

|R-G|>15 , R>G , R>B

For images taken in daylight illumination:

R>220 ,G>210 ,B>170 ,|R–G|≤15 , R>B , G>B

Kong et al. presented rules that use the information from both HSV and normalized RGB color spaces [10]. They suggested that although in normalized RGB the effect of intensity has been reduced, it is still sensitive to illumination. Therefore, they also use HSV for skin detection. Each pixel that satisfies these rules is considered to be a human skin pixel:

2.3. Neural Network Methods

Neural network has been used in skin color de-tection in a number of research projects. Doukim et al. use YCbCr as the color space with a Multi-Layer Perceptron (MLP) neural network [6]. They used two types of combination strategies, and several rules are applied. A coarse to fine search method was used to find the number of neurons in the hidden layer. The combination of Cb/Cr and Cr features produced the best result.

Seow et al. use the RGB as the color space which is used with a three-layered neural network [14]. Then the skin regions are extracted from the planes and are interpolated in order to obtain an optimum decision boundary and the positive skin samples for the skin classifier.

Yang et al. use YCbCr color space with a back prop-agation neural network [21]. They take the luminance Y and sort it in ascending order, dividing the range of Y values into a number of intervals. Then the pixels whose luminance belong to the same luminance in-terval are collected. In the next step, the covariance and the mean of Cb and Cr are calculated and are used to train the back propagation neural network. Anoth-er example of methods of human skin color detection using neural network can be found in [1].

3. Skin Color DetectionThe novel approach presented in this paper is

based on skin detection using neural networks with hybrid color spaces.

Neural network is a strong tool in learning, so it was decided to use neural network for learning pix-els’ colors, in order to distinguish between what is face skin pixel and what is a non-face skin pixel. We decided to use information from more than one color space instead of using just the information from one color space. We gathered around 100,000 pixels for face and 200,000 for non-face pixels from images cho-sen from the Web.

Choosing images for the non-skin is a rather dif-ficult task, because that is an enormous category, i.e., everything which is not human skin is non-skin. We tried to choose images from different categories, es-


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pecially those which are very similar to human skin color, such as sand, surfaces of some desks, etc. We used such things in training the neural network so that the network can distinguish them from human skin.

For the implementation, a multi-layer perceptron (MLP) neural network was used. Several entities can be used as the input to the neural network, namely, RGB, HSV (in this case V is not used because it has the illumination information which is not suitable for skin detection), YCbCr (Y is also not used because it has the illumination information). The number of outputs can be one or two. If there is just one output, then a threshold can be used. For example, an output greater than 0.5 indicates that the input pixel belongs to skin, and less than that shows that it belongs to non-skin. For two outputs, one output belongs to skin and the other to non-skin. The larger value of the two outputs identifies the class of the pixel.

Around half of the samples were used for training and the rest for testing/validation. Different num-bers of neurons were examined in the hidden layer, ranging from two nodes to 24 nodes. The networks which produced better results were chosen for the test images. For most of the networks, having 16 or 20 nodes in the hidden layer produced better results in comparison to other number of neurons in the hid-den layer. A combination of the different color space CbCrRGBHS was used as the input. Y and V were elim-inated from YCbCr and HSV because they contain il-lumination information.

We trained several different neural networks [7] and tested the results on the UCD database, using MATLAB (developed by MathWorks) for implementa-tion. The UCD database contains 94 images from dif-ferent ethnicities. The images vary from one person in the image to multiple people. The UCD database also contains the images after cropping the face skin. The Feed Forward neural network was used in all the ex-periments. We considered one node in the output. If the value of the output node is greater than 0.5, then the pixels belongs to human skin, otherwise it is not a human skin.

The experimental results are reported as preci-sion, recall, specificity and accuracy.

Precision or positive predictive value (PPV):PPV = TP⁄((TP+FP))

Sensitivity or true positive rate (TPR) equivalent with hit rate, recall:

TPR = TP⁄P = TP⁄((TP+FN))

Specificity (SPC) or true negative rate:

SPC = TN⁄N = TN⁄((FP+TN))

Accuracy (ACC):

ACC = ((TP+TN))⁄((P+N))

In the skin detection experiments, P is the number of the skin pixels; N is the number of the non-skin pix-

els. TP is the number of the skin pixels correctly clas-sified as skin pixels. TN is the number of the non-skin pixels correctly classified as non-skin pixels. FP is the number of the non-skin pixels incorrectly classified as skin pixels. FN is the number of the skin pixels incor-rectly classified as non-skin pixels.

4. Experimental ResultsWe generated a vector consisting of the informa-

tion of the color spaces CbCrRGBHS and yielded the results in Table 1.

Another neural network was designed with having the same input but different nodes in the output. In this experiment two nodes were chosen for the out-put, one for the skin and the other for the non-skin (higher value determines class).

The results for CbCrRGBHS vector are listed in Ta-ble 2. The results show that in case of recall and pre-cision we have some improvement, but the precision has decreased.

Table 3 shows the result of other methods dis-cussed compared to our best results on using the UCD database. Comparing the other methods with the re-sult we have from the CbCrRGBHS vector shows that our result is better in precision, specificity and accu-racy. Our method [7] accepts fewer non-skin pixels as skin comparing to other methods.

It should be noted that there is a tradeoff between precision and recall. If we want to have high recall (recognizing more skin pixels correctly) then it is highly possible to recognize many non-skin pixels as human skin which will reduce the precision and vice versa.

Figures 1 to 7 illustrate some of our experimental results on images from the UCD database. These are produced using the CbCrRGBHS vector and two out-puts for the neural network. The second image is the output from the neural network and the third image is after applying morphological operation. We first filled the holes that were in the image. After that, we applied erosion, followed by dialation operation [7]. The structuring element which was used by us was 3*3. This size had better results than other structur-ing elements.

5. Methods for Face DetectionAfter the skin detection phase, the next step is to

use a face detection algorithm to detect the faces in the image. Several methods have been used for face detection. In this section we discuss the common methods which have been used in this field, namely, Rowley et al. [13] and Viola, Jones [19].

5.1. Rowley Method for Face DetectionRowley et al. used neural networks, detecting up-

right frontal faces in gray-scale images [13]. One or more neural networks are applied to portions of an image and absence or presence of a face is decided. They used a bootstrap method for the training, which means that they add the images to the training set as the training progresses. Their approach has two stages. First a set of neural network-based filters are


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applied to an image. These filters look for faces in the image at different scales. The filter is a 20*20 pixel re-gion of the image and the output of the image is 1 or -1, where 1 indicates that the region belongs to face and -1 indicates that the region contains no face. This filter moves pixel by pixel through the entire image. To solve the problem for faces bigger than this size, the image is subsampled by a factor of 1.2.

They use a preprocessing method [17], where first the intensity values across the window are equalized. A linear function is fitted to the intensity values in the window and then it is subtracted, which corrects some extreme lightening conditions. Then histogram equalization is applied, in order to correct the cam-era gain and also to improve the contrast. Also an oval mask is used to ignore the background pixels.

The window is then passed to a neural network. Three types of hidden units are used. Four units which looked at 10*10 sub regions, 16 which looked at 5*5 sub re-gions, and 6 which looked at overlapping 20*5 horizontal stripes. These regions are chosen in order to detect differ-ent local features of the face. For example the horizontal stripes were chosen to detect eyes, eyebrows, etc.

Around 1050 face images are used for training. Images (black and white) are chosen from Web and some popular databases. For the non-face images an-other method is used. The reason is the face detection is quite different from other problems. The set of non-face images is much larger than face images. The steps of their method are:– An initial set consisting of 1000 random images

are generated. The preprocessing method is applied to these images.

– A network is trained using the face and non-face images.

The network is tested on an image that contained no face. The misclassified sub images is chosen (those which were considered as faces wrongly).

– 250 of these sub images are chosen randomly, the preprocessing methods are applied to them and these sub images are added into the training set as negative examples. The process is continued from the second step.Other new ideas were utilized by [13]. In the areas

which contain face, there are lots of detection because of the moving pixel by pixel of the window over the image. Also several detections are required because of using different scales over the image. They used a threshold and counted the number of the detections in each location. If the number of detections is above a specified threshold, then that location is considered as a face otherwise rejected. Other nearby detections that overlap the location classified as face are consid-ered as error, because two faces cannot overlap. This method is called overlap elimination.

Another method that is used to reduce the num-ber of false positives is using several networks and arbitration method between them to produce the final decision. Each network is trained with differ-ent initial weights, different random sets of non-face images, and different permutations of the im-ages that are presented to the network. Although the networks had very close detection and error rates, the errors were different from each other. They use a combination of the networks using AND, OR and voting methods.

Precision Recall Specificity Accuracy

CbCrRGBHS 77.73 41.35 95.92 81.93

Table 1. Accuracy results for CbCrRGBHS


CbCrRGBHS 71.30 50.25 93.43 82.36

Table 2. Accuracy results for CbCrRGBHS


Gaussian 54.96 66.82 81.12 77.46

Chen 63.75 51.13 89.98 80.02

Kovac 62.51 69.09 85.71 81.45

Kong 37.47 14.58 91.61 71.87

CbCrRGBHS 71.30 50.25 93.43 82.36

Table 3. Accuracy results for other methods


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5.2. Viola Method for Face DetectionViola et al. trained a classifier using a large num-

ber of features [19]. A set of large weak classifiers are used, and these weak classifiers implemented a threshold function on the features. They use three types of Haar features. In two-rectangle feature, the value is the subtraction between the sums of the pix-els within two regions. In three-rectangle feature, the value is the sum within two outside rectangles sub-tracted from the inside rectangle. In four-rectangle feature, the value is the difference between diagonals of the rectangle. They use the integral image that al-lowed the features to be computed very fast.

Their AdaBoost learning algorithm is as follows:– The first step is initializing the weights

Where m is the number of positive examples and l is the number of negative examples. yi = 0 for nega-tive examples and

yi = 1 for positive examples.

– For t = 1,…,T

– Normalize the weights using

Now the value of the weights will be be-tween 0 and 1 and so is a probability distribu-tion.

– For each feature j a classifier hj is trained and uses just a single feature. The error is:

– The classifier ht with the lowest error Ɛt is chosen and the weights are updated using

If example xi is classified correctly then ei = 0, otherwise ei = 1 and

=

– The final classifier is:

∑ ∑

h

Viola et al. made another contribution which was constructing a cascade of classifiers which is de-signed to reduce the time of finding faces in an im-age [19]. The beginning cascades reject most of the images, images which pass the first cascade will go to the second one, and this process continues till to the end cascade of classifiers.

Similar to the Rowley method, the Viola method includes a window that is moving on the image and decides if that window contains a face. However, Viola showed that their method is faster than Rowley [19].

5.3. Other MethodsThere are some other methods which have been

used for face detection. Principal component analy-sis (PCA) method which generates Eigen faces has been used in some approaches for detecting faces [3]. Other types of neural networks have also been used in [12] and [22]. Shavers used Support Vector Machines (SVM) for face detection [15]. Jeng used geometrical facial features for face detection [9]. They have shown that their method works for de-tecting faces in different poses. Hjelmas has a survey in face detection methods from single edge based

Figure 1. Experimental results


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Figure 5. Experimental results, two faces with complex background


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algorithms to high level approaches [8]. Yang also has published another survey in face detection and numerous techniques have been described in it [23].

6. Face Detection Research ApproachRowley and Viola methods both search all areas

of image in order to find faces; however, in our ap-proach, we first divide the image into two parts, the parts than contain human skin and the other parts. Af-ter this step the search for finding human face would be restricted to those areas that just contain human skins. Therefore face detection using color images can be faster than other approaches. As mentioned in [8]

due to lack of standardized test, there is not a com-prehensive comparative evaluation between different methods, and in case of color images the problem is much more because there are not many databases with this characteristic. Because of this problem it is not easy to compare different methods like Viola and Rowley methods with color based methods. But face detection using color based is faster than other meth-ods because unlike Viola and Rowley method it does not need a window to be moved pixel by pixel on the whole image. Other papers such as [4] has also men-tioned that color based methods is faster comparing to other methods.

Figure 6. Experimental results, when two faces are close to each other


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Figure 7. Experimental results, when two faces are close to each other

In color images, we use the idea that we can sepa-rate the skin pixels from the other part of the image and by using some information we can recognize the face from other parts of the body. The first step in face detection is region labeling. In this case the binary im-age, instead of having values 0 or 1, will have value of 0 for the non-skin part and values of 1, 2… for the skin segments which was found in the previous step [4].

The next step that can be used is the Euler test [4]. Because there are some parts in image like the eyes, eyebrows, etc. that their colors differ from the skin. By using Euler test one can distinguish face compo-nents from other components such as the hands and

arms. The Euler test counts the number of holes in each component. One main problem in Euler test is that there may be some face components which has no holes in them and also some components belong-ing to hands or other parts of the body with holes in them. So Euler test cannot be a reliable method and we did not use it.

At the next step, the cross correlation between a template face and grayscale image of the original image is calculated. The height, width, orientation and the centroid of each component are calculated. The template face is also resized and rotated. The cen-ter of the template is then placed on the center of the


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component. The cross correlation between these two region is then calculated. If that is above a specified threshold, the component would be considered as a face region; otherwise it will be rejected [4].

We have modified this algorithm. The first revi-sion is that we discard the components where the proportion of the height to the width was larger than a threshold, except for some of these compo-nents which will be discussed later. In this case we were sure that no arms or legs would be considered as face. Second, the lower one fourth part of image is less probable to have faces and so we set a high-er threshold for that part, as that part of the image most likely belongs to feet and hands. Increasing the threshold for the lower one forth part decreased the false positive of that part of the images.

Third, for the components which are rejected we used a window consisting of the upper part of the face. We move the window across each bit of the components and calculate the correlation between the window and the area with the same size of the window. If the correlation is above certain threshold that part is considered to be face. For covering dif-ferent sizes, we down sample the image (size*0.9) seven times. In this case, there may be some parts with overlapping rectangles. The rectangles around the face which had more than a specified area in common with each other are deleted and just one of them is kept.

This novel method is useful for those components where the skin detection part has not distinguished between the skin pixels and the other pixels cor-rectly. For example, in some images some pixels from the background are also considered as skin pixels, in this case these components will fail the template correlation test. Although this method increases the detection time and it is not guaranteed to work al-ways, but it can be useful in some images where the background has a color similar to human skin. This method is similar to the method that was used by Rowley [13], however Rowley did it for the whole image and used a neural network to check that the component belongs to a face or not.

Images included in Figures illustrate our method on several images from the UCD database [18]. The first image is the original image. The second image is produced after applying the skin detection algo-rithm. The third image is after filling the holes and applying the morphological operations. The forth image shows the black and white image, as the back-ground changes to black and the skin pixels to white. The fifth image shows each component with a color. The sixth image show placing the template on the component which has been considered as a face. The last (seventh) image is the final output of the pro-posed and implemented detection process.

In some images there may be two or three or more faces which are so close to each other that can become one component.

The method that we have introduced to detect faces in these cases is as follows:1. Compute the height to the width of the compo-

nent.

2. If the ratio is smaller than a threshold, then it means that the components may belong to more than one face. Due to the value of the ratio this component can consist of three or more faces; however it is not probable that a component con-sists of more than three faces.

3. Find the border of the two faces which are stuck together. For finding the border we count the number of pixels on the horizontal axes. The two maximums (if the threshold suggests there are two faces) are placed on the first and last third of the component, and the minimum on the second third of the component. The minimum is found and the two new components are now tested to find faces on them. If the correlations of these two new components (or more) are more than the correlation of the single component before splitting, then it means there were two (or more) faces in this component. This part is done so we can differ between two faces which are stuck to-gether and a face which is rotated 90 degree. In this case the correlation of the whole component would be more than the correlation of the two new components, so the component will not be separated.Face obeys the golden ratio, so the height to the

width of the face is around 1.618. Sometimes with considering the neck which is mostly visible in imag-es this ratio will increase to 2.4. So a height to width ratio between 0.809 and 1.2 shows that the compo-nent may belong to two faces. A value less than 0.809 shows that the component may consist of more than two faces. These values are calculated along the im-age orientation.

Figure 6 illustrate this situation. This image is not part of the UCD database. The same approach can be applied when the ratio of the height to the width is higher than a certain threshold. In this case it means that there may be two or more faces which are above each other. The same algorithm can be applied with some modification. Figure 7 shows this case. This image is not part of the UCD database. For two faces this threshold will be between 3.2 and 4.

Finding the border as mentioned in part 3 is fast-er and more accurate than using erosion (using as another method to separate two or more faces) be-cause when using erosion, the process may need to be done several times so the two faces become sepa-rated, also in erosion while separating the two faces, some other parts of the image is also being eroded.

5. ConclusionIn this paper we have presented a novel method-

ology to detect faces on color images, with certain modifications in order to improve the performance of the algorithm. In some images when the faces are so close to each other that they cannot be separated after skin detection, we introduced a method for separating the face components. For the skin detec-tion phase we used neural networks for recognizing human skin in color images. For future work, the face recognition phase can be added, where the faces which are detected and cropped can be recognized.


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Unfortunately there is no database in this field. There are databases for face detection and databases for face recognition, but no database that covers both. So a database should be generated for this purpose.

AUTHORSMohammadreza Hajiarbabi – Department of Electrical Engineering and Computer Science, University of Kansas, Lawrence, Kansas, USA. E-mail: [email protected]

Arvin Agah * – Department of Electrical Engineering and Computer Science, University of Kansas, Law-rence, Kansas, USA. E-mail: [email protected]

*Corresponding author

RefeRenceS

[1] Al-MohairH., Saleh J., Suandi S., “Human skincolor detection: A review on neural network perspective”, International Journal of Innova-tive Computing, Information and Control, vol. 8, no.12,2012,pp.8115–8131.

[2] AlshehriS.,“NeuralNetworksPerformanceforSkin Detection”, Journal of Emerging Trends in Computing and Information Sciences, vol. 3,no.12,2012,pp.1582–1585.

[3] BakryE.,ZhaoH.M.,ZhaoQ.,“FastNeuralimple-mentationofPCAforfacedetection”. In:Inter-national Joint Conf. on Neural Networks, 2006, pp.806–811.

[4]ChandrappaD.N.,RavishankarM.,RameshBabuD.R.,“Facedetectionincolorimagesusingskincolor model algorithm based on skin color in-formation”. In: 2011 3rd International Conference on Electronics Computer Technology(ICECT), 2011,pp.254–258.

[5]ChenH.,HuangC.,FuC.,“Hybrid-boostlearningfor multi-pose face detection and facial expres-sionrecognition”,PatternRecognition,Elsevier,vol.41,no.3,2008,pp.1173–1185.DOI:http://dx.doi.org/10.1016/j.patcog.2007.08.010.

[6]DoukimC.A.,DarghamJ.A.,ChekimaA.,OmatuS.,“Combiningneuralnetworksforskindetec-tion”, Signal & Image Processing: An Internation-al Journal(SIPIJ),vol.1,no.2,2010,pp.1–11.

[7]HajiarbabiM.,AgahA., “HumanSkinColorDe-tectionusingNeuralNetworkswithBoosting”,Journal of Intelligent Systems, under review, 2014.

[8]HjelmasE.,KeeLowB.,“FaceDetection:ASur-vey”, Computer Vision and Image Understanding (CVIU),vol.83,no.3,2001,pp.236–274.DOI:http://dx.doi.org/10.1006/cviu.2001.0921.

[9] Jeng S., Liao H., Liu Y., ChernM., “An efficientapproach for facial feature detection using Geometrical FaceModel”, Pattern Recognition,

vol.31,no.3,1998,pp.273.DOI:http://dx.doi.org/10.1016/S0031-3203(97)00048-4.

[10]KongW.,ZheS.,“Multi-facedetectionbasedondown sampling and modified subtractive clus-tering for color images”, Journal of Zhejiang Uni-versity,vol.8,no.1,2007,pp.72–78.

[11]Kovac J., Peer P., Solina F., “Human Skin ColorClusteringforFaceDetection”,EUROCON2003.Computer as a Tool. The IEEE Region, vol. 8,no. 2, 2003, pp. 144–148. DOI: http://dx.doi.org/10.1109/EURCON.2003.1248169.

[12]LinS.H.,KungS.Y.,LinL.J.,“Facerecognition/detection by probabilistic decision- based neu-ral network”, IEEE Trans. on Neural Networks, vol.8,1997,pp.114–132.

[13] Rowley H., Baluja S., Kanade T., “Neural net-work-based face detection”, IEEE Pattern Analysis and Machine Intelligence, vol. 20,no. 1, 1998. pp. 22–38. DOI: http://dx.doi.org/10.1109/34.655647.

[14] SeowM.,ValaparlaD.,AsariV.,“Neuralnetworkbased skin colormodel for facedetection”. In:Proceedings of the 32nd Applied Imagery Pat-tern Recognition Workshop (AIPR’03), 2003,pp.141–145.

[15] ShaversC., LiR., LebbyG., “AnSVM-basedap-proach to face detection”. In: 2006 Proc. of 38th Southeastern Symposium on System The-ory, 2006, pp. 362–366. DOI: http://dx.doi.org/10.1109/SSST.2006.1619082.

[16] Singh S., Chauhan D. S., Vatsa M., Singh R., “ARobust SkinColorBasedFaceDetectionAlgo-rithm”, Tamkang Journal of Science and Engi-neering,vol.6,no.4,2003,pp.227–234.

[17] SungK.,Learning and example selection for ob-ject and pattern detection, PhDThesis,MITAILab, 1996

[18]UCDdatabase:http://ee.ucd.ie/~prag/[19] ViolaP.,JonesM.J.,“Robustreal-timeobjectde-

tection”.In:Proc. of IEEE Workshop on Statisti-cal and Computational Theories of Vision,2001.

[20]Wu Y., Ai X., “Face detection in color imagesusing Adaboost algorithm based on skin color information”.In:2008 Workshop on Knowledge Discovery and Data Mining, 2008,pp.339–342.

[21]Yang G., Li H., Zhang L., Cao Y., “Research ona skin color detection algorithm based on self-adaptive skin color model”. In: InternationalConference on Communications and Intelligence Information Security,2010,pp.266–270.

[22]YangK., ZhuH., Y. J. Pan, “Human Face detec-tionbasedonSOFMneuralnetwork”. In:2006 IEEE Proc. Of International Conf. on Information Acquisition,2006,pp.1253–1257.

[23]YangM.H.,KriegmanD.J.,AhujaN.,“DetectingFaces in Images: A Survey”, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.24,no.1,2002,pp.34–58.


C W , P L D S :T N N L B D M K

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D TSubmi ed: 15th May 2014; accepted: 24th June 2014

Janusz Kacprzyk, Sławomir Zadrożny

DOI: 10.14313/JAMRIS_4-2013/27

Abstract:We show how Zadeh’s idea of compu ng with wordsand percep ons, based on his concept of a precisiatednatural language (PNL), can lead to a new direc on inthe use of natural language in data mining, linguis cdata(base) summaries. We emphasize the relevance ofZadeh’s another idea, that of a protoform, and show thatvarious types of Yager type linguis c data summariesmay be viewed as items in a hierarchy of protoforms ofsummaries. We briefly present an implementa on fora sales database of a computer retailer as a convincingexample that these tools and techniques are imple-mentable and func onal. These summaries involve bothdata from an internal database of the company and datadownloaded from external databases via the Internet.

Keywords: compu ng with words, linguis c summaries,protoform

1. Introduc onThe purpose of this article is to shortly present our

opinion on what might be considered to be the mostin luential and far reaching idea conceived by Zadeh,i.e. computing with words (CWW), and – on a moretechnical level – protoforms. We do not mention herehis ”grand inventions” like fuzzy sets and possibilitytheories or foundations of the state space approach insystemsmodeling, which has been probably more rel-evant in a general sense, for various ields of science.To follow the spirit of this volume, our exposition willbe concise and comprehensible. This article is an ex-tended version of a short reserach note by Kacprzykand Zadrozny [34]

Computing with words (and perceptions), intro-duced by Zadeh in the mid-1990s, and best and mostcomprehensively presented in Zadeh and Kacprzyk’sbooks [48], may be viewed to be a new ”technology”in the representation, processing and solving of vari-ous real life problems when a human being is a cru-cial element, one that makes it possible to use naturallanguage,with its inherent imprecision, an an effectiveand ef icient way.

To formally represent elements and expressionsof natural language, Zadeh proposed to use the so-called PNL (precisiated natural language) in whichstatements about values, relations, etc. between vari-ables are represented by constraints. In PNL, state-ments -–written ”x isrR” -–may be different, and cor-respond to numeric values, intervals, possibility disc-

tributions, verity distributions, probability distribu-tions, usuality quali ied statements, rough sets repre-sentations, fuzzy relations, etc. For our purposes andin most our works, the usuality quali ied representa-tion has been be of special relevance. Basically, it says”x is usuallyR” that is meant as ”in most cases, x isR”.PNL may play various roles among which crucial are:description of perceptions, de inition of sophisticatedconcepts, a language for perception based reasoning,etc. Notice that theusuality is an example ofmodalitiesin natural language. Clearly, the above tools are meantfor the representation and processing of perceptions.

Another concept that Zadeh has subsequently in-troduced is that of a protoform. In general, most per-ceptions are summaries, exempli ied by ”most Swedesare tall”which is clearly a summary of the Swedeswithrespect to height. It can be represented in Zadeh’s no-tation as ”most As are Bs”. This can be employed forreasoning under various assumptions. One can go astep further, and de ine a protoform as an abstractedsummary. In our case, this would be ”QAs areBs”. No-tice that we now have a more general, deinstantiatedform of our point of departure (most Swedes are tall),and also of ”mostAs areBs”. Needless to say thatmosthuman reasoning is protoform based, and the avail-ability of such a more general representation is veryvaluable, and provides tools that can be used in manycases.

Basically, the essence of our work over the yearsboiled down to showing that the concept of a precisi-ated natural language, and in particular of a proto-form, viewed from the perspective of CWW, can be ofuse in attempts at a more effective and ef icient useof vast information resources, notably through linguis-tic data(base) summaries which are very characteris-tic for human needs and comprehension abilities.

We will brie ly discuss an approach based on theconcept of a linguistic data(base) summary that hasbeen originally proposed by Yager [43,44] and furtherdeveloped mainly by Kacprzyk and Yager [19], andKacprzyk, Yager and Zadrozny [20]. The essence ofsuch linguistic data summaries is that a set of data, e.g.,concerning employees, with (numeric) data on theirage, sex, salaries, seniority, etc., can be summarizedlinguistically with respect to a selected attribute or at-tributes, say age and salaries, by linguistically quanti-ied propositions, e.g., ”almost all employees are wellquali ied”, ”most young employees are well paid”, etc.which are simple, extremely human consistent and in-tuitive, and do summarize in a concise yet very infor-mative formwhatwemay be interested in. Thiswill be

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done from the perspective of Zadeh’s CWW paradigm(cf. Zadeh and Kacprzyk [48]), and we will in particu-lar indicate the use of Zadeh’s concept of a protoformof a fuzzy linguistic summary (cf. Zadeh [47], Kacprzykand Zadrozny [23]) that can provide an easy general-ization, portability and scalability.

We will mention both the classic static linguisicsummaries, notably showing that a class of summariesof interest is mined via Kacprzyk and Zadrozny’s [22,25] FQUERY for Access, and that by relating varioustypes of linguistic summaries to fuzzy queries, withvarious known and sought elements, we can arriveat a hierarchy of protoforms of linguistic data sum-maries. Moreover, we will also brie ly mention newprotoforms of linguistic summaries of time series asproposed by KAcprzyk, Wilbik and Zadrozny [17,18].

2. Linguis c Data Summaries via Fuzzy Logicwith Linguis c Quan fiersThe linguistic summary is meant as a sentence

[in a (quasi)natural language] that subsumes the veryessence (from a certain point of view) of a set of data.Here this set is assumed to be numeric, large and notcomprehensible in its original form by the human be-ing. In Yager’s approach (cf. Yager [43], Kacprzyk andYager [19], and Kacprzyk, Yager and Zadrozny [20])we have:- Y = y1, . . . , yn is a set of objects (records) in adatabase, e.g., the set of workers;

- A = A1, . . . , Am is a set of attributes characteriz-ing objects from Y , e.g., salary, age, etc. in a databaseof workers, and Aj(yi) denotes a value of attributeAj for object yi.A linguistic summary of data setD consists of:

- a summarizer S, i.e. an attribute together with a lin-guistic value (fuzzy predicate) de ined on the do-main of attribute Aj (e.g. “low salary” for attribute“salary”);

- a quantity in agreementQ, i.e. a linguistic quanti ier(e.g. most);

- truth (validity)T of the summary, i.e. a number fromthe interval [0, 1] assessing the truth (validity) of thesummary (e.g. 0.7); usually, only summaries with ahigh value of T are interesting;

- optionally, a quali ier R, i.e. another attribute to-gether with a linguistic value (fuzzy predicate) de-ined on the domain of attribute Ak determining a(fuzzy subset) of Y (e.g. “young” for attribute “age”).Thus, the linguistic summary may be exempli ied

by

T (most of employees earn low salary) = 0.7 (1)

A richer form of the summary may include a qual-i ier as in, e.g.,

T (most of young employees earn low salary) = 0.7(2)

Thehe core of a linguistic summary is a linguisti-cally quanti ied proposition in the sense of Zadeh [46],

the one corresponding to (1)written as

Qy’s are S (3)

and the one corresponding to (2) written as

QRy’s are S (4)

The T , i.e., the truth value of (3) or (4), m maybe calculated by using either original Zadeh’s calcu-lus of linguistically quanti ied statements (cf. [46]), orother interpretations of linguistic quanti iers (cf. Liuand Kerre [38]), including Yager’s OWAoperators [45]and Dubois et al. OWmin operators [6], or via gener-alized quanti ier, cf. Hajek and Holena [13] or Glock-ner [12].

Recently, Zadeh [47] introduced a relevant conceptof a protoform which is de ined as a more or less ab-stract prototype (template) of a linguistically quanti-ied proposition. The most abstract protoforms cor-respond to (3) and (4), while (1) and (2) are exam-ples of fully instantiated protoforms. Thus, evidently,protoforms form a hierarchy, where higher/lower lev-els correspond to more/less abstract protoforms. Go-ing down this hierarchy one has to instantiate partic-ular components of (3) and (4), i.e., quanti ier Q andfuzzy predicates S andR. The instantiation of the for-mer one boils down to the selection of a quanti ier. Theinstantiation of fuzzy predicates requires the choiceof attributes together with linguistic values (atomicpredicates) and a structure they formwhen combinedusing logical connectives. This leads to a theoreticallyin inite number of potential protoforms. However, forthe purposes of mining of linguistic summaries, thereare obviously some limits on a reasonable size of a setof summaries that should be taken into account. Theseresults from a limited capability of the user in the in-terpretation of summaries as well as from the compu-tational point of view.

The concept of a protoformmay provide a guidingparadigm for the design of a user interface supportingthemining of linguistic summaries. It may be assumedthat the user speci ies a protoform of linguistic sum-maries sought. Basically, the more abstract protoformthe less should be assumed about summaries sought,i.e., the wider range of summaries is expected by theuser. There are two limit cases, where:- a totally abstract protoform is speci ied, i.e., (4),- all elements of a protoform are totally speci ied asgiven linguistic terms,

and in the former case the system has to construct allpossible summaries (with all possible linguistic com-ponents and their combinations) for the context of agiven database (table) and present to the user thoseverifying the validity to a degree higher than somethreshold. In the second case, the whole summary isspeci ied by the user and the system has only to ver-ify its validity. Thus, the former case is usually moreinteresting from the point of view of the user but atthe same time more complex from the computationalpoint of view. There is a number of intermediate casesthat may be more practical. In Table 1 basic types

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of protoforms/linguistic summaries are shown, corre-sponding to protoforms of a more and more abstractform.

Basically, each of fuzzy predicates S and R maybe de ined by listing its atomic fuzzy predicates (i.e.,pairs of ”attribute/linguistic value”) and structure,i.e., how these atomic predicates are combined. InTable 1 S (orR) corresponds to the full description ofboth the atomic fuzzy predicates (referred to as lin-guistic values, for short) as well as the structure. Forexample: ”Q young employees earn a high salary”is a protoform of Type 2, while”Most employees earn a ”?” salary” is a protoformof Type 3. In the irst case the system has to selecta linguistic quanti ier (usually from a prede ineddictionary) that when put in place of Q makes theresulting linguistically quanti ied proposition validto the highest degree, and in the second case, thelinguistic quanti ier as well as the structure of sum-marizer S are given and the system has to choosea linguistic value to replace the question mark (”?”)yielding a linguistically quanti ied proposition asvalid as possible.

Thus, the use of protoforms makes it possible todevise a uniform procedure to handle a wide class oflinguistic data summaries so that the system can beeasily adaptable to a variety of situations, users’ inter-ests and preferences, scales of the project, etc.

Usually, most interesting are linguistic summariesrequired by a summary of Type 5. They may be in-terpreted as fuzzy IF-THEN rules, and many interpre-tations are proposed (cf., e.g., Dubois and Prade [8])there are considered many possible interpretationsfor fuzzy rules), and some of them were directly dis-cussed in the context of linguistic summaries later on.

There are many views on the idea of a linguisticsummary, for instance a fuzzy functional dependency,a gradual rule, even a typical value. Though they do re-lect the essence of a human perception of what a lin-guistic summary should be, they are beyond the scopeof this paper which focuses on a different approach.

3. Mining of Linguis c Data SummariesIn the process of mining of linguistic summaries,

at the one extreme, the systemmay be responsible forboth the construction and veri ication of summaries(which corresponds to Type 5 protoforms/summariesgiven in Table 1). At the other extreme, the userproposes a summary and the system only veri iesits validity (which corresponds to Type 0 proto-forms/summaries in Table 1). The former approachseems to be more attractive and in the spirit of datamining meant as the discovery of interesting, un-known regularities in data. On the other hand, the lat-ter approach, obviously secures a better interpretabil-ity of the results. Thus, we will discuss now the pos-sibility to employ a lexible querying interface for thepurposes of linguistic summarization of data, and in-dicate the implementability of a more automatic ap-proach.

3.1. A fuzzy querying add-on for formula ng linguis csummariesIn Kacprzyk and Zadrozny’s [24,29] approach, the

interactivity, i.e. a user assistance, in the mining of lin-guistic summaries is a key point, and is in the de ini-tion of summarizers (indication of attributes and theircombinations). This proceeds via a user interface of afuzzy querying add-on. In Kacprzyk and Zadrozny [22,25, 30], a conventional database management systemis used with a fuzzy querying tool, FQUERY for Access.An important component of this tool is a dictionaryof linguistic terms to be used in queries. They includefuzzy linguistic values and relations as well as fuzzylinguistic quanti iers. There is a set of built-in linguis-tic terms, but the user is free to add his or her own.Thus, such a dictionary evolves in a natural way overtime as the user is interacting with the system. For ex-ample, an SQL query searching for troublesome ordersmay take the following WHERE clause:

WHERE Most of the conditions are met out ofPRICE*ORDERED-AMOUNT IS LowDISCOUNT IS HighORDERED-AMOUNT IS MuchGreater Than ON-STOCK

Obviously, the condition of such a fuzzy query di-rectly correspond to summarizerS in a linguistic sum-mary. Moreover, the elements of a dictionary are per-fect building blocks of such a summary. Thus, thederivation of a linguistic summary of type (3)maypro-ceed in an interactive (user-assisted) way as follows:- the user formulates a set of linguistic summaries ofinterest (relevance) using the fuzzy querying add-on,

- the system retrieves records from the database andcalculates the validity of each summary adopted,and

- a most appropriate linguistic summary is chosen.Referring to Table 1, we can observe that Type 0

as well as Type 1 linguistic summaries may be easilyproduced by a simple extension of FQUERY for Access.Basically, the user has to construct a query, a candi-date summary, and it is to be determined which frac-tion of rows matches that query (and which linguisticquanti ier best denotes this fraction, in case of Type1). For Type 3 summaries, a query/summarizerS con-sists of only one simple condition built of the attributewhose typical (exceptional) value is sought. For exam-ple, using: Q = ”most” and S = ”age=?” we look for atypical value of ”age”. From the computational pointof view Type 5 summaries represent the most generalform considered: fuzzy rules describing dependenciesbetween speci ic values of particular attributes. Thesummaries of Type 1 and 3 have been implementedas an extension to Kacprzyk and Zadrozny’s [26–28]FQUERY for Access.

The discovery of general, Type 5 rules is dif icult,and some simpli ications about the structure of fuzzypredicates and/or quanti ier are needed, for instanceto obtain association rules which have been initially

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Tab. 1. Classifica on of protoforms/linguis c summaries

ParametersType Protoform Given Sought0 QRy’s are S All validity T1 Qy’s are S S Q2 QRy’s are S S andR Q3 Qy’s are S Q and structure of S linguistic values in S4 QRy’s are S Q,R and structure of S linguistic values in S5 QRy’s are S Nothing S,R andQ

de ined for binary valued attributes as (cf. Agraval andSrikant [1]):

A1 ∧A2 ∧ . . . ∧An −→ An+1 (5)and note that much earlier origins of that concept arementioned in the work by Hajek and Holena [13]).

The use of fuzzy association rules to mine linguis-tic summaries through a fuzzy q uerying interface wasproposedbyKacprzyk andZadrozny [26–28,31] advo-cated the use of fuzzy association rules for mining lin-guistic summaries in the framework of lexible query-ing interface.

In particular, fuzzy association rulesmaybe consid-ered:A1 ISR1 ∧A2 ISR2 ∧ . . . ∧An ISRn −→ An+1 IS S

(6)where Ri is a linguistic term de ined in the domainof the attribute Ai, i.e. a quali ier fuzzy predicate interms of linguistic summaries (cf. Section 2) and S isanother linguistic term corresponding to the summa-rizer. The con idence of the rule may be interpretedin terms of linguistic quanti iers employed in the def-inition of a linguistic summary. Thus, a fuzzy associ-ation rule may be treated as a special case of a lin-guistic summary of type de ined by (4). The struc-ture of the fuzzy predicates Ri and S is to some ex-tent ixed but due to that ef icient algorithms for rulegeneration may be employed. These algorithms areeasily adopted to fuzzy association rules. Usually, theirst step is a preprocessing of original, crisp data. Val-ues of all attributes considered are replaced with lin-guistic terms best matching them. Additionally, a de-gree of this matching may be optionally recorded andlater taken into account. Then, each combination ofattribute and linguistic term may be considered asa Boolean attribute and original algorithms, such asApriori [1], may be applied. They, basically, boil downto an ef icient counting of support for all conjunctionsof Boolean attributes, i.e., so-called itemsets (in fact,the essence of these algorithms is to count supportfor as small a subset of itemsets as possible). In caseof fuzzy association rules attributes may be treatedstrictly as Boolean attributes –- they may appear ornot in particular tuples -– or interpreted in terms offuzzy logic as in linguistic summaries. In the latter casethey appear in a tuple to a degree and the supportcounting should take that into account. In our con-text we employ basically the approach by Lee and Lee-Kwang [37] and Au and Chan [2], Hu et al. [14] who

simplify the fuzzy association rules sought by assum-ing a single speci ic attribute (class) in the consequent.Kacprzyk, Yager and Zadrozny [20, 26–28, 31, 36] ad-vocated the use of fuzzy association rules for min-ing linguistic summaries in the framework of lexiblequerying interface. Chen et al. [5] investigated the is-sue of generalized fuzzy rules where a fuzzy taxon-omyof linguistic terms is taken into account. Kacprzykand Zadrozny [32] proposed to use more lexible ag-gregation operators instead of conjunction, but stillin context of fuzzy association rules.More informationon fuzzy association rules, from various perspectives,may be found later in this volume.

As to some other approaches to the derivation offuzzy linguistic summaries, we can mention the fol-lowing ones. George and Srikanth [10], [11] use a ge-netic algorithm tomine linguistic summaries in whichthe summarizer is a conjunction of atomic fuzzy pred-icates. Then, they search for two linguistic summaries:the most speci ic generalization and the most gen-eral speci ication, assuming a dictionary of linguisticquanti iers and linguistic values over domains of allattributes. Kacprzyk and Strykowski [15,16] have alsoimplemented theminingof linguistic summaries usinggenetic algorithms. In their approach, the itting func-tion is a combination of a wide array of indices: a de-gree of imprecision (fuzziness), a degree of covering,a degree of appropriateness, a length of a summary,etc. (cf. also Kacprzyk and Yager [19]). Rasmussen andYager [41, 42] propose an extension, SummarySQL,to SQL to cover linguistic summaries. Actually, theydo not address the mining linguistic summaries butmerely their veri ication. The SummarySQL may alsobe used to verify a kind of fuzzy gradual rules (cf.Dubois and Prade [7]) and fuzzy functional dependen-cies. Raschia and Mouaddib [40] deal with the miningof hierarchies of summaries, and their understandingof summaries is slightly different than here becausethey consider them as a conjunction of atomic fuzzypredicates (each referring to just one attribute). How-ever, these predicates are not de ined by just one lin-guistic valuebut possibly by fuzzy sets of linguistic val-ues (i.e., fuzzy sets of higher levels are considered).The mining of summaries (a whole hierarchy of sum-maries) is based on a concept formation (conceptualclustering) process.

An interesting extension of the concept of a lin-guistic summary to the linguistic summarization oftime series data was shown in a series of works by

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Kacprzyk, Wilbik and Zadrozny [17, 18]. In this casethe array of possible protoforms is much larger as itre lects various perspectives, intentiones, etc. of theuser. Just to give an examples, the protoforms usedin those works may be exemplifed by: “Among all y’s,Q are P ”, exempli ied by “among all segments (of thetime series) most are slowly increasing”, and “Amongall R segments, Q are P ”, exempli ied by “among allshort segments almost all are quickly decreasing”, aswell as more sphisticated protoforms, for instancetemporal ones like: “ET among all y’s Q are P ”, ex-empli ied by “Recently, among all segments, most areslowly increasing”, and “ET among all Ry’s Q are P ”,exempli ied by “Initially, among all short segments,most are quickly decreasing”; they both go beyond theclassic Zadeh’s protoforms.

It is easy tonotice that theminingof linguistic sum-maries may be viewed to be closely related to natu-ral language generation (NLG) and this path was sug-gested in Kacprzyk and Zadrozny [33]. This may be apromising direction as NLG is a well developed areaand software is available.

A very relevant issue of comprehensiveness of lin-guistic data summaries, inMichalski’s sense, that is re-lated to howwell they can be understandable to an av-erage user is considered in a recent paper byKacprzykand Zadrozny [35].

4. Concluding RemarksWe have shown how Zadeh’s idea of computing

with words, often called computing with words andperceptions, based on his concepts of a precisiatednatural language (PNL) and linguistically quanti iedpropositions can lead to a new direction in the use ofnatural language in data mining and knowledge dis-covery, namely a linguistic data(base) summary. Wehave in particular focused our attention on the rele-vance of Zadeh’s another idea, that of a protoform, andshow that various types of linguistic data summariesmay be viewed as items in a hierarchy of protoforms oflinguistic data summaries. We have brie ly presentedan implementation of linguistic data summaries for asales database of a computer retailer as a convincingexample that these tools and techniques are imple-mentable and practically functional. These summariescan involve both data from a company database anddata downloaded from external databases via the In-ternet.

ACKNOWLEDGEMENTSThis research has been partially supported by theNational Centre of Science under Grant No. UMO-2012/05/B/ST6/03068.

AUTHORSJanusz Kacprzyk∗ – Systems Research Institute Pol-ish Academy of Sciences, ul.Newelska 6, 01–447Warszawa, Poland, e-mail: [email protected]ławomir Zadrożny – Systems Research InstitutePolish Academy of Sciences, ul. Newelska 6, 01–447

Warszawa, Poland, e-mail: [email protected].∗Corresponding author

REFERENCES[1] Agrawal R., Srikant R., ”Fast algorithms for

mining association rules”. In: Proceedings ofthe 20thInternational Conference on Very LargeDatabases, Santiago de Chile, 1994.

[2] Au W.-H., Chan K.C.C., ”FARM: A data mining sys-tem for discovering fuzzy association rules”. In:Proceedings of the 8th IEEE International Con-ference on Fuzzy Systems, Seoul, Korea, 1999,1217–1222.

[3] Berzal F., Cubero J.C., Marın N., Vila M.A.,Kacprzyk J. and Zadrozny S. , ”A General frame-work for computing with words in object-oriented programming”, International Journal ofUncertainty, Fuzziness and Knowledge-Based Sys-tems, vol. 15, 2007, 111–131. DOI: http://dx.doi.org/10.1142/S0218488507004480.

[4] Bosc P. , Dubois D., Pivert O. , Prade H., de CalmesM., ”Fuzzy summarization of data using fuzzycardinalities”. In: Proceedings of IPMU 2002, , An-necy, France, 2002, 1553–1559.

[5] Chen G., Wei Q., Kerre E., ”Fuzzy data mining:discovery of fuzzy generalized association rules”.In: G. Bordogna and G. Pasi (Eds.): Recent Issueson Fuzzy Databases. Springer-Verlag, Heidelbergand New York, 2000, 45–66. DOI: http://dx.doi.org/10.1007/978-3-7908-1845-1.

[6] Dubois D., Fargier H., Prade H., ”Beyond minaggregation in multicriteria decision: (ordered)weighted min, discri-min,leximin”. In: R.R. Yagerand J. Kacprzyk (Eds.): The Ordered WeightedAveraging Operators. Theory and Applications,Kluwer, Boston, 1997, 181–192.

[7] Dubois D., Prade H., ”Gradual rules in approx-imate reasoning”, Information Sciences, vol. 61,1992, 103–122.

[8] Dubois D., Prade H., ”Fuzzy sets in approximatereasoning, Part 1: Inference with possibility dis-tributions”, Fuzzy Sets and Systems, vol. 40, 1991,143–202. DOI: http://dx.doi.org/10.1016/0165-0114(91)90050-Z.

[9] Bosc P., Dubois D., Prade H., ”Fuzzy functionaldependencies – an overview and a critical dis-cussion”. In: Proceedings of 3rd IEEE Interna-tional Conference on Fuzzy Systems, Orlando,USA, 1994, 325–330. DOI: http://dx.doi.org/10.1109/FUZZY.1994.343753.

[10] George R. , Srikanth R., ”Data summarization us-ing genetic algorithms and fuzzy logic”. In: F.Herrera, J.L. Verdegay (Eds.): Genetic Algorithmsand Soft Computing, Springer-Verlag, Heidelberg,1996, 599–611.

[11] George R. , Srikanth R., ”A soft computing ap-proach to intensional answering in databases”,

56

http://dx.doi.org/10.1142/S0218488507004480.

http://dx.doi.org/10.1142/S0218488507004480.

http://dx.doi.org/10.1007/978-3-7908-1845-1.

http://dx.doi.org/10.1007/978-3-7908-1845-1.

http://dx.doi.org/10.1016/0165-0114(91)90050-Z.

http://dx.doi.org/10.1016/0165-0114(91)90050-Z.

http://dx.doi.org/10.1109/FUZZY.1994.343753.

http://dx.doi.org/10.1109/FUZZY.1994.343753.


Information Sciences, vol. 92, no. 1–4, 1996,313–328. DOI: http://dx.doi.org/10.1016/0020-0255(96)00049-7.

[12] Glockner I., ”Fuzzy quanti iers, multiple vari-able binding, and branching quanti ication”. In:T.Bilgi c et al.: IFSA 2003. LNAI 2715, Springer-Verlag, Berlin and Heidelberg, 2003, 135–142.

[13] Hajek P., Holena M., ”Formal logics of dis-covery and hypothesis formation by machine”,Theoretical Computer Science, vol. 292, 2003,345–357. DOI: http://dx.doi.org/10.1007/3-540-49292-5_26.

[14] Hu Y.-Ch., Chen R.-Sh., Tzeng G.-H, ”Mining fuzzyassociation rules for classi ication problems”,Computers and Industrial Engineering, vol. 43, no.4, 2002, 735–750. DOI: http://dx.doi.org/10.1016/S0360-8352(02)00136-5.

[15] Kacprzyk J., Strykowski P., ”Linguistic data sum-maries for intelligent decision support”. In: R. Fe-lix (Ed.): Fuzzy Decision Analysis and RecognitionTechnology for Management, Planning and Opti-mization - Proceedings of EFDAN’99, Dortmund,Germany, 1999, 3–12.

[16] Kacprzyk J., Strykowski P., ”Linguitic summariesof sales data at a computer retailer: a case study”.In: Proceedings of IFSA’99, vol. 1, 1999, Taipei,Taiwan R.O.C, 29–33.

[17] Kacprzyk J., Wilbik A., Zadrozny S., ”Linguisticsummarization of time series using a fuzzy quan-ti ier driven aggregation”, Fuzzy Sets and Systems,vol. 159, no. 12, 2008, 1485–1499. DOI: http://dx.doi.org/10.1016/j.fss.2008.01.025.

[18] Kacprzyk J., Wilbik A., Zadrozny S., ”An approachto the linguistic summarization of time series us-ing a fuzzy quanti ier driven aggregation”, Inter-national Journal of Intelligent Systems, vol. 25, no.5, 2010, 411–439. DOI: http://dx.doi.org/10.1002/int.20405.

[19] Kacprzyk J., Yager R.R., ”Linguistic summariesof data using fuzzy logic”, International Jour-nal of General Systems, vol. 30, no. 2, 2001,33–154. DOI: http://dx.doi.org/10.1080/03081070108960702.

[20] Kacprzyk J., Yager R.R., Zadrozny S., ”A fuzzylogic based approach to linguistic summariesof databases”, International Journal of AppliedMathematics and Computer Science, 10, 2000,813–834.

[21] Kacprzyk J., Yager R.R., Zadrozny S., ”Fuzzy lin-guistic summaries of databases for an ef icientbusiness data analysis and decision support. InW. Abramowicz and J. Zurada (Eds.): KnowledgeDiscovery for Business Information Systems, pp.129-152, Kluwer, Boston, 2001.

[22] Kacprzyk J., Yager R.R., Zadrozny S., ”FQUERYfor Access: fuzzy querying for a Windows-based DBMS”. In: P. Bosc and J. Kacprzyk(Eds.): Fuzziness in Database Management

Systems, Springer-Verlag, Heidelberg, 1995,415-433. DOI: http://dx.doi.org/10.1007/978-3-7908-1897-0_18.

[23] Kacprzyk J., Zadrozny S., ”Protoforms of lin-guistic data summaries: towards more generalnatural-language-based datamining tools”. In: A.Abraham, J. Ruiz-del-Solar, M. Koeppen (Eds.):Soft Computing Systems, pp. 417 - 425, IOS Press,Amsterdam, 2002.

[24] Kacprzyk J., Zadrozny S., ”Data Mining via Lin-guistic Summaries of Data: An Interactive Ap-proach”. In: T. Yamakawa and G. Matsumoto(Eds.): Methodologies for the Conception, De-sign and Application of Soft Computing. Proc. ofIIZUKA’98, Iizuka, Japan, 1998, 667–668.

[25] Kacprzyk J., Zadrozny S., ”The paradigm ofcomputing with words in intelligent databasequerying”. In: L.A. Zadeh and J. Kacprzyk(Eds.): Computing with Words in Informa-tion/Intelligent Systems. Part 2. Foundations,Springer–Verlag, Heidelberg and New York,1999, 382–398. DOI: http://dx.doi.org/10.1007/978-3-7908-1872-7.

[26] Kacprzyk J., Zadrozny S., ”Computing withwords: towards a new generation of linguisticquerying and summarization of databases”.In: P. Sincak and J. Vascak (Eds.): Quo VadisComputational Intelligence?, Springer-Verlag,Heidelberg and New York, 2000, 144–175, .

[27] Kacprzyk J., Zadrozny S., ”On a fuzzy queryingand data mining interface”, Kybernetika, vol. 36,2000, 657–670.

[28] Kacprzyk J., Zadrozny S., ”On combining intelli-gent querying and data mining using fuzzy logicconcepts”. In: G. Bordogna and G. Pasi (Eds.): Re-cent Research Issues on theManagement of Fuzzi-ness in Databases, Springer–Verlag, Heidelbergand New York, 2000, 67–81.

[29] Kacprzyk J., Zadrozny S., ”Data mining via lin-guistic summaries of databases: an interactiveapproach”. In: L. Ding (Ed.): A New Paradigm ofKnowledge Engineering by Soft Computing,WorldScienti ic, Singapore, 2001, 325–345. DOI: http://dx.doi.org/10.1142/4606.

[30] Kacprzyk J., Zadrozny S., ”Computing withwords in intelligent database querying: stan-dalone and Internet-based applications”,Information Sciences, vol. 134, no. 1–4, 2001,71–109. DOI: http://dx.doi.org/10.1016/S0020-0255(01)00093-7.

[31] Kacprzyk J., Zadrozny S., ”On linguistic ap-proaches in lexible querying and mining of as-sociation rules”’. In: H.L. Larsen, J. Kacprzyk,S. Zadrozny, T. Andreasen and H. Christiansen(Eds.): Flexible Query Answering Systems. RecentAdvances, Springer-Verlag, Heidelberg and NewYork, 2001, 475–484.

[32] Kacprzyk J., Zadrozny S., ”Linguistic summariza-tion of data sets using association rules”. In: Pro-

57

http://dx.doi.org/10.1016/0020-0255(96)00049-7.

http://dx.doi.org/10.1016/0020-0255(96)00049-7.

http://dx.doi.org/10.1007/3-540-49292-5_26.

http://dx.doi.org/10.1007/3-540-49292-5_26.

http://dx.doi.org/10.1016/S0360-8352(02)00136-5.

http://dx.doi.org/10.1016/S0360-8352(02)00136-5.

http://dx.doi.org/10.1016/j.fss.2008.01.025.

http://dx.doi.org/10.1016/j.fss.2008.01.025.

http://dx.doi.org/10.1002/int.20405.

http://dx.doi.org/10.1002/int.20405.

http://dx.doi.org/10.1080/03081070108960702.

http://dx.doi.org/10.1080/03081070108960702.

http://dx.doi.org/10.1007/978-3-7908-1897-0_18.

http://dx.doi.org/10.1007/978-3-7908-1897-0_18.

http://dx.doi.org/10.1007/978-3-7908-1872-7.

http://dx.doi.org/10.1007/978-3-7908-1872-7.

http://dx.doi.org/10.1142/4606.

http://dx.doi.org/10.1142/4606.

http://dx.doi.org/10.1016/S0020-0255(01)00093-7.

http://dx.doi.org/10.1016/S0020-0255(01)00093-7.


ceedings of The IEEE International Conference onFuzzy Systems, St. Louis, USA, 2003, 702–707.

[33] Kacprzyk J., Zadrozny S., ”Computing with wordsis an implementable paradigm: fuzzy queries,linguistic data summaries, and natural languagegeneration”, IEEE Transactions on Fuzzy Systems,vol. 18, no. 3, 2010, 461–472. DOI: http://dx.doi.org/10.1109/TFUZZ.2010.2040480.

[34] Kacprzyk J., Zadrozny S., ”Computing with wordsand protoforms: powerful and far reachingideas”. In: Rudolf Seising, Enric Trillas, ClaudioMoraga, and Settimo Termini (Eds.): On Fuzzi-ness. Springer-Verlag, Berlin Heidelberg 2013,255–270. DOI: http://dx.doi.org/10.1007/978-3-642-35641-4.

[35] Kacprzyk J., Zadrozny S., ”Comprehensiveness ofLinguistic Data Summaries: A Crucial Role ofProtoforms”. In: Ch. Moewes and A. Nurnberger(Eds.): Computational Intelligence in IntelligentData Analysis. Springer-Verlag, Berli, Heidelberg2013, 207–221. DOI: http://dx.doi.org/10.1007/978-3-642-32378-2.

[36] Kacprzyk J., Zadrozny S., ”Derivation of Linguis-tic Summaries is Inherently Dif icult: Can Asso-ciation Rule Mining Help?” In: Borgelt Ch., GilM. A., Sousa J. M. C., Verleysen M. (Eds.): To-wards Advanced Data Analysis by Combining SoftComputing and Statistics, Springer-Verlag, 2013,291–303. DOI: http://dx.doi.org/10.1007/978-3-642-30278-7.

[37] Lee J.-H., Lee-Kwang H., ”An extension of associa-tion rules using fuzzy sets”. In: Proceedings of theSeventh IFSA World Congress, Prague, Czech Re-public, 1997, 399–402.

[38] Liu Y., Kerre E.E., ”An overview of fuzzy quanti-iers. (I). Interpretations”,Fuzzy Sets and Systems,vol. 95, 1998, 1–21.

[39] Mannila H., Toivonen H., Verkamo A.I., ”Ef icientalgorithms for discovering association rules”. In:U.M. Fayyad and R. Uthurusamy (Eds.): Proceed-ings of the AAAI Workshop on Knowledge Discov-ery in Databases, Seattle, USA, 1994, 181–192.

[40] Raschia G., Mouaddib N., ”SAINTETIQ: a fuzzyset-based approach to database summarization”,Fuzzy Sets and Systems, vol. 129, no. 2, 2002, pp.137–162. DOI: http://dx.doi.org/10.1016/S0165-0114(01)00197-X.

[41] Rasmussen D., Yager R.R, ”Fuzzy query languagefor hypothesis evaluation”. In: Andreasen T., H.Christiansen and H. L. Larsen (Eds.): FlexibleQuery Answering Systems, pp. 23 - 43, Kluwer,Boston, 1997. DOI: http://dx.doi.org/10.1007/978-1-4615-6075-3_2.

[42] Rasmussen D., Yager R.R, ”Finding fuzzy andgradual functional dependencies with Summa-rySQL”, Fuzzy Sets and Systems, vol. 106, no. 2,1999, 131–142. DOI: http://dx.doi.org/10.1016/S0165-0114(97)00268-6.

[43] Yager R.R, ”A new approach to the summariza-tion of data”, Information Sciences, vol. 28, no.1, 1982, 69–86. DOI: http://dx.doi.org/10.1016/0020-0255(82)90033-0.

[44] Yager R.R, ”On linguistic summaries of data”.In: W. Frawley and G. Piatetsky-Shapiro (Eds.):Knowledge Discovery in Databases. AAAI/MITPress, 1991, 347–363.

[45] Yager R.R, Kacprzyk J. (Eds.), The OrderedWeighted Averaging Operators: Theory andApplications, Kluwer, Boston, 1997.

[46] Zadeh L.A., ”A computational approach to fuzzyquanti iers in natural languages”, Computers andMathematicswithApplications, vol. 9, no. 1, 1983,149–184. DOI: http://dx.doi.org/10.1016/0898-1221(83)90013-5.

[47] Zadeh L.A., A prototype-centered approach toadding deduction capabilities to search engines-– the concept of a protoform, BISC Semi-nar, 2002, University of California, Berkeley,2002. DOI: http://dx.doi.org/10.1109/IS.2002.1044219.

[48] Zadeh L.A., Kacprzyk J. (Eds.), Computing withWords in Information/Intelligent Systems. Part 1.Foundations. Part 2. Applications, Springer – Ver-lag, Heidelberg and New York, 1999. DOI: http://dx.doi.org/10.1007/978-3-7908-1873-4(part 1) and DOI: http://dx.doi.org/10.1007/978-3-7908-1872-7.

[49] Zadrozny S., Kacprzyk J., ”Computing with wordsfor text processing: an approach to the text cat-egorization”, Information Sciences, vol. 176, no.4, 006, 415–437. DOI: http://dx.doi.org/10.1016/j.ins.2005.07.017.

[50] Zadrozny S., Kacprzyk J., ”Issues in the practi-cal use of the OWA operators in fuzzy query-ing”, Journal of Intelligent Information Systems,vol. 33, no. 3, 2009, 307–325. DOI: http://dx.doi.org/10.1007/s10844-008-0068-1.

58

http://dx.doi.org/10.1109/TFUZZ.2010.2040480.

http://dx.doi.org/10.1109/TFUZZ.2010.2040480.

http://dx.doi.org/10.1007/978-3-642-35641-4.

http://dx.doi.org/10.1007/978-3-642-35641-4.

http://dx.doi.org/10.1007/978-3-642-32378-2.

http://dx.doi.org/10.1007/978-3-642-32378-2.

http://dx.doi.org/10.1007/978-3-642-30278-7

http://dx.doi.org/10.1007/978-3-642-30278-7

http://dx.doi.org/10.1016/S0165-0114(01)00197-X.

http://dx.doi.org/10.1016/S0165-0114(01)00197-X.

http://dx.doi.org/10.1007/978-1-4615-6075-3_2

http://dx.doi.org/10.1007/978-1-4615-6075-3_2

http://dx.doi.org/10.1016/S0165-0114(97)00268-6

http://dx.doi.org/10.1016/S0165-0114(97)00268-6

http://dx.doi.org/10.1016/0020-0255(82)90033-0.

http://dx.doi.org/10.1016/0020-0255(82)90033-0.

http://dx.doi.org/10.1016/0898-1221(83)90013-5.

http://dx.doi.org/10.1016/0898-1221(83)90013-5.

http://dx.doi.org/10.1109/IS.2002.1044219.

http://dx.doi.org/10.1109/IS.2002.1044219.

http://dx.doi.org/10.1007/978-3-7908-1873-4

http://dx.doi.org/10.1007/978-3-7908-1873-4

http://dx.doi.org/10.1007/978-3-7908-1872-7.

http://dx.doi.org/10.1007/978-3-7908-1872-7.

http://dx.doi.org/10.1016/j.ins.2005.07.017.

http://dx.doi.org/10.1016/j.ins.2005.07.017.

http://dx.doi.org/10.1007/s10844-008-0068-1.

http://dx.doi.org/10.1007/s10844-008-0068-1.


59

The Bi-partial Version of the p-median / p-center Facility Location Problem and Some Algorithmic Considerations

Jan W. Owsinski

Submitted: 15rh April 2014; accepted: 20th May 2014

DOI: 10.14313/JAMRIS_3-2014/28

Abstract: The paper introduces the bi-partial version of the well known p-median or p-center facility location problem. The bi-partial approach, developed by the author, pri-marily to deal with the clustering problems, is shown here to work for a problem that does not possess some of the essential properties, inherent to the bi-partial for-mulations. It is demonstrated that the classical objective function of the problem can be correctly interpreted in terms of the bi-partial approach, that it possesses the essential properties that are at the core of the bi-partial approach, and, finally, that the general algorithmic pre-cepts of the bi-partial approach can also be applied to this problem. It is proposed that the use of bi-partial ap-proach for similar problems can be beneficial from the point of view of flexibility and interpretation.

Keywords: facility location, p-median, p-center, cluster-ing, bi-partial approach

1. Introducing the Bi-partial ApproachThe bi-partial approach was developed by the

present author at the beginning of the 1980s (see [5], [6]) primarily as a way of dealing with the problems of cluster analysis, its strongest point being the capacity of providing the solution to the clustering problem in-cluding the optimum number of clusters, without the need of referring to any external (usually statistical) criteria. The approach has been recently described in a formal manner in Owsiński [7], [8], and its applica-tion to some special task in data analysis was provid-ed in Owsiński [9]. Dvoenko [1] applied the approach to the well-known k-means-type procedure.

The approach is based on the use of the bi-partial objective function, which is composed, according to the name, of two terms, which, in very general way, can be subsumed for clustering as representing the inner cohesion of the clusters and the outer sepa-ration of the clusters1. If cohesion within clusters is measured by some function of distances between the objects, or measurements, or samples, inside individ-ual clusters, denoted QD(P), where P is a partition of the set of n objects, indexed i = 1,…,n, into clusters Aq, q = 1,…,p, and subscript D means that we consider dis-tances inside clusters, then we put as measure of sep-aration of different clusters QS(P), meaning a function

of similarities of objects in different clusters, and the sum of the two, QD

S(P), is minimised (possibly small distances inside clusters and possibly small similari-ties among clusters).

This function, QDS(P), has a natural dual, namely

QSD(P), in which the two components represent, re-

spectively, cohesion within clusters, measured with similarities (proximities) inside the particular clus-ters, QS(P), and distances between different clusters, measured with distances between objects, belonging to different clusters, QD(P). The function QS

D(P) is, of course, maximised.

Even though this concept, at its general level, may appear to be close to trivial, there exist concrete implementations of the two dual objective functions, which form novel and interesting approaches, es-pecially regarding cluster analysis. Moreover, if the components of the objective functions are endowed with definite, quite plausible properties, the approach leads to effective solution algorithms.

2. Problem FormulationThe problem we address here is different from the

majority of problems taken as instances of applica-tion of the bi-partial approach. Namely, the problem we address is a classical question in operations re-search, related to location analysis. Not only, though, the interpretation of the problem is quite specific, but also the very form is in a way not appropriate for the treatment through the bi-partial formalism, as intro-duced here.

We deal, namely, in a very simplistic, but also very general manner, with the following problem

min Σq(Σi∈Aq d(xi,xq) + c(q)) (1)

with minimisation being performed over the choice of the set of p points (objects) xi that are selected as the central or median points xq, q = 1,…,p. For our further considerations it is of no importance whether these points belong to the set X of objects (medians) or not – i.e. they are only required to be the elements of the space EX (centers), to which all the objects, either ac-tually observed, or potentially existing, belong. It is, however, highly important that the second compo-nent of the objective function, namely Σqc(q), does not involve any notion of distance or proximity.

While d(.,.) is some distance, like in the general formulation of the bi-partial approach, where it en-


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ters either QD(P) or QD(P), c(q) is a non-negative value, interpreted as some cost, related to a facility q. The problem regarding (1) is to find a set of p (q = 1,…,p) locations of facilities, such that the overall cost, com-posed of the sum of distances between points, as-signed to the individual facilities, and these facilities, and the sum of costs, related to these facilities, is mi-nimised. It is, of course, assumed that the costs c(q) and distances d(.,.) are appropriately scaled, in order for the whole to preserve interpretative sense.

The costs may be given in a variety of manners: as equal constants for each arbitrary point from X or from EX, i.e. c, so that the cost component in (1) is simply equal pc, or as (more realistically) the values, determined for each point separately, i.e. c(i), or as a function, composed of the setup component (say, c1, if this setup cost is equal for all locations) and the component that is proportional to the number of loca-tions, assigned to the facility q, with the proportional-ity coefficient equal c2 (i.e. the cost for a facility is then c1 + cardAqc2). Of course, more complex, nonlinear cost functions, also with c1 replaced by c1(i), can, as well, be (and sometimes are) considered.

This problem has a very rich literature, with spe-cial numerical interest in its “pure” form, without the cost component, mainly devoted to mathematical and geometric properties and the respective (approxima-tion) algorithms and their effectiveness. Notwith-standing this abundant tradition, the issues raised and the results obtained, we shall consider here the form of (1) in one of its basic variants.

3. Some Hints at Cluster AnalysisAny Reader with a knowledge in cluster analysis

shall immediately recognise the first component of (1) as corresponding to the vast family of the so-called “k-means” algorithms, where such a form is taken as the minimised objective function. Indeed, this fact is the source of numerous studies, linking facility location problems with clustering approaches. One can cite in this context, for instance, the work of Pierre Hansen (e.g. [2]), but most to the point here is the recent pro-posal from Liao and Guo [3], this proposal explicitly linking k-means with facility location, similarly as this was done several decades ago by Mulvey and Beck [4].

The latter proposal by Liao and Guo [3] is insofar interesting as the facility of realisation of the basic k-means algorithm allows for the relatively straight-forward accommodation of additional features of the facility location problem (e.g. definite constraints on facilities and their sets).

Thus, while the first component of the function (1) could be treated with some clustering approaches, e.g. those based on the k-means type of procedure, the issue is in the way the entire function (1) is to be minimised.

4. An ExampleFor the sake of illustration, we shall consider the

problem (1) in the following more concrete, even though very simple, indeed, form:

minP Σq(Σi∈Aq d(xi,xq) + c1 + c2card(Aq)) (2)

where c1 is the (constant) “facility setup cost”, while c2 is the (constant) unit cost, associated with the ser-vicing of each object i ∈ Aq, except for the “first one”, this cost being included in the setup cost. Such a for-mulation, even if still quite stylised, seems to be fully plausible as an approximation. It can, of course, be transformed to

min (ΣqΣi∈Aq d(xi,xq) + pc1 + c2n), (2a)

where it is obvious that we could deal away with the component, associated with the unit cost c2. We shall keep it, though, for illustrative purposes, since the part, related to unit costs may, and usually does, take more intricate, nonlinear forms.

The problem (2) can be, quite formally, and with all the obvious reservations, mentioned, anyway, be-fore, moulded into the general bi-partial scheme, i.e.

minP QSD(P) = QD(P) + QS(P), (3)

where partition P encompasses, in this case, both the composition of Aq, q = 1,…,p, taken together with the number p of facilities, and the location of these facili-ties, i.e. choice of locations from (say) X as the places for facilities q.

Consider the simple case, shown in Fig. 1, with d(.,.) defined as Manhattan distance, the cost compo-nent of (2) being based on the parameter values c1 = 3, c2 = 1. Again, these numbers, if appropriately in-terpreted, can be considered plausible (e.g. distance, corresponding to annual transport cost, and c1 corre-sponding to annual write-off value).

Locations

0; 0 1; 0

1; 2

2; 3 3; 3

3; 4

5; 7

6; 8

7; 7

1; 8

2; 7

2; 9

0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5 6 7 8

X

Y Locations

Figure 1. A simple academic example for the facility lo-cation problem

Table 1 shows the exemplary values of QSD(P) =

QD(P) + QS(P), according to (2), for a series of parti-tions P. This is a nested set of partitions, i.e. in each consecutive partition in the series one of the subsets of objects, a cluster Aq, is the sum of some of the clus-ters from the preceding partition, with all the other clusters being preserved. Such a nested sequence of


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partitions is characteristic for a very broad family of cluster algorithms – the progressive merger or pro-gressive split algorithms.

The character of results from Table 1, even if close to trivial, is quite telling, and indeed constitutes a rep-etition of the observations made for other cases, in which the bi-partial approach has been applied. Note that the values of QD(P) increase along the series of partitions, while the values of QS(S) – decrease, and QS

D(P) has a minimum, which, for his simple case, cor-responds, indeed, to the solution to the problem.

5. Some Algorithmic Considerations: the Use of the k-means ProcedureAs indicated before, the problem lends itself to the

k-means-like procedure, which, in general and quite rough terms, at that, takes the following course:

0o Generate p 2 points as initial (facility location) seeds (in this case, the case of p-centers, the points generated belong to X), usually p << n

1o Assign to the facility location points all the n points from the set X, based on minimum distance, es-tablishing thereby clusters Aq, q = 1,…, p

2o If the stop condition is not fulfilled, determine the representatives (facility locations) for the clusters Aq, otherwise STOP

3o Go to 1o.This procedure, as we know, converges very quick-

ly, although it can get stuck in a local minimum. Yet, owing to its positive numerical features, it can be restarted from various initial sets of p points many times over, and the minimum values of the objective function obtained indicate the proper solution.

In the here analysed problem of facility location, since such problems rarely are really large in the stan-dard sense of data analysis problems, it is quite fea-sible to run the k-means procedure, as outlined above, for consecutive values of p in order to check whether a minimum over p can be found for a definite formu-

lation of the facility-location-related QSD(P). Although

we shall not be demonstrating this here, in view of the opposite monotonicity of both components of QS

D(P) along p, the minimum found over p is a global minimum (although, of course, it is not necessarily the solution to the problem considered, since we deal here only with an approximation of the actual objec-tive function). This procedure can be simplified so as to encompass only a part of the sequence of values of p, starting, say from p = 2 upwards, until a minimum is encountered.

6. Algorithmic Considerations Based on the Bi-partial ApproachWe shall now present the algorithmic approach

that is based on the basic precepts of the bi-partial ap-proach. Assuming, namely, the property that we have observed for the case of the concrete objective func-tion (2), that is – the opposite monotonicity of the two components of the objective function, we can refor-mulate it, obtaining, in the general case, the following parametric problem:

minP QSD(P,r) = rQD(P) + (1-r)QS(P), (4)

where the parameter r∈[0,1] corresponds to the weights we may attach to the two components of the objective function. Actually, it is used only for algorith-mic purposes, and not to express any sort of weight, and we assume that we weigh equally the two compo-nents (r = ½). Here, we make no a priori assumptions as to the value of p, in distinction from the approach, outlined above, based on the k-means procedure. The form (4) enables the construction of a suboptimisa-tion algorithm, provided the two components of the objective function are endowed with certain proper-ties. We shall outline the construction of this algo-rithm for the case of the objective function (2).

Table 1. Values of QSD(P) = QD(P) + QS(P) for a series of partitions, according to (2)

QD(P) QS(P) – calculation QS(P) - value QS

D(P) Partitions (facility locations in bold) p

0 12*3+12*1 48 48 All locations are facility locations 12

1 11*3+10*1+1*2 45 46 Merger of (0,0) and (1,0) 11

2 10*3+8*1+2*2 42 44 Merger of (2,3) and (3,3) 10

3 9*3+7*1+2+3 39 42 Addition of (3,4) to (2,3) and (3,3) 9

13 4*3+4*3 24 37(0,0), (1,0), (1,2) (2,3), (3,3), (3,4), (5,7), (6,8), (7,7), (1,8), (2,7), (2,9)

4

22 3*3+6+3+3 21 43(0,0), (1,0), (1,2), (2,3), (3,3), (3,4),

(5,7), (6,8), (7,7), (1,8), (2,7), (2,9)3

55 1*3+12 15 70(0,0), (1,0), (1,2), (2,3), (3,3), (3,4), (5,7),

(6,8), (7,7), (1,8), (2,7), (2,9)1


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Thus, the above general form is equivalent, for (2), to the following one:

minP (rΣqΣi∈Aq d(xi,xq) + (1-r)Σq(c1 + c2cardAq)). (5)

Now, take the iteration step index, t, starting with t = 0. Consider (5) for r0 = 1. We obtain

minP (1⋅ΣqΣi∈Aq d(xi,xq) + 0⋅Σq(c1 + c2cardAq) = ΣqΣi∈Aq d(xi,xq)). (6)

Since we did not make any assumptions, concern-ing the value of p, we can easily see that the global minimum for (6) is obtained for p = n, i.e. when each object (location) contains a facility (each location constitutes a separate cluster). Denote this particu-lar, extreme partition by P0. The situation described is illustrated in the first line of Table 1. The value of the original objective function is, therefore, equal n(c1 + c2), since the first component disappears, we deal with n facilities, and all cardAq = cardAi are equal 1.

Then, we decrease the value of r from r0 = 1 down. At some point, for r1, the value of the parameter is low enough to make the value of the second component of the objective function, (1-r)Σq(c1 +c2cardAq), weigh suffi-ciently to warrant aggregation of two locations into one cluster, with one facility, serving the two locations. This happens when the following equality holds:

QSD(P0,r1) = QS

D(P1,r1), (7)

where P1 is the partition, which corresponds to the aggregation operation mentioned, the equality from (7) being equivalent, in the case here considered, to

r1⋅0 + (1-r1) n(c1 + c2) = r1d(i*,j*) + (1-r1) (n(c1 + c2) – c1) (8)

where i*,j* is the pair of locations, for which the value of r1 is determined. This value, conform to (8) equals

r1(i*,j*) = c1/(d(i*,j*) + c1). (9)

This relation is justified by the fact that for each passage from p to p-1, accompanying aggregation, the value of the second component decreases by c1, while a value of distance, or a more complex function of dis-tances, is added to the first component.

As we look for the highest possible r1, which fol-lows r0 = 1, it is obvious, that the d(i*,j*) we look for must be smallest one among those not yet contained inside the clusters (i.e., for this step – among all dis-tances). In the subsequent steps t we use the equation (7) in its more general form, i.e.

QSD(Pt-1,rt) = QS

D(Pt,rt), (10)

and derive from it the expression analogous to (9). In this particular case – which is, anyway, quite similar to several of the implementations of the bi-partial ap-proach for clustering – the equation, analogous to (9) is obtained from (10), meaning that at each step t the minimum of distance is being sought, exactly as in the classical progressive merger procedures, like single link, complete link etc.

The procedure stops when, for the first time, rt is obtained in the decreasing sequence of r0, r1, r2,…, lower than ½ (the sequence of rt, if realised until the aggregation of all locations into one cluster, will, of course, end at t = n-1). Falling below ½ means, name-ly, that “on the way” the partition Pt was obtained, which was generated by the algorithm for r = ½, cor-responding to the equal weights of the two compo-nents of the objective function.

Thus, we deal with a procedure that is entirely analogous to the simple progressive merger algo-rithms, but has an inherent capacity of indicating the “solution” to the problem, without any reference to an external criterion. We used the quotation marks, when speaking of “solution”, because the procedure does not guarantee in any way the actual minimum of (2), since the operations, performed at each step, are limited to aggregation. The experience with other cas-es shows that a simple search in the neighbourhood of the suboptimal solution found suffices for finding the actual solution, if it differs from the suboptimal one.

7. Some Comments and the OutlookThe illustration, here provided, even though extreme-

ly simple, is sufficient to highlight the capacity of the bi-partial approach to deal with the p-median / p-center type of facility location problems. In fact, for (slightly) more complex formulations of the problem, like

minP Σq(Σi∈Aq d(xi,xq) + c1(q) + c2f(card(Aq))) (11)

i.e. where setup costs are calculated for each poten-tial facility location separately, and f(.) is an increas-ing concave function, the relation analogous to (10) yields only marginally more intricate procedure, analogous to that based on (9), where for each aggre-gation the minimum has to be found for the two loca-tions or clusters aggregated.

The issue, worth investigation, which arises there from is: what realistic class of the facility location prob-lems can be dealt with through the bi-partial approach?

Concerning the comparison with the here pro-posed procedure, based on the classical k-means, the following points must be raised:– k-means outperform progressive merger procedures for data sets with numerous objects (locations), but not too many dimensions (here: by virtue of definition, either very few, or just two), when storing of the distance matrix and operating on it is heavier than calculating np (much less than n2) distances at each iteration; in the cases envisaged n would not exceed thousands, and p is expected not to be higher than 100, so that the two types of procedures might be quite comparable;– there exists a possibility of constructing a hybrid procedure, in which k-means would be performed for a sequence of values of p at the later stages of the bi-partial procedure, with the result of the aggregation, performed by the bi-partial procedure being the starting point for the k-means algorithm;– given the proposal by Dvoenko [1], there exists also a possibility of implementing directly the bi-partial


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version of k-means, with specially designed form of the two components of the objective function; this, however, would require, indeed, additional studies.

ACKNOWLEDGMENTThis research has been partially supported by the Na-tional Centre of Science of the Republic of Poland un-der Grant No. UMO-2012/05/B/SsT6/03068.

Notes

1 In some other circumstances the two can be re-ferred to as “precision” and “distinguishability”, which brings us quite close, indeed, to the standard oppositions, known from various domains of data analysis, such as “fit” and “generalisation” or “pre-cision” and “recall”.

2 We use the classical name of the k-means algo-rithm, although the number of clusters, referred to in this name as “k”, is denoted in the present paper, conform to the notation adopted in the bi-partial approach, by p.

AUTHORJan W. Owsinski – Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01–447 Warszawa, Poland. E-mail: [email protected].

REFERENCES[1] Dvoenko S., “Meanless k-means as k-meanless

clustering with the bi-partial approach”. In: Pro-ceedings of PRIP 2014 Conference, Minsk, May 2014.

[2] Hansen P., Brimberg J., Urosević D., Mladenović, N., “Solving large p-median clustering problems by primal-dual variable neighbourhood search”, Data Mining and Knowledge Discovery, vol. 19, 2009, 351–375.

[3] Liao K., Guo D., “A clustering-based approach to the capacitated facility location problem”, Trans-actions in GIS, vol. 12, no. 3, 2008, 323–339.

[4] Mulvey J. M., Beck M. P., “Solving capacitated clustering problems”, European Journal of Op-erational Research, vol., 18, no. 3, 1984, 339–348. DOI: http://dx.doi.org/10.1016/0377-2217(84)90155-3.

[5] Owsiński J.W., Regionalization revisited: an explic-it optimization approach, CP-80-26. IIASA, Laxen-burg 1980.

[6] Owsiński J.W., “Intuition vs. formalization: local and global criteria of grouping”, Control and Cy-bernetics, vol. 10, no. 1–2, 1981, 73–88.

[7] Owsiński, J.W., “The bi-partial approach in clus-tering and ordering: the model and the algo-

rithms,. Statistica & Applicazioni, 2011, Special Issue, 43–59.

[8] Owsiński J. W., “Clustering and ordering via the bi-partial approach: the rationale, the model and some algorithmic considerations”. In: J. Pociecha & Reinhold Decker, eds., Data Analysis Methods and its Applications, Wydawnictwo C.H. Beck, Warszawa, 2012a, 109–124.

[9] Owsiński J. W., “On the optimal division of an em-pirical distribution (and some related problems)”, Przegląd Statystyczny, Special Issue 1, 2012b, 109–122.


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A Novel Generalized Net Model of the Executive Compensation Design

Krassimir T. Atanassov, Aleksander Kacprzyk, Evdokia Sotirova

Submitted: 3rd April 2014; accepted: 30th May 2014

DOI: 10.14313/JAMRIS_3-2014/29

Abstract: In the paper we are concerned with a structured ap-proach to the process of design of an executive com-pensation system in a company which is one of most relevant issues in corporate economics that can have a huge impact on a company, with respect to finances, competitiveness, etc. More specifically, we present a novel application of Atanassov’s concept of a General-ized Net (GN) which is a powerful tool for the represen-tation and handling of dynamic discrete event problems and systems. First, to present the problem specifics, a broader Total Reward system is discussed together with the importance of proper structuring of the compensa-tion system for executives to support company’s goals, allowing attracting, motivating and retaining managers. The proposed compensation design model starts from incorporating a broad spectrum of benchmarks, expec-tations and constraints to those already incorporated in the early phase of the design of the executive com-pensation. In the design and testing phase a significant emphasis is placed on the flexibility and adjustability of the executive compensation package to external factors by testing, dynamically adjusting and stress testing the proposed compensation package already in the design phase. Then, we apply some elements of the theory of Generalized Nets (GNs) to construct the model of execu-tive compensation design using the proposed approach.

Keywords: rewards systems, compensation design, banking activities, corporate activities, Generalized Net, modelling, Discrete Event System Modeling

1. IntroductionThe present paper is a continuation of our pre-

vious investigations on the use of some elements of the theory of Generalized Nets (GNs) proposed by Atanassov [2, 3] for the mathematical modeling of banking activities [8, 11], executive compensation [9], as well some technological and business activities of a petrochemical company (cf. [5]).

In this paper, by extending the ideas of [9], we fo-cus on the development of a system for compensation design for bank executives. We star by discussing the role of compensation in the reward systems to identi-fy the key objectives placed on the executive compen-sation as well as key requirements of the compensa-tion design process. Later we discuss the importance

of updating procedures in the compensation design, which includes continuous cycle of developing, imple-menting, using, evaluating and adjusting of executive compensation. Based on those principles and objec-tives we propose a comprehensive approach to execu-tive compensation design.

We continue show the application of some ele-ments of Atanassov’s theory of Generalized Nets to construct the model of executive compensation de-sign which incorporates the process for executive compensation design to be proposed. Finally we iden-tify some promising areas for future research.

2. Reward Systems and Their Role in Attaining Company Goals

The primary goal of a reward system in a company, firm, corporation, etc. is commonly described in the literature as the supporting of business goals, and attracting, motivating and retaining competent em-ployees (cf. [13]). It is also referred to as a system that aligns the rewards to executives with is critical for the company to succeed in both a short-term and long-term perspective, and to accomplish its strategic plan (cf. [12]). Yet another approach is presented by Ellig (2007) who defines the Reward Management as the one concerned with the formulation and implementa-tion of strategies and policies that aim at rewarding people fairly, equitably and consistently in accordance with their value to the organization (cf. [7]).

Rewards strategy is a significantly complex issue which ties the business strategy with medium and short term tactics and with day to day tasks and deci-sion, and therefore a proper rewards strategy requires the incorporation of large number of elements a list of which is listed below as proposed by Armstrong [1] and WorldatWork [13]: • Rewards strategy philosophy – statement about how

rewards strategy will support business strategy and needs of the company’s stakeholders,

• Goals of Rewards Strategy – their prioritization and success criteria for evaluation,

• Types of Rewards – list of reward types including their description and relative importance,

• Relative importance of various rewards -setting the importance of rewards relative to other tools ap-plied in influencing employees behaviors,

• Selection of measures – selection of measures that should be used in the design of rewards includ-


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ing decision about the level in the organization at which the criteria will be measured (organization-wide, SBU, team, individual) and decision about which elements of total rewards will be associated with those measures,

• Selection of competitive market reference points – selection of peers and competitors that should form the benchmarks and to which employees will benchmark their compensation in terms of its competitiveness,

• Competitiveness of rewards strategy – decision on desired competitive position versus selected com-petitive market reference points, company’s level of rewards to be be below, on par or above the market,

• Updating of Rewards Strategy – defining criteria and process for updating of Rewards Strategy or decision of which elements can be updated individually,

• Data and information management – selection of information sources, approach and methods of data processing, tools used in decision support as well as reporting,

• Guidelines for solving conflicts – methods for ap-proaching to conflict and processes for resolving conflicts,

• Communication Strategy – decision about the in-tensity of communication of rewards strategy with key stakeholders as well as content of such com-munication.The Total Rewards approach targets very closely

the issues faced today by majority of banks operating in fast changing environment with increased scrutiny of shareholders, regulators and public on their per-formance and in particular on compensation of their executives. While banks are expected to be more mod-est in their compensation they also operate in a highly complex and fast changing environment where they need to attract, develop and retain top talent. There-fore the historical simplified approach to rewards management needs to be expanded into a total re-wards system. The Total Rewards approach proposed by WorldatWork [13] promises to address key con-cerns of today’s banks in managing their executive workforce with:1. Increased flexibility2. Improved Recruitment and Retention3. Reduced Labor Costs/Cost of Turnover4. Heightened Visibility in a Tight Labor Market5. Enhanced Profitability

Given our task of structuring and codifying the bank process that we started in our previous paper, as well as with the current significant visibility and pub-lic scrutiny of compensation of executives in banks, we commence our analysis with compensation pro-cesses and systems.

3. Role of Compensation Systems in Motivating Executives

While executives are motivated by diverse el-ements, compensation program, when properly structured and controlled, remains the most potent

weapon for CEO and HR department in their arsenal of reward and punishment devices. Compensation is highly effective at motivating individual executives to higher levels of performance as described by Bruce R. Ellig [6]. This approach is consistent with agency theory that suggests performance pay as a substitute to monitoring [7]. Compensation is by any mean the largest component of rewards system and a major cost for the organization [13]. At the same time, while Total Rewards Strategy as presented earlier is highly complex to design and implement, the well-designed compensation system can benefit even smallest or-ganizations and can become a centerpiece of human resource strategy when it comes to attracting and re-taining top talent and good performers.

The challenge of proper structuring and imple-mentation of compensation system is further compli-cated in the professional organization, such as bank, where there is a significant number of professionals, which not only have various targets set but they also tend to work with different lines of responsibility and reporting to multiple superiors or operating in cross functional teams. In addition to this, given the various ownership changes and mergers divestments the typ-ical career in “siloses” or within certain departments or parts of organization is no longer the rule. Today’s professionals tend to change assignments or special-ties, levels of responsibility regularly; they also take advantage of horizontal promotions. In those cases what seems natural from the organizational point of view, that certain position has attached to it compen-sation package is not accepted by employees that are to relocated from the department or position with more attractive or just differently structured com-pensation package. Those challenges of today’s banks call for a highly dynamic and flexible compensation design process.

Another important external factor faced by banks in the US and in Western Europe, in particular banks that required state bailout or struggling with lack of growth is an increased public scrutiny of compensa-tion in banks. At the same time banks in the emerging economies face different sets of challenges related to reduced access to liquidity, increased regulatory over-sight, foreign ownership and need for operational ex-cellence [9]. The famous year-end bonuses enjoyed by many bank professionals for reaching sales or profit targets are questioned as they promote taking size-able risk that only later are realized and that do not impact the executives that took those risks.

One more characteristic of banks today is the need to quickly react to changes in the marketplace and to changing bank objectives that put an additional pres-sure on compensation systems as recent research from Towers Perrin [12] points out that compensa-tion and benefits can be easily copied by competitors vs. other types of rewards, in particular intangible, that maybe more difficult to imitate.

Therefore the compensation systems while re-mains the most important element of reward sys-tems at banks require a support in the design pro-cess performed by HR professionals. We believe


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that well-structured compensation design process that incorporates broad information sourcing with high level of flexibility and adjustability that can be implemented in a decision support system would be of significant help and would improve decision making and help banks in increasing their results and efficiency while providing well balanced moti-vation to bank executives.

4. Proposed Approach to the Structuring Process of the Executive Compensation DesignIn our approach to the structuring of the process

of executive compensation design we have decided to first focus on internal company goals and initially set aside external constituencies and considerations which we will analyze in our future works.

While setting the goals for structuring and codi-fying the executive compensation design process, based on the available literature and research results reported (in particular: [13], [6], and [10]) we have identified and set three goals for the process and model considered:1. To optimize executive compensation to maximize

the value to a company (to fit its goals) and to an executive (to be able to attract and retain the best people).

2. To dynamically calculate the cost of executive compensation to the company and benefits to an executive to respond to a fast changing and highly competitive environment.

3. To provide a tool for a compensation committee/CEO/HR department to evaluate alternatives and conditions of the executive pay package and their impact on the company in static and highly dy-namic scenarios.With the three goals for the structuring and cod-

ifying of executive compensation design process presented above, we wish to propose an approach that focuses on the incorporation of a diverse sets of source date but also that puts a significant effort into dynamic analyses of the incorporation of those sets of sources, evaluation and readjustments that can be performed throughout the compensation de-sign process.

The proposed process, presented in Fig. 1 below, is composed of five action steps:1. Description of the current compensation mod-

el – an important goal of this step is to understand the current drivers, variables and constraints of the existing compensation model as well as em-ployee expectations and past performance.

2. Benchmarks and constraints – this step allows for the introduction of various benchmarks, survey data as well as external and internal constraints.

3. Design phase – the most important element that reshapes the standard blue print for the compen-sation model with data inputs from the existing compensation system and external benchmarks, with internal and external rules and constraints in an iterative and dynamic process of designing, analyzing and testing.

Fig. 1. Compensation design process steps and tasks


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4. Finalization – in this phase the proposed new compensation model is codified as well as alter-natives are modeled and it is stress tested for ex-treme cases. This phase ends with the implemen-tation.

5. Assessment – in this step the new compensation model is used, its effectiveness is monitored and potential weaknesses are spotted, documented and evaluated.

4.1. Description of the Current Compensation Model

The first step in the proposed process, depicted in Fig. 2, focuses on the compilation of source infor-mation about the current salary levels for different positions and grades of the executives together with benefits as well as short term (ST) and long term (LT) rewards such as target and result oriented bonuses.

By compiling those sets of information, first, trends or inconsistencies of the existing model can be spotted and properly marked for future analyses. This data set also allows for performing the verification of the existing compensation model to targets and bud-gets of the company in question, as well as its fit with company goals and strategy.

The second element of this step is the compilation of employee expectations, both monetary and non-monetary ones, as well as related to the structure of their compensation or mechanics of pay for their per-formance together with information of the employee performance related to targets of the company. Based

Fig. 2. Description of current compensation model

on this data the first partial analysis can be performed to identify if the current compensation model is act-ing properly to stimulate the performance of the indi-vidual executive, its efficiency and effectiveness.

The key outputs of this step are tables with pay levels and pay grades together with rewards and ben-efits (primarily monetary), sets of rules for the cal-culation of benefits and their eligibility, and a list of condition rules for testing in the new model.

4.2. Benchmarks and ConstraintsThe second step, presented in Fig. 3, is focused on the

assembling of sets of benchmarks as well as rules and constraints that describe the competitive environment and allow for a dynamic modeling of the new compen-sation model. The comparable universe of benchmarks is to include data from internal benchmarking (between bank subsidiaries or countries of operation), industry benchmarking (primary in the same country or a simi-lar financial center) and position specific benchmarking as well as information about company/bank sizes and compensation budgets for similar sized competitors. This set of data will allow the determination of sets of ranges, medians and distributions to be later used in the modeling process.

Another group of data to be elicited and included is the external constraints that need to be considered in the design of compensation model. In particular this should include the local legal and tax considerations as well as industry specific requirements. Those sets


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Fig. 3. Benchmarks and constraints

of rules and constraints will be used in the following step to adjust and test the proposed compensation model for compliance and efficiency.

4.3 Design PhaseThe design phase, shown in Fig. 4, is the most

important and the most complex element of the pro-posed approach as it is the process in which the data inputs together with rules and constraints are used to

develop the compensation model blueprint which is transformed into a proposal of a new compensation model and finally into the new compensation model. The proposed approach starts with a compensation model template which includes all elements of the compensation system such as a base pay, base pay modifiers (such as pay grades or bands), target-relat-ed and results related rewards, etc. but without any numerical data.

Fig. 4. Design Phase


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The first phase of the design process is an iterative inclusion of the data inputs and rules/constraints that forms a blue print of the new compensation model, high-lighting the elements consistently meeting the criteria and elements that are contradictory or outside of the constraints placed.

The second phase includes an evaluation of pref-erences and trade-offs to eliminate the criteria that cannot be met and to finalize core elements of the compensation model. This phase of the process in-volves an iterative testing of the proposed model ver-sus present goals and a present system and new tar-gets and goals to verify its applicability and efficiency (in particular a cost – effect type analysis). The final product of this action step is a proposal of a new com-pensation model which consists of a core model and sets of variable elements together with performance criteria and rules/constraints.

4.3. Finalization and AssessmentThe final action steps in the design and implemen-

tation of the new compensation model, shown in Fig. 5, start with the finalization phase in which the proposed model is stress tested to verify its flexibility and to pos-sibly correct any improper performance for outliers and various compensation alternatives. At the same time the compensation model is codified into procedures and manuals, and at the same time its practicality and cohe-siveness is verified and corrected.

The final step includes the implementation and assessment which includes an implementation in the company or organization, starting with a pilot imple-mentation and a later staged rollout. At this action step the new compensation model is constantly moni-tored and fine-tuned by verifying the executive per-formance versus the company targets and individual targets set as well as versus the past performance and also the simulated performance of the old model.

5. Application of Theory of Generalized Nets to the Proposed Approach to Executive Compensation Design The Generalized Nets (GNs) have been introduced

by Atanassov [2], [3] as a powerful, general and com-prehensive tool to conceptualize, model, analyze and design of all kinds of discrete event type processes and systems that evolve over time. They can effective-ly and efficiently model various aspects of processes whose behavior over time is triggered and influenced by some external and internal events.

These characteristic features of the GNs do clearly suggest that they can be a powerful, effective and ef-ficient model for the executive compensation problem considered in this paper. We will show this in detail in the next subsection.

However, let us first start with a brief description of basic elements of the theory of GNs that will be of use for our next considerations. Some GNs may not have some of the components, thus giving rise to spe-cial classes of GNs called reduced GNs. For the needs of the present research we shall use (and describe) one of the reduced types of GNs.

Fig. 6. GN-transition

Fig. 5. Finalization and Assessment


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Formally, each transition of this reduced class of GNs is described by (cf. Fig. 6):

, (1)

where: (a) L and L are finite, non-empty sets of places (the transition’s input and output places, respectively). For the transition in Fig. 1 these are ''

2'1 ,...,,' mlllL = and

''''2

''1 ,...,,'' mlllL = ;

(b) r is the transition’s condition determining which tokens will pass (or transfer) from the transition’s in-puts to its outputs; it has the form of an Index Matrix (IM); cf. Atanassov ([2], [4]):

where ri,j is the predicate which corresponds to the i-th input and j-th output places. When its truth val-ue is “true”’, a token from the i-th input place can be transferred to the j-th output place; otherwise, this is not possible;

(c) is a Boolean expression. It contains as vari-ables the symbols which serve as labels for transi-tion’s input places, and it is an expression built up from variables and the Boolean connectives “conjunc-tion” and “disjunction”. When the value of a type (cal-culated as a Boolean expression) is “true”, the transi-tion can become active, otherwise it cannot.

The ordered four-tuple E = (A, K, X, F) is called the simplest reduced GN (briefly, we shall use again “GN”) if: (a) A is a set of transitions; (b) K is the set of the GN’s tokens. (c) X is the set of all initial characteristics the

tokens can receive when they enter the net; (d) F is a characteristic function which assigns new

characteristics to each token when it transfers from an input to an output place of a given tran-sition.

Over the GNs a lot of types of operators are de-fined. One of these types is the set of hierarchical op-erators. One of them changes a given GN-place with a whole subnet, cf. Atanassov ([2], [3]). Below, having in mind this operator, we will use three places that will represent three separate GNsas shown in the au-thors earlier works (cf. [9]).

6. A GN-model of the Design of an Executive Compensation Scheme

Now we will present the use of elements of the theory of the GNS presented in Section 5, to develop a novel model of the executive compensation scheme. The essence and problems related to this design pro-cess have been extensively described in the preced-ing sections.

The GN model (Fig. 7) consists of nine transitions that represent, respectively:– the process of Description of the current

compensation model (transitions Z1 and Z2),– the analysis of Benchmarks and Constraints

(transitions Z3 and Z4),– the Design phase (transitions Z5, Z6 and Z7),– the process of Finalization (transition Z8),– the process of Assessment (transition Z9).

Initially, the tokens a and b stay in places l4 and l7. They will be in their own places during the whole time during which the GN functions. All tokens that enter transitions Z1 and Z2 will unite with the corre-sponding original token (a and b, respectively). While the a and b tokens may split into two or more tokens, the original token will remain in its own place the whole time.

The original tokens have the following initial and current characteristics:– token a in place l4 with the characteristic:

= “Current salary levels and benefits, List of benefits available and costs,

ST rewards – bonuses (target related, results re-lated, discretionary),

LT rewards – bonuses (target related, company value related, discretionary”,

– token b in place l7 with the characteristic: = “Benchmarks: Internal benchmarks, Industry benchmarks, Position specific benchmarks;

Company size/compensation budget”.

Transition Z1 has the form

Z1 = ⟨l1, l4, l2, l3, l4, r1, ∨( l1, l4)⟩,

where

,

WWWltruefalsefalsellll

r

,,, 4434244

1

4321 =

in which:W4,2 – “Tables with pay levels and pay grades, rewards and benefits are prepared”,W4,3 – “Sets of rules for calculation of benefits and eli-gibility are prepared”,W4,4 – W4,2 & W4,3.

The a0-token that enters place l4 (from place l1) does not obtain the new characteristic. It unites with the a-to-ken in place l4 with the above mentioned characteristic.

The a token can be split into tree tokens. As we mentioned above, the original a token continues to stay in place l4. The other tokens (a1 and a2) enter places l2 and l3 and obtain the following characteristics:– Token a1 enters place l2 with the characteristic:

a1x = “Tables with pay levels and pay grades, re-

wards and benefits”;– Token a2 enters place l3 with the characteristic:

a2x = “Sets of rules for calculation of benefits

and eligibility”.


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Transition Z2 has the form:

Z2 = ⟨l5, l8, l6, l7, l8, r2, ∨( l5, l8)⟩,

where:

,

WWWltruefalsefalsellll

r

,,, 8878688

5

8762 =

in which:W8,6 – “Sets of ranges, medians, distributions are de-termined”,W8,7 – “Levels and rules for maximum/ minimum con-straints are determined”,W8,8 – W8,6 & W8,7.

The b0-token that enters place l8 (from place l5) does not obtain the new characteristic. It unites with the b-token in place l8 with the above mentioned char-acteristic.

The b token can split to tree tokens. As we mentioned above, the original b token continues to stay in place l8, while the other tokens (b1 and b2) enter places l6 and l7 and obtain the following characteristics:– Token b1 enters place l6 with the characteristic:

b1x = “Sets of ranges, medians, distributions”;

– Token a2 enters place l3 with the characteristic:b2x = “Levels and rules for the maximum/ minimum con-

straints”.

The g1 and g2-tokens enter the GN net via places l9 and l10 with the following characteristics, respectively:– Token g1 in place l9

with the characteristic:g1x = “Employee expectations”;

– Token g2 in place l10 with the characteristic:g2x = “Employee performance – past, expected future”.


Z3 = ⟨l9, l10, l11, r3, ( l9, l10)⟩,

where:

Z1 l2 l1

Z2

l5

Z3

l10

Z4

l14

Z5

Z6 Z7

l22

l20

l19

Z8

l27

l26

l25

l24

Z9

l16

l17

l18

l9

l13

l12

l3

l11

l4

l8

l7

l6

l30

l29

l23

l26

l28

l15

Fig. 7. A GN model of the design of the executive compensation design model


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in which:W9,11 = W10,11 = “The identification of strengths and weaknesses of the existing compensation model is performed”.

The g1 and g2-tokens unite with token g in place l11 with the characteristic:

gx = “Lists of conditions, rules for testing in new model”.

The d1 and d2-tokens enter the GN net via places l12 and l13 with the following characteristics, respec-tively:

– Token d1 in place l12 with the characteristic:d1x = “Tax treatment of pay and benefits”;

– Token d2 in place l13 with the characteristic:d2x = “Legal/regulatory requirements”.


Z4 = ⟨l12, l13, l14, r4, ( l12, l13)⟩,

where:

in which:W12,14 = W13,14 = “The external constraints are given”.

The d1 and d2-tokens unite with token d in place l14 with the characteristic

dx = “Sets of rules, constraints”.


Z5 = ⟨l2, l3, l6, l7, l11, l14, l15, l16, r5, (l2, l3, l6, l7, l11, l14, l15)⟩,

where:

In place l15 there is one z0-token with the charac-teristic

z0x = “Compensation model template”.

Tokens a1 and a2 (from places l2 and l3), b1 and b2 (from places l6 and l7), g (from place l11), d (form place l14) and z0 (form place l15) merge in a z-token that en-ter place l16 with the characteristic

zx = “Compensation model blueprint”.


Z6 = ⟨l16, l17, l21, l24, l18, r6, ∨(∧(l16, l17), ∧(l16, l21), ∧(l16, l24)⟩,

where:

From place l17 h-token enters the net with the characteristic

hx = “Preferences and trade-offs”.

The q-token that enters place l18 obtain the char-acteristic

qx = “Compensation model proposal”.


Z7 = ⟨l18, l19, l22, l19, l20, l21, l22, r7, ∨(l18, l19, l22)⟩,

where

in which:W19,19 = “The new system is tested vs. today’s system (total compensation budget, changes per employee)”,W19,20 = “The result from testing the new system vs. today’s system is positive”,W19,21 = “The result from testing the new system vs. today’s system is negative”,W22,20 = “The result from testing the new system vs. Next year/future’s is positive”,W22,21 = “The result from testing the new system vs. Next year/future’s is negative”,W22,22 = “The new system is tested vs. next year/fu-ture’s (e.g., impact of pay progression, indexation)”.

The q1 and q2 tokens that enter places l19 and l22 obtain the following characteristics, respectively:

q1x = “Test new system vs. today’s” in place l19,

and q2x = “Test new system vs. Test new system vs.

Next year/future’s” in place l22.


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The q-token that enters place l21 (form places l19 or l22) does not obtain the new characteristic.

With the truth values of the predicates W19,20 and W22,20, the u-token enters place l20 with the characteristic

ux = “New compensation model”.


Z8 = ⟨l20, l25, l26, l27, l23, l24, l25, l26, l27, r8, ∨( l20, l25, l26, l27)⟩,

where:

in which:W26,23 – “The alternatives are modeled”,W26,24 – W27,24 = “New compensation model have to be corrected”,W26,26 – W26,23,W27,23 – “The stress testing of the new compensation model is ready”,W27,27 – W27,23.

The u1, u2 and u3 tokens that enter places l25, l26 and l27 obtain the following characteristics, respectively:

u1x = “New compensation model, modeled

alternatives” in place l25, u

2x = “New compensation model, evaluated impact on executive compensation of unlikely but probable

developments” in place l26, and

u3x = “New compensation model, written summary

of compensation rules and levels as well as description of targets to be achieved” in place l27.

The u-token that enters place l24 (form places l26 or l27) does not obtain the new characteristic.

With the truth values of the predicates W26,23 and W27,23, the k-token enters place l23 with the characteristic

kx = “New compensation model for implementation”.


Z9 = ⟨l23, l28, l29, l30, l1, l5, l15, l28, l29, l30, r9, ∨( l23, l28, ∧(l29, l30))⟩,

where:

The k1, k2 and k3 tokens that enter places l28, l29 and l30 obtain the following characteristics, respectively:

k1x = “Application of the new compensation model

for implementation” in place l28, k2x = “New compensation model for implementation,

assess results against targets” in place l29, and

k3x = “New compensation model for implementation,

identification of weaknesses, areas of misuse” in place l30.

The a0 and b0 tokens that enter places l1 and l5 ob-tain the characteristic:

ba = 00 xx = “Current compensation model”.

The e token that enters place l15 obtains the char-acteristic

ex = “Compensation model template”.

7. Concluding Remarks In this paper we have presented a novel approach

to the structuring of the design of executive com-pensation in companies, corporations, firms, etc., and showed that it can be effectively and efficiently implemented by using a Generalized Net model. Our purpose has been to identify, organize and structure the key components required for the development, testing, implementation and assessment of the com-pensation model, and to show how they can be re-flected using concepts, tools and techniques of the GNs. In particular, we have identified the type of the information input, the way of processing it and types of outputs to be used in the subsequent phases of the design process.

Due to the novelty of the presented approach, both in terms of the first use of the GNs for the class of problems considered as well as the first approach to the design of an executive compensation scheme by using not only GN based analyses but more generally a net analysis related models, we have concentrated on the representation of basic variables and relations. Other variables that are relevant for the problem con-sidered, such as external stakeholders exemplified by shareholders, board of directors, international and lo-cal regulators or competition for talent, will be dealt with in subsequent papers, and included in a compre-hensive model to be developed.

In our future research we plan first of all to focus on a deeper analysis and testing of each step of the proposed approach to the compensation design by in-corporating some findings and conclusions obtained from earlier research performed as well as by testing the approach proposed on real data of various kinds and sizes of companies and organizations. We also


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plan to compile and test the benchmark tables and constraints tables from the fragmented source data available and work on improving their reliability and applicability with the help of mathematical modeling.

AUTHORSKrassimir T. Atanassov – Department of Bioinfor-matics and Mathematical Modelling, Institute of Bio-physics and Biomedical Engineering, Bulgarian Aca-demy of Sciences, 105 Acad. G. Bonchev Str. 1113 Sofia, Bulgaria. E-mail: [email protected]

Aleksander Kacprzyk* – Resource Partners, Zebra Tower, ul. Mokotowska 1, 00–640 Warsaw, Poland. E-mail: [email protected],

Evdokia Sotirova – Department of Computer and In-formation Technologies, Faculty of Technical Scienc-es, “Prof. Assen Zlatarov” University, 1 Prof. Yakimov Str. 8010 Bourgas, Bulgaria. E-mail: [email protected]

∗Correspondingauthor

REFERENCES

[1] Armstrong M., Handbook of Reward Manage-ment Practice: Improving Performance Through Reward, Kogan Page 2012.

[2] Atanassov K.T., Generalized Nets, Singapore/New Jersey: World Scientific, 1991. DOI: http://dx.doi.org/10.1142/1357.

[3] Atanassov K.T., On Generalized Nets Theory, Sofia: Prof. M. Drinov Academic Publishing House, 2007.

[4] Atanassov K.T., Index Matrices: Towards an Aug-mented Matrix Calculus, Heidelberg and New York: Springer, 2015 (in press).

[5] Atanassov K.T., Kacprzyk A., Skenderov V., Kryu-chukov A., “Principles of a generalized net model of the activity of a petrochemical combine”. In: Proceedings of the 8th International Workshop on Generalized Nets, Sofia, Bulgaria, June 26, 2007, pp. 38-41.

[6] Ellig B. R., The complete guide to executive com-pensation, McGraw Hill, 2007.

[7] Holmstrom B., “Moral hazard in teams”, Bell Journal of Economics, vol. 13, no. 2, 1982. DOI: http://dx.doi.org/10.2307/3003457.

[8] Kacprzyk A., Mihailov I.,“Intuitionistic fuzzy es-timation of the liquidity of the banks. A general-ized net model”. In: Proceedings of the 13th Inter-national Workshop on Generalized Nets, London, UK, 2012, 34-42.

[9] Kacprzyk A., Sotirova E., Atanasssov K.T. , “Mod-elling the executive compensation design model using a generalized net”. In: Proceedings of the 14th International Workshop on Generalized Nets, Burgas, Bulgaria, 29th–30th November, 2013, 71–77.

[10] Lipman F.D., Hall S.E., Executive compensation Best Practices, John Wiley & Sons, 2008.

[11] Mihailov I., “Generalized Net Model for Describ-ing Some Banking Activities”. In: Proceedings of the, New Developments in Fuzzy Sets, Intuitionis-tic Fuzzy Sets, Generalized Nets and Related Top-ics, vol II: Applications, Warsaw, Poland, 2013, 115–122.

[12] Towers Perrin, “Compensation Strategies for an Uncertain Economy: The Evolution Continues”, Towers, Watson & Co., 2009.

[13] WorldatWork, The WorldatWork Handbook of Compensation, Benefits & Total Rewards: A com-prehensive Guide for HR Professional, New York, John Wiley & Sons, 2007.

jamris 2014 vol 8 no 3

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