Tracking of a Moving Object with Occlusion by Using anActive Vision System

Takaya Hada* and Tetsuo Miyake

Department of Production Systems Engineering, Toyohashi University of Technology, Toyohashi, 441-8580 Japan

SUMMARY

A person can keep an object which moves accordingto rules in roughly the center of their field of vision at alltimes. Even if the object is occluded during its movement,the person can continue to track it by estimating its latermotion. In this paper, this kind of human system is takeninto consideration for an automatic monitoring system, andsuch a system is constructed using an active vision systemwith a pan and tilt rotary mechanism. In order to automat-ically monitor a scene over a wide area at high resolution,the object to be monitored must be tracked while changingthe pan and tilt using active vision. The tracking principleused in this system consists of detecting a moving objectand estimating its motion. Detection is accomplished byusing a background subtraction method which uses a back-ground database, and motion estimation is handled by aKalman filter. An experiment is performed on a person in atypical room environment, and it is confirmed that theperson can be tracked by the proposed system even whenoccluded. © 2003 Wiley Periodicals, Inc. Syst Comp Jpn,34(13): 92–102, 2003; Published online in Wiley Inter-Science (www.interscience.wiley.com). DOI 10.1002/scj.1222

Key words: active vision; motion estimation; Kal-man filter; occlusion; automatic monitoring system.

1. Introduction

In recent years there has been considerable researchdone on automatic monitoring systems using visual infor-mation as a result of improvements in image processingtechnology [1–6]. At present, monitoring using camerasgenerally involves having a human monitor judge the situ-ation based on images from monitoring cameras set up inseveral locations [7]. However, under this approach errorsdue to operator fatigue or inattention are inevitable. As aresult, there are increasing expectations for the develop-ment of automatic monitoring systems. In an automaticmonitoring system, when a wide area of view is monitored,what is to be monitored is taken as a small size of projectedimage. Therefore, in order to monitor at high resolutionwhat is to be monitored, it must be tracked by changing thepan and tilt of the camera, what is termed active vision.

When tracking an object which moves in three di-mensions, the object inevitably is occluded by obstacles. Atsuch times, under an approach to track an object by input-ting consecutive images [8, 9], when the object is notoccluded it can be tracked stably, and when it is occluded,position information for the object cannot be obtained, andso tracking cannot be maintained until the object reappearsin the camera’s field of vision.

On the other hand, a human can keep an object whichmoves in a relatively regular way within the center of heror his field of vision. Even if the object is occluded whilein motion, people can continue to track it by predicting itsfuture motion. In this paper the authors create a human-likesystem using an active vision system with a pan and tilt

© 2003 Wiley Periodicals, Inc.

Systems and Computers in Japan, Vol. 34, No. 13, 2003Translated from Denshi Joho Tsushin Gakkai Ronbunshi, Vol. J84-D-II, No. 1, January 2001, pp. 93–101

*Presently with Toyo Steel Co., Ltd.

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rotation mechanism, and then demonstrate its validitythrough experiments.

There are two principles used for tracking in thissystem: detecting a moving object and estimating its mo-tion. The background subtraction method is used to detectthe moving object. This method has a comparatively simplemechanism in which object motion can be detected effi-ciently by comparing the background image that has al-ready been taken with an observed image. In addition, aKalman filter is used for motion estimation of the movingobject. There are many practical examples in the literatureof motion estimation using a Kalman filter being performedin real time at a high degree of precision [4, 10–14].

The background subtraction method and the Kalmanfilter both have been used previously. The proposed systemattempts to maintain tracking even when the moving objectis occluded by combining these two methods. When detect-ing a moving object using the background subtractionmethod, at the same time that the object is detected, thestatus of object occlusion is also determined. Moreover, inmotion estimation using a Kalman filter, irregular humanmovement is represented using the variance of system noiseover short periods of time. Below, Section 2 describes themethod to detect a moving object, and Section 3 explainsthe motion estimation method for a moving object. Section4 offers a discussion of the object occlusion status andmultistage estimation. Section 5 presents the experimentalresults for tracking people in an indoor environment, anddemonstrates the validity of the proposed system.

2. A Detection Method for Moving Objects

2.1. The background subtraction methodusing a background database

The background subtraction method is one way todetect a moving object in a scene using video images. Thismethod involves a comparatively simple mechanism inwhich object motion can be detected efficiently by compar-ing a background image that has already been taken withan observed image. In this system, a background databasefor the camera’s range of motion is created beforehand inorder to use this method with active vision. Then an objectis detected by subtracting the background image generatedusing the database from the observed image.

2.2. Principles of background databasecreation

When rotating the camera while keeping the lenscenter fixed in place, the resulting image changes becausethe optical axis and camera plane change, even though the

same rays of light enter the lens from the same direction. Inthis system this property is used to create the backgrounddatabase. In other words, the background database is cre-ated based on the intensity of the set of light rays obtainedthrough observation by fixing in place the spatial positionof the center of the camera lens.

2.2.1. Conversion to three dimensions

The camera generally used in a vision system has sixexternal parameters and five internal parameters. The inter-nal parameters are related to central projection, and theirvalues do not vary with respect to the camera’s motion.Therefore, when using a camera whose internal parametersare already known, the relationship between the three-di-mensional coordinates of a point in space and the two-di-mensional coordinates of its projected image on an imageplane can be determined.

Figure 1 shows the coordinate system defined in thispaper. O−xyz, Oc−uvw, and Op−UV represent the worldcoordinate system, the camera coordinate system, and theimage coordinate system, respectively, Oc the position ofthe center of the camera lens, and f the distance betweenOc and the UV plane. In order to simplify the model, theposition Oc in the world coordinate system is taken to bethe point of origin O. The camera coordinate system rotateswith Oc being the center of rotation; the rotational angle formovement on the x axis is φ, and the rotational angle formovement on the y axis is θ. When the camera coordinatesystem matches the world coordinate system, the rotationalangles of φ and θ are both equal to 0, with a right-twistingmovement vis-à-vis the x and y axes being positive. More-over, the scaling factors for the U and V axis of the imagecoordinate system are KU and KV, respectively, with thecenter of the image being U0 and V0. If a point on the image

Fig. 1. The coordinate system.

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plane is PI (U, V), then the camera coordinates for that pointcan be represented using

When the direction of the optical axis of the camerais (θ, φ), then the coordinates PI (u, v, w) for this point inthe camera coordinate system can be converted to coordi-nates for the world coordinate system using Eq. (2) whereT(θ, φ) is a transformation matrix shown in Eq. (3):

2.2.2. Creating a panorama image

A panorama image is created by pasting togetherseveral observed images taken one next to the other. At thispoint, if the position of the center of the camera lens is fixedin place, then the light rays in the overlapping area on imageplane I1 and image plane I2 should match perfectly, asshown in Fig. 2. However, because of lens properties, theobserved images actually are distorted, and so the light raysin the overlapping areas do not coincide with each other.The effect of this distortion is lower as it occurs closer tothe center of the image. Thus, in this system, the overlap-

ping area near the center of the lens is used. In other words,a panorama image is created by pasting together small areasnear the axis of light.

When the camera coordinate axis for which the opti-cal axis direction is (θ0, φ0) is used as the reference, theequation for the image plane for which the optical axisdirection is (θ, φ) is

Here, each row of the transformation matrix for the rotation(θ0, φ0) can be expressed using

l, m, and n are expressed in Eq. (6) where n is the directioncosine for the optical axis of the camera in the worldcoordinate system shown in Eq. (7):

Note that “<, >” represent inner products. Based on Eq. (4),the intersection between the image plane I1 for which thedirection of the optical axis is (θ0, φ0) and the image planeI2 for which it is (θ, φ) can be represented using the equation

The image plane regions are divided using thisstraight line, and the data around the center of each imageis then extracted. Based on Eq. (8), the region which in-cludes the center in the image plane I1 can be representedusing

All of the images in this region are pasted together,and a panorama image without duplication or defect is thencreated.

2.2.3. Projection onto the reference screen

When creating a background image from a databasewhile using the panorama image created above as thedatabase, the data must be projected from multiple planes,and so processing can become complicated. Thus, the pano-rama image is projected onto a single reference screen.

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Fig. 2. Two image planes overlapping each other.

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Although a flat plane can be used as the reference screen,the focal distance is constant regardless of the direction ofthe optical axis, and the image plane is always perpendicu-lar to the axis. As a result, the set of light rays shown in Fig.3(a) are stored at a nonuniform density. Thus, the densityof the light rays in the database can be made almost uniformby projecting the panorama image onto a sphere whosecenter is the center of the camera lens.

As illustrated in Fig. 4, the flat data is projected on asphere with radius r whose center is the lens center Oc.Here, O−rqf represents the polar coordinate system, andthe point P(x, y, z) on the image plane in three-dimensionalspace is projected onto the point P′(θp, φp) on the sphere.The following equation can be obtained from the relation-ship between the points P and P′:

Based on this relationship, the panorama image inthree-dimensional space can be transformed to a polarcoordinate system. Figure 5 shows an example of the back-ground database.

2.3. Detecting the position of an object

The movement of an object can be detected by sub-tracting the background image created using the databasefrom the observed image. The background image can beeasily generated by cutting out the area from the databasesphere. The area is the oppositely projected area of theobserved image. A moving object is extracted from thesubtracted image by the luminance thresholding method,and the position of the center of gravity is taken to be theposition of the moving object.

3. A Method to Estimate the Motion of aMoving Object

A Kalman filter is used to estimate the motion of amoving object. Here, the Kalman filter is set up assumingthat the object moves in a circle with a center at the centerof the camera lens with uniform angular acceleration andthat its motion changes smoothly. A Kalman filter is typi-cally defined in a discrete time domain. In this paper, thesystem noise covariance matrix in a continuous time do-main is transformed in the discrete time domain, and theKalman filter is set up [15]. As a result, estimates can bemade in line with the changes in the system [10].

3.1. Determine the system equations

Use the following equation for the state variablevector for time t:

Fig. 3. Projection onto reference screen.

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Fig. 4. Projection onto a spherical surface.

Fig. 5. An example of the background database.

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A system to which uncertain randomness is added is repre-sented as

Here, A represents the constant matrix shown below

and W(t) represents the six-dimensional normal white noiseprocess. The state transition matrix F(t) of the system isshown as

By discretizing Eq. (12) with ∆ as the sampling interval, weobtain

In Eq. (15), F and Wk are as follows:

The covariance matrix associated with W(t) in this continu-ous time domain is assumed to be given by Q. Based on Eq.(17), the system noise covariance matrix in the discrete timedomain is given as

Here, if Q is given by Eq. (19), then X is represented by Eq.(20):

where σθ and σφ are as follows:

3.2. Setup of the Kalman filter

If the state variable vector is given by Eq. (11) andthe observed vector by

then the observation equation is

C is the constant matrix shown below, and Vk is thetwo-dimensional normal white noise process:

The Kalman filter is set up based on Eqs. (15) and (23). Thealgorithm is as follows:

R represents the observed noise covariance matrix, and isgiven by

Setting X and R is important for improving the precision ofthe estimates.

3.3. Setting the system noise covariance matrix

In a Kalman filter, setting the system noise covariancematrix greatly affects the precision of the estimates, and sosetting this value is important. In this paper, the variance ofthe system noise is calculated for a short period of time, andthe system noise covariance matrix is set based on this

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value. Here, only the change of the angular acceleration ofthe moving object from time (k – 1)∆ to k∆ is consideredas a system noise, and it is assumed that there is no corre-lation between θ and φ. The change of the angular accelera-tion of the moving object from time (k – 1)∆ to k∆ is givenby

The angular acceleration terms sθk and sφk in the systemnoise covariance matrix are calculated as

Here, N represents the number of data points, and ∆aθk

____ and

∆aφk

____ are as follows:

Because only the change of the angular accelerationof the moving object is assumed as the system noise, thevalues of qθ, rθ, qφ, and rφ are taken to be 0. sθk and sφk aresubstituted into Eqs. (20) and (21), yielding the systemnoise covariance matrix X.

4. Multistage Estimation of an OccludedObject

4.1. Detecting the state of occlusion

The position of the object is represented by the grav-ity center of the projected image of the object. When a partof the object is occluded, the position of the object isevaluated by that of the occluded object, which is differentfrom the position of the real center of gravity. Therefore,even when the object is detected, whether or not the objectis occluded must be judged.

The ratio of change with respect to the projected areaof the object in two consecutive images is used for deter-mining the state of occlusion. When the object is notoccluded, the projected area of the object is assumed lesschanged between two images. If the projected area of thedetected moving object is S, then the ratio of change of theprojected area between images is given by

Because the projected area decreases when the object isoccluded, only positive values are taken into considerationin Eq. (32). When the value exceeds a set threshold value,the object is taken to be occluded, and the camera’s orien-tation is controlled using multistage estimation.

4.2. Multistage estimation and object capture

When the object is occluded, the directional positionof the object cannot be known at that time. The estimateddirectional position at stage m is given using Eq. (33) wherethe point in time at which the object is occluded is thefirst-stage estimate:

If the object is in the field of view whose center is thedirection estimated at a single stage or a multiple stagealong the blind track of the moving object based on theestimation, then the tracking can be continued. In a single-stage estimation, the next estimation is made so as toeliminate any difference between the estimated directionand the real direction. Because this difference cannot becorrected while the object is occluded, when the object isagain observed, it cannot necessarily be captured in the fieldof vision. In order to finally minimize the difference, reduc-ing the difference between the apparent position of thegravity center of the projected image of the object observedat the point in time at which occlusion starts and the positionof the real center of gravity is important.

In order to eliminate this difference, the thresholdvalue for the ratio of change in the projected area must beset to as small a value as possible, and the occluded statemust be excluded. However, the projected area of the objectusually changes to a certain extent in images, and it maydecrease when the object is moving away or the shape ofthe object changes. As a result, these states are regarded asoccluded states. Conversely, if the threshold value is sethigh, this can lead to a large observational error. Thus, ifmultistage estimation is started based on these states as thefirst state, the estimation error will rise rapidly, and theobject will exit from the estimated field of vision.

Thus, the simulation was conducted using the modelshown in Fig. 6 for clarifying the relationship between theangle of movement of the object and the accompanyingestimation error with respect to the threshold for the ratioof change of the projected area. The object in simulationwas a cylinder with a 100-mm radius, and two types ofmotion were considered: circular motion at a uniformspeed, and linear motion at a uniform speed. For the sake

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of comparison, the conditions for the circular motion usedalmost the same values as those for the later experiment.The path and velocity of the linear motion were determinedin the following way. The path of the motion was parallelto the x-axis and it passes through the point Q shown in Fig.6. A range of motion from 0° to 45° was concerned, whichangle was formed between the z axis and the line connectingthe point of origin O to the object. The distance from O toQ was determined such that the average distance from O tothe object in the moving range concerned was almost equalto 5000 mm which was the radius of the circular motion.The velocity was determined such that the apparent averagevelocity in the moving range concerned was almost equalto the peripheral velocity of the circular motion. The start-ing point of occlusion in the linear motion was the point P

in the figure where the apparent velocity was almost thesame as the peripheral velocity of the circular motion.

When the estimation error exceeds the field of visionangle, the object cannot be tracked. For instance, for circu-lar motion when the field of vision angle is ±10°, if thethreshold for the ratio of change of the projected area is20%, based on Fig. 7, then the angle at which the object canmove in a state in the field of vision is roughly 17°. Forlinear motion under the same conditions, the angle at whichthe object can move is roughly 13°, based on Fig. 8. Theelapsed time for this motion is roughly 10 seconds in bothcases. For linear motion, when the object passes through asection that includes point Q in Fig. 6, the apparent angularacceleration changes from positive to negative. Therefore,if the object is occluded in this section, the estimation errorwill exceed the field of vision angle in a short time.

5. Tracking Experiment

5.1. System configuration

The proposed system consists of a CCD camera, acamera rotary stage that can pan and tilt, ordinary imageprocessing equipment, and a personal computer. Figure 9shows the system configuration for the active vision system.A CCD camera is mounted on the camera rotary stage, andit is set up so that the center of the camera lens coincideswith the center of rotation of the two axes in the camerarotary stage. The pan and tilt rotation of the camera rotarystage can be controlled very precisely using a pulse motor.The video information from the camera is sent to an ordi-nary image processor, and the image processor is connectedto a computer using a PCI bus. The two-axis controller ofthe camera rotary stage is connected to the computer using

Fig. 6. Simulation model.

Fig. 7. Limit of tracking (circular motion).

Fig. 8. Limit of tracking (linear motion).

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an RS-232C interface. The computer calculates the direc-tional position of the moving object based on the imageinformation from the image processor and position infor-mation from the two-axis controller and then controls therotary stage. It also controls the timing for processingoverall.

5.2. Processing procedures

The processing procedures in this system are outlinedbelow and its flowchart is shown in Fig. 10.

[Step 0] A background database is created for therange of the camera’s motion.

[Step 1] The image is acquired, and it is subtractedby the background image generated from the backgrounddatabase.

[Step 2] After starting tracking, estimation using theKalman filter cannot be performed, and as a result thecamera is directed to the orientation in which the object wasdetected and the process returns to Step 1.

[Step 3] The camera is pointed in the estimateddirection based on the detected position of the center ofgravity, then the process returns to Step 1. If the object wasnot detected, or if the ratio of change of the projected areaexceeded the threshold, then the camera’s orientation iscontrolled using multistage estimation, and the process thenreturns to Step 1.

5.3. Experiment

An experiment on a person was conducted in anordinary room environment. The observed noise covariancematrix R was set after taking the quantized error in theimage into consideration. By assuming that the observationnoise follows a normal distribution and the width of ±3σ is

equal to the size of one pixel, the variance of the observationnoise was determined, and each element of R was set. Theresults of the experiment are shown in Fig. 11. The sam-pling interval for the images was 1.5 s, and the optical axisof the camera (pan and tilt) at each sampling time is shownin the upper portion of each image. The number of pixelsin each image is 73 × 63, the angle of the field of vision is–10.08 to 10.08° in the θ direction, and –8.68 to 8.68° inthe φ direction. The threshold value for the ratio of changeof the projected area in the experiment was 20%.

In this system, since past sampled data of the objectmotion are used to set the system noise covariance matrixX after tracking starts, the camera tracks the object byorienting the optical axis to the direction in which the objectwas detected at one sampling before. After several times ofsampling have been done, the method for tracking isswitched to orient the camera in the direction estimated bythe Kalman filter. In Fig. 11, the results are shown for afterthe point in time when the method of tracking is switched.

In Nos. 1 to 4, since the person was not occluded, itis clear that the person could be captured near the center ofthe image in a stable manner. Based on this, it can be saidthat the method for setting the system noise covariancematrix and the observation noise covariance matrix is valid.In No. 5, the person was determined as being occluded, and

Fig. 9. System configuration.

Fig. 10. Flowchart.

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so the orientation of the camera was adjusted based onmultistage estimation until No. 10. In No. 10 the personreappeared, and was stably tracked until No. 30. In No. 31,the person was again determined to be occluded, and theorientation of the camera was adjusted using multistageestimation until No. 36, after which the person reappeared,and tracking continued using single-stage estimation there-after.

In this experiment the person was occluded twotimes, and moved roughly 13.5° in either case. Comparedto the simulation results in which the threshold value for theratio of change of the projected area was 20%, it is clearthat the estimated error for when the person reappeared wasrather small. This is thought to be because the front part ofthe body was not occluded when the multistage estimation

started, the state of movement related to forward motionwas estimated accurately.

Based on Fig. 11, it is confirmed that by using aKalman filter as a method to measure movement, when aperson was not occluded, the person could be continuouslyheld near the center of the image, and even when the personwas temporarily occluded, the system could also track himor her as long as there were no sudden changes in angularacceleration.

6. Conclusion

An automatic monitoring system using video infor-mation can be expected to be used in various ways, includ-

Fig. 11. Experimental results (upper: observed image; lower: detected object).

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ing building security management. In this paper we createda tracking system for moving objects using active visionwith a pan and tilt mechanism in order to monitor a widearea at high resolution. In order to deal with situations inwhich the object to be tracked is occluded by an obstacle,we used a Kalman filter as a way to estimate the motion ofthe moving object, and applied multistage estimation so asto be able to track even when the object was temporarilyoccluded.

One factor which determined whether or not an ob-ject could be captured again after multistage estimation wasthe change in the apparent motion status of the object whileit was occluded. Because the apparent speed of objects thatare in uniform linear motion changes, if the object is oc-cluded a long time, the object may be lost. In addition, it isimportant to determine whether or not the position of theobject’s center of gravity observed at the start of occlusionis valid. In this paper, this was determined using the ratioof change of the projected area. Although the threshold ofdetermination was fixed, because the degree of the effect ofobservation errors due to changes in the object’s motionvelocity varies, regulating the threshold value depending onthe velocity must be considered.

The experimental results confirmed that the systemcan track an object even when it is temporarily occluded.At the present time, estimations are performed by detectingthe direction where the moving object exists based onimage information from a single camera. If position infor-mation for the object is obtained in three dimensions, thereliability of the estimates should rise. Future topics includethe development of an object search algorithm for when theobject is deemed to have been lost, acquisition of depthinformation on the object, tracking multiple objects, andimprovements in processing speed.

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AUTHORS (from left to right)

Takaya Hada (member) graduated from the Department of Electrical Engineering at Ube National College of Technologyin 1996 and joined Toyo Steel Co. He received his B.S. and M.S. degrees from the Department of Production SystemsEngineering at Toyohashi University of Technology in 1998 and 2000. His research interests include machine vision. He is amember of the Institute of Electrical Engineers of Japan and the Society of Instrument and Control Engineers.

Tetsuo Miyake (member) received his B.S. and M.S. degrees in agricultural mechanical engineering and doctoral degreein electrical and electronic engineering from Tokyo University in 1975, 1978, and 1987. He worked in the Central ResearchLaboratory of Asahi Glass Co. from 1984 to 1990. He is currently an associate professor at Toyohashi University of Technology.His research interests include noncontact measurement, motion tracking, and human interface. He is a member of the InformationProcessing Society of Japan, the Institute of Image Information and Television, the Society of Instrument and Control Engineers,and the IEEE Computer Society.

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