International Journal of Rock Mechanics & Mining Sciences 48 (2011) 1215–1223

Contents lists available at SciVerse ScienceDirect

International Journal ofRock Mechanics & Mining Sciences

1365-16

doi:10.1

n Corr

vation (

fax: þ3

E-m

journal homepage: www.elsevier.com/locate/ijrmms

Influence of range measurement noise on roughness characterization of rocksurfaces using terrestrial laser scanning

Kourosh Khoshelham a,c,n, Dogan Altundag a, Dominique Ngan-Tillard b, Massimo Menenti a

a Optical and Laser Remote Sensing, Delft University of Technology, Delft, The Netherlandsb Faculty of Civil Engineering and Geosciences, Department of Geotechnology, Delft University of Technology, Delft, The Netherlandsc ITC, Faculty of Geoinformation Science and Earth Observation, University of Twente, The Netherlands

a r t i c l e i n f o

Article history:

Received 19 February 2010

Received in revised form

14 July 2011

Accepted 6 September 2011Available online 4 October 2011

Keywords:

Roughness length

Fractal dimension

Wavelet de-noising

Laser scanning

Noise

09/$ - see front matter & 2011 Elsevier Ltd. A

016/j.ijrmms.2011.09.007

esponding author at: Faculty of Geoinformat

ITC), University of Twente, The Netherlands.

1 53 4874335.

ail address: khoshelham@itc.nl (K. Khoshelha

a b s t r a c t

The application of laser scanning in studying rock surfaces is limited by the range measurement noise

inherent in the laser scanner data. In this paper we investigate the influence of range measurement

noise on the quantification of rock surface roughness. Roughness measures derived from the laser

scanner data are compared with those derived from manual measurements. The comparison shows that

the presense of noise in range measurements leads to an overestimation of the fractal dimension and

amplitude of roughness profiles. Experiments with wavelet decomposition and thresholding methods

for reducing noise in the laser range data are presented. The results indicate that wavelet de-noising

methods in general lead to more realistic estimates of the roughness of the laser profiles.

& 2011 Elsevier Ltd. All rights reserved.

1. Introduction

In recent years there has been a growing interest in theapplication of terrestrial laser scanning to the characterizationof rock surface properties. The potential of laser scanner data hasbeen shown in studying coastal cliffs [1,2], measurement of highrock slopes and monitoring of rockslides [3–5], measurement ofdiscontinuity orientation [6,7] and characterization of rock sur-face roughness [8–15]. Surface roughness is an important para-meter that controls the hydro-mechanical behavior of rockmasses. Rock surface roughness affects the shear strength of adiscontinuity, especially at low stresses, when shear movementalong a rough surfaced discontinuity must be accompanied byvertical dilation. Several theories relate the surface roughness tothe shear strength of a discontinuity [16–22]. Roughness is oftencharacterized by statistical parameters based on the averageand standard deviation of asperity heights or angles on the rocksurface [23].

The advantages of terrestrial laser scanning over manualmeasurement methods in measuring rocks include large cover-age, high resolution, and the ability to reach inaccessible highrock faces. A fundamental limitation of the technique, particularly

ll rights reserved.

ion Science and Earth Obser-

Tel.: þ31 53 4874477;

m).

in the measurement of fine scale surface roughness, is themeasurement noise inherent in the laser scanner data. In general,error in the laser scanner data may originate from the followingmain sources [24]: the imprecision of the scanning mechanism,the ranging technique and the physical and geometric propertiesof the laser beam [25], environmental conditions [26] and thephysical and geometric properties of the scanned surface itself[27,28]. Normally the systematic components of the error areeliminated or modeled through a proper calibration procedure [29].The remaining random error is in the order of a few millimeters for atypical medium-range (1–150 m) terrestrial laser scanner and iswhat is referred to as measurement noise.

The effect of laser scanner measurement noise on roughnesscharacterization has been pointed out in a few previous studies.In principle, any form of measurement noise appears as exagger-ated surface roughness. Fardin et al. [10] reported that the fractaldimension obtained from raw laser data of a rock face is largerthan the expected range (1.2–1.7 for 1D profiles and 2.2–2.7 for2D patches according to Kulatilake and Um [30]). They attributedthe overestimated roughness to the irregular distribution of thepoints in the original point cloud, and performed an interpolationof the points into a uniform distribution to reduce the fractaldimension to within the expected range. Rahman et al. [11]suggested that the overestimation of the surface roughnessobtained from raw laser data is due to the fact that the roughnessmeasures actually measure noise in the data, rather than theroughness of the surface. They used radial basis functions to

K. Khoshelham et al. / International Journal of Rock Mechanics & Mining Sciences 48 (2011) 1215–12231216

interpolate the data into a smooth surface, which resulted inroughness measures within the expected range. Although datasmoothing in conjunction with interpolation methods has beenthe common approach to reduce the influence of noise onroughness characterization, it is generally not considered anadequate noise reduction method [31]. The basic assumption indata smoothing is that the measured surface is actually smoothand so by smoothing one can reduce the noise without degradingthe data related to the actual surface. As this assumption is notvalid when dealing with rough surfaces, the result of datasmoothing is the loss of roughness information. Thus, a carefultreatment of noise in laser range data is of great significance if arealistic characterization of rock surface roughness is of concern.

The objective of this paper is to investigate the influence ofrange measurement noise on the roughness characterizationof rock surfaces using the roughness length method [32]. Weanalyze the sensitivity of roughness measures to different levelsof noise for different scales of roughness. We also demonstratethe application of wavelet transform [33,34] to reducing noise inroughness profiles derived from laser scanner point clouds, andcompare the performance of various wavelet decomposition andthresholding methods.

The paper proceeds with an overview of the laser scanningtechnique and the derivation of roughness profiles from laser rangedata in Section 2. In Section 3, the principles of wavelet-basedde-noising are presented along with a description of variousdecomposition and thresholding methods. Section 4 presents anexperimental analysis of the influence of noise on roughness charac-terization and the results of wavelet de-noising of roughness profiles.The paper concludes with some general remarks in Section 5.

Fig. 1. Wavelet de-noising procedure.

2. Rock surface roughness from laser range data

Laser scanning is an active measurement technique based onemitting laser beams to a surface of interest and recording thereflections. A scanning mechanism, usually a rotating mirror,directs the emitted beam towards the surface in such a way thatthe entire surface is scanned at regular horizontal and verticalangular intervals. The range measurement principle in medium-range terrestrial laser scanners is most often based on the phasedifference between the emitted and received waveforms. Fromthe measured range and horizontal and vertical scan angles, 3Dcoordinates are computed for each point in a Cartesian coordinatesystem with its origin at the center of the scanner. Today’s laserscanners can measure more than a hundred thousand pointsper second at an angular resolution smaller than 0.01 degrees (seefor instance Faro [35]). By scanning at such high resolution from afew tens of meters distance to a rock face one can acquire a densepoint cloud that represents the geometry of the scanned surfacein great detail.

Before roughness information is derived from a point cloud itis convenient to rotate the point cloud such that the surfaceroughness corresponds to variations in the direction of the Z-axis.Based on the assumption that the point cloud represents a moreor less flat surface, the rotation can be computed simply byperforming the principal components analysis [36]. The eigen-vectors and eigenvalues of the covariance matrix of the pointsdescribe the axes of maximum and minimum variation in thepoint cloud, and provide a transformation of the points to theseprincipal axes. By fitting a smooth (usually planar) surface to thisrotated point cloud a representation of the roughness as theresidual height of the points can be obtained.

A common method for roughness characterization, which isalso adopted in this paper, is the fractal-based roughness lengthmethod [32]. In this method, roughness is characterized by two

measures: fractal dimension and amplitude. Both measures canbe derived from a 1D profile or a 2D patch extracted from thepoint cloud, though 2D fractals do not support directional analysisof the surface roughness [12,37,38]. In either case, the roughnessmeasures are estimated based on a power law relation betweenthe standard deviation of the residual height of the points, s, andthe length of a sampling window w:

sðwÞ ¼ AwH ð1Þ

where parameters A and H are called amplitude and the Hurstexponent, respectively. These parameters are estimated from theintercept and slope of a log–log plot of s versus w for severallengths of the sampling window. The main measure of roughnessis the fractal dimension, which is derived from the Hurst expo-nent as D¼2�H for a 1D profile, and D¼3�H for a 2D patch.A large fractal dimension indicates a very rough surface withabrupt changes of the residual height, whereas a small fractaldimension implies a smooth surface without much roughness.Fractal dimension has implications in the shear strength of rockjoints. Kulatilake et al. [39] quantitatively related self-affinefractal dimensions to surface roughness characteristics and accu-rately predicted, using a shear strength criterion based on fractalparameters, the shear resistance of joints measured in the labora-tory. More details on the estimation of fractal dimension for 1Dprofiles can be found in [30], and for 2D patches in [10]. In the restof the paper we focus on the characterization of roughness in 1Dprofiles.

3. Wavelet de-noising of roughness profiles

Noise is characterized by high frequency fluctuations in themeasured profile. Therefore, if a profile can be decomposed intohigh frequency and low frequency components, the high fre-quency components are more likely to contain noise than the lowfrequency components that contain the general trend of theprofile. Wavelet de-noising is based on the wavelet transform[34] for decomposing a signal into several components of differ-ent scales and resolutions. Comparing to other data decomposi-tion methods such as the Fourier transform [40], wavelets oftenprovide a better multi-resolution representation of complex data[41]. The principle of wavelet de-noising is to remove the noiseonly from the high frequency components in order to preservethe low frequency content of the data as much as possible. Theprocedure for the wavelet de-noising of a roughness profileconsists of several steps as shown in Fig. 1. The first step is thedecomposition, which can be done by the discrete wavelettransform or by the wavelet packet method. The actual de-noisingis performed by applying a threshold to the high-frequencycomponents. The value of the threshold depends on an estimationof the level of noise in the data and the threshold selectionmethod. The application of the threshold can also be done in softmode as well as hard mode. The final step involves the recon-struction of the thresholded components to yield the de-noised

K. Khoshelham et al. / International Journal of Rock Mechanics & Mining Sciences 48 (2011) 1215–1223 1217

profile. The following sections provide a more detailed descrip-tion of the wavelet de-noising procedure.

3.1. Wavelet decomposition and reconstruction

The wavelet decomposition process consists of two opera-tions: filtering and downsampling. Filtering separates the signalinto components of different scales: convolution with a low-passfilter generates the low-frequency components known as approx-imation coefficients, and convolution with a high-pass filterresults in the high frequency components known as detailcoefficients. The down-sampling operation reduces the resolutionof the coefficients to one-half. The decomposition process may beiterated in several levels. In multi-level decomposition we distin-guish between two decomposition principles. In the discretewavelet transform (DWT), the decomposition is applied toapproximation coefficients only. In the wavelet packet method(WP) both the approximations and the details are decomposed.Fig. 2 illustrates the decomposition of a roughness profile in threelevels using both the discrete wavelet transform and the waveletpacket method.

Wavelet reconstruction is the process of recovering the origi-nal profile from its components. The reconstruction processconsists of two operations: upsampling and filtering. The compo-nents are upsampled by inserting zeros between the samples andthen convolved with the reconstruction filters. The approximationcoefficients are convolved with a dual low-pass filter, and thedetail coefficients are convolved with a dual high-pass filter. Thereconstructed approximations and details are then summed up toyield the reconstructed profile. The decomposition and recon-struction filters should meet certain requirements in order toguarantee a perfect reconstruction of the data from the coeffi-cients. A detailed description of the design of wavelet filters canbe found in Strang and Nguyen [34].

3.2. Thresholding of wavelet coefficients

De-noising by the thresholding of wavelet coefficients is basedon an important property of wavelet decomposition that trans-forms white noise into white noise [42]. Since normally systema-tic errors are eliminated from the laser scanner data it is prudentto assume that the remaining error is white noise with Gaussiandistribution. The thresholding is usually applied to the detailcoefficients to ensure the preservation of the actual data. Thereare several methods for the estimation of the threshold value.

Fig. 2. Decomposition of a roughness profile by discrete

In this paper, we compare two main threshold estimation meth-ods: fixed-form thresholding and penalized thresholding.

The fixed-form thresholding method was proposed by Donohoand Johnstone [43]. For the detail coefficients of a profile obtainedby the discrete wavelet transform the fixed-form threshold isestimated as

tf ¼ sn

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2logðdÞ

pð2Þ

where d is the length of the detail coefficients at the first level ofdecomposition, and sn is the standard deviation of noise. For thewavelet packet decomposition of a profile the fixed-form thresh-old is estimated as

tf ¼ sn

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2logðd logðdÞ=logð2ÞÞ

qð3Þ

To estimate the standard deviation of noise from the data themedian absolute deviation (MAD) of the coefficients has beenproposed by Donoho and Johnstone [42]:

sn ¼1

0:6745Medianð9wk9Þ ð4Þ

where wk are the detail coefficients at the first decompositionlevel.

The penalized thresholding method was proposed by Birgeand Massart [44]. This method is based on minimizing a penaltyfunction defined as

tn ¼ arg mint ¼ 1,:::,n

�Xðw2

k ,kotÞþ2ts2n aþ log

n

t

� �� �h ið5Þ

where a is a sparsity parameter and n is the number of detailcoefficients wk sorted in descending order. The penalized thresh-old for both the discrete wavelet transform and the waveletpacket is then estimated as

tp ¼ 9wtn 9 ð6Þ

The sparsity parameter a can be tuned to obtain differentthreshold values. Three levels of penalized thresholding arecommon: penalized low (a¼1.5); penalized medium (a¼2); andpenalized high (a¼5).

The application of the threshold can also be done in twomodes. The standard hard thresholding criterion is defined as

whj,k ¼

wj,k if 9wj,k9Zt

0 if 9wj,k9ot

(ð7Þ

wavelet transform (left) and wavelet packet (right).

K. Khoshelham et al. / International Journal of Rock Mechanics & Mining Sciences 48 (2011) 1215–12231218

where t is the threshold and wj,k are wavelet coefficients. The softthresholding criterion is defined as

wsj,k ¼

signðwj,kÞð9wj,k9�tÞ if 9wj,k9Zt

0 if 9wj,k9ot

(ð8Þ

The soft thresholding criterion for wavelet de-noising wassuggested by Donoho [45]. In contrast to hard thresholding,which can result in discontinuities (sharp drops) in the de-noisedprofile, soft thresholding yields a smooth output. Fig. 3 demon-strates the difference between the hard and soft thresholdingmodes. In the hard thresholding mode data beyond the thresholdare preserved, but discontinuities are inevitable. Soft thresholdingon the other hand shrinks the entire profile in order to preventthe occurrence of discontinuities.

4. Experiments and results

In this section experiments with roughness profiles measuredmanually and by a laser scanner on a rock surface are presented.First, the study area and data preparations are described. Then,the influence of various levels of noise on profiles of differentroughnesses is shown through two simulations. Finally, the resultsof the de-noising methods are compared and discussed.

4.1. Study area

The scanned rock is situated in Tailfer, about 20 km south ofthe city of Namur and on the east side of the Meuse River insouthern Belgium. The geological character of the scanned rock is

Fig. 3. The concept of hard and soft thresholding.

Fig. 4. Manual measurement of roughness profiles (left) and cutout of the rotate

a slightly metamorphosed limestone that is part of Lustin forma-tion of carbonate mounts.

4.2. Data preparation

The rock surface was scanned with a Faro LS880 terrestriallaser scanner [35]. The scanner was positioned at approximately5 m distance to the rock surface, and operated at the highestpossible angular resolution, i.e. 0.0091. The resulting point cloudcontained about 1.2 million points on the rock surface with apoint-spacing of 1 mm on average. According to the technicalspecifications of the laser scanner, the nominal range precision ata perpendicular incidence angle, which was roughly the case inour scan, is between 0.7 mm and 5.2 mm, respectively, for objectsof 90% and 10% reflectivity at a distance of 10 m.

Roughness data were also collected manually along threeprofiles on the rock surface using a carpenter’s profile gage withmetallic rods at 1 mm intervals. These profiles were markedwith white chalk and were visible in the reflectance image of thelaser scanner data. Fig. 4 shows the profiles along which manualmeasurements were made, and their traces in the reflectance dataof the point cloud.

The principal components were computed for a cutout of thepoint cloud that contained the profiles. The transformation para-meters were then applied to rotate the point cloud into a more orless horizontal surface. Guided by the chalk traces in the reflectanceimage, three corresponding roughness profiles were extracted fromthe point cloud with samples interpolated at regular 1 mm intervals.The results of this procedure were three pairs of roughness profilesderived correspondingly from the manual and laser measurementswith the same length and spatial resolution. We refer to these as thehorizontal, diagonal and vertical profiles. Fig. 5 depicts the corre-sponding manual and laser roughness profiles in the horizontaldirection.

4.3. Results

Using the roughness length method the fractal dimension andamplitude were estimated for the roughness profiles from boththe laser scanner data and the manual measurements. The unit ofprofile length was chosen as 1 cm for all profiles to guarantee anappropriate density of ten points per unit length. The power lawrelation was determined for each profile by calculating the standarddeviation of the profile height within windows of eight differentsizes ranging from 3% to 10% of the profile length. Fig. 6 illustratesthe power law relation between the window size and the standarddeviation of the profile height for the laser and manual profiles inthe horizontal direction. Here, the estimated fractal dimensions are1.17 for the manual profile, and 1.96 for the laser profile. Consider-ing the expected range of 1.2–1.7, the laser profile yields a clearly

d point cloud of the rock surface visualized with reflectance values (right).

Fig. 6. The log–log plot of the standard deviation of profile height against window

length for the laser and manually measured profiles in the horizontal direction.

Fig. 5. Manually measured and laser scanned roughness profiles in the horizontal direction.

K. Khoshelham et al. / International Journal of Rock Mechanics & Mining Sciences 48 (2011) 1215–1223 1219

overestimated measure of roughness, while the fractal dimension ofthe manual profile is also slightly below the expected range. Theestimated amplitude values are 0.02 mm and 0.21 mm, respec-tively, for the manual profile and the laser profile.

4.3.1. Simulation results

To investigate the influence of noise on the estimation offractal dimension different levels of white noise were added tothe manually measured profile in the horizontal direction and thefractal dimension was estimated for each resulting profile. Fig. 7shows the resulting fractal dimensions of the simulated noisyprofiles as a function of the noise standard deviation. As it can beseen, the fractal dimension is quite sensitive to noise and quicklyreaches its upper bound at a noise standard deviation of only1 mm. This is an important observation, and has significantimplications in the analysis of the shear behavior of rock joints,which is related to roughness. The influence of noise on rough-ness measures directly impacts the estimation of shear strengthand results in overestimated values.

To analyze the effect of noise on profiles of different rough-nesses a number of profiles with different fractal dimensions andamplitude parameters were simulated. To each profile white noisewith a standard deviation of 1 mm was added, and the estimatedroughness measures were compared with the initial values. Fig. 8shows the increase in the estimated fractal dimension of thesimulated noisy profiles as a function of the fractal dimension ofthe initial noiseless profiles. It is clear that the influence of noise islarger on profiles of smaller fractal dimension. For a very roughprofile with D¼1.7 the effect of the additive noise is 6% increase inthe estimated D, whereas for a smoother profile with D¼1.2 theincrease in D due to noise is 42%. In Fig. 9 the increase in theamplitude of the simulated profiles caused by the additive noise isshown. Here also the profiles with smaller amplitude are more

affected by the additive noise as judged by the larger increase inthe estimated A.

4.3.2. De-noising results

To study the role of wavelet de-noising, different waveletdecompositions and thresholding methods were applied to thelaser profiles and the estimated fractal dimension and amplitudevalues for the de-noised profiles were compared with those of themanual profiles. For all profiles the decomposition was performedin 3 levels using a Daubechies wavelet of order 3 (db3). Thestandard deviation of noise was found to be 1.8 mm, 1.3 mm and1.5 mm, respectively, for the laser profile in the horizontal,diagonal and vertical direction. From these estimated noise levelsthresholds were computed using the methods described inSection 3.2, and were applied to the detail coefficients globallyat all decomposition levels. Table 1 summarizes the fractaldimension and amplitude values estimated for the de-noisedprofiles obtained using the discrete wavelet transform as thedecomposition method. The same measures estimated for the de-noised profiles obtained using the wavelet packets are summar-ized in Table 2. It can be seen that the fractal dimensions of thede-noised profiles vary across different thresholding methods.The variation is however smaller across different decompositionmethods. The amplitudes of the de-noised profiles also exhibitsome variation, but are overall closer to the amplitude of thecorresponding manually measured profile.

Fig. 10 shows the fractal dimensions of the de-noised profilesin the horizontal direction against different decomposition andthresholding methods. As it can be seen, the choice of thedecomposition method has a minor impact on the fractal dimen-sion of the de-noised profiles: the fractal dimensions pertaining tothe discrete wavelet transform are only slightly larger than thoseof the wavelet packets.

A noticeable difference in the performance of the de-noisingmethods can be seen in the application of hard and soft thresh-olding modes. Fig. 11 shows the effect of hard and soft threshold-ing on the fractal dimension obtained for the de-noised profiles inthe horizontal direction. Soft thresholding results in too smoothde-noised profiles for which the estimated fractal dimensions aresmaller than that of the manually measured profile and below theexpected range. On the contrary, the de-noised profiles obtainedby hard thresholding yield fractal dimensions that are within theexpected range, except when penalized-high thresholding methodis used. The fractal dimensions corresponding to the penalizedhigh thresholding with both decomposition methods are in factsmaller than 1.

The amplitude measures given in Tables 1 and 2 seem to beless sensitive to the choice of wavelet decomposition and thresh-olding method. Fig. 12 shows that the amplitude values of the de-noised profiles obtained by different decomposition methods arevery close. The choice between hard and soft thresholding modesresults in a more noticeable change of the amplitude of the de-noised profiles, as shown in Fig. 13. The amplitude values for thede-noised profiles are overall close to that of the manuallymeasured profile, although amplitudes corresponding to the hard

Fig. 7. Effect of different levels of white noise on fractal dimension estimated for the manually measured profile.

Fig. 8. Effect of white noise with s¼1 mm on profiles of different fractal dimensions.

Fig. 9. Effect of white noise with s¼1 mm on profiles of different amplitudes.

Table 1Fractal dimension and amplitude values estimated for the de-noised profiles using discrete wavelet transform as the decomposition method.

Horizontal profile Diagonal profile Vertical profile

D A D A D A

Original profile extracted from laser data 1.96 0.21 1.89 0.19 1.90 0.19

De-noised profiles

obtained by discrete

wavelet transform

Soft threshold Fixed-form 1.05 0.02 1.23 0.05 0.81 0.03

Penalized Low 1.23 0.03 1.38 0.06 1.19 0.04

Medium 1.07 0.02 1.32 0.05 1.07 0.03

High 0.94 0.02 1.19 0.04 0.62 0.02

Hard threshold Fixed-form 1.51 0.05 1.46 0.07 1.33 0.06

Penalized Low 1.68 0.08 1.76 0.13 1.68 0.11

Medium 1.51 0.05 1.69 0.12 1.59 0.09

High 0.94 0.02 1.44 0.07 0.62 0.02

Manually measured profile 1.17 0.02 1.32 0.02 1.20 0.02

K. Khoshelham et al. / International Journal of Rock Mechanics & Mining Sciences 48 (2011) 1215–12231220

Fig. 10. Performance of decomposition methods with different thresholds evaluated by the fractal dimension of de-noised profiles.

Fig. 11. Effect of soft and hard thresholds on the fractal dimension of de-noised profiles.

Table 2Fractal dimension and amplitude values estimated for the de-noised profiles using wavelet packets as the decomposition method.

Horizontal profile Diagonal profile Vertical profile

D A D A D A

Original profile extracted from laser data 1.96 0.21 1.89 0.19 1.90 0.19

De-noised profiles

obtained by

wavelet packets

Soft threshold Fixed-form 0.95 0.02 1.09 0.04 0.74 0.02

Penalized Low 1.10 0.02 1.40 0.06 1.11 0.04

Medium 1.10 0.02 1.26 0.05 0.95 0.03

High 0.94 0.02 1.08 0.04 0.66 0.02

Hard threshold Fixed-form 1.42 0.05 1.38 0.06 1.30 0.05

Penalized Low 1.52 0.06 1.79 0.14 1.66 0.10

Medium 1.52 0.06 1.74 0.12 1.47 0.07

High 0.94 0.02 1.19 0.05 1.18 0.04

Manually measured profile 1.17 0.02 1.32 0.02 1.20 0.02

K. Khoshelham et al. / International Journal of Rock Mechanics & Mining Sciences 48 (2011) 1215–1223 1221

thresholding mode are larger than those corresponding to thesoft mode.

From these results it is clear that the selection of a suitablethresholding method is not straightforward. A comparison ofthe thresholding modes suggests that soft thresholding possiblydegrades the actual roughness information and therefore itsapplication for de-nosing roughness profiles is not recommended.The fixed-form threshold applied in hard mode to the coefficientsobtained by the wavelet packet decomposition yields roughnessmeasures that are close to those of the manually measured profilesand are also within the expected range. Fig. 14 shows the result offixed-form hard thresholding applied to the WP coefficients of thehorizontal laser profile, which compares reasonably well with thecorresponding manually measured profile.

5. Concluding remarks

In this paper we investigated the influence of noise on thequantification of rock surface roughness in laser range data,and the role of wavelet de-noising in obtaining more reliableestimates of roughness parameters. From the presented experi-mental results and analyses the following main points can beconcluded:

�

The fractal dimension is very sensitive to noise. The presenceof only 1 mm white noise increases the fractal dimension to itsmaximum possible value. This finding has important implica-tions in the estimation of shear strength from the roughnessderived from laser range data. The influence of noise on

Fig. 13. Effect of soft and hard thresholds on the amplitude of de-noised profiles.

Fig. 14. De-noised laser profile obtained by fixed-form hard thresholding of the WP coefficients compared with the corresponding manually measured profile.

Fig. 12. Performance of decomposition methods with different thresholds evaluated by the amplitude of de-noised profiles.

K. Khoshelham et al. / International Journal of Rock Mechanics & Mining Sciences 48 (2011) 1215–12231222

roughness measures directly affects the estimation of shearstrength and results in overestimated values.

� The effect of noise is larger on roughness profiles with smaller

fractal dimension and amplitude (less rough profiles).

� The application of wavelet de-noising methods in general led

to more realistic estimates of the roughness of the laserprofiles. However, the choice of the thresholding method isnot straightforward. Our results suggest that hard threshold-ing yields more reliable de-noised profiles for which theestimated roughness measures are close to those of themanually measured profiles. Soft thresholding results in pos-sible degradation of the actual roughness information and itsuse is not recommended.

In this research, we focused on the roughness length methodand the fractal dimension for the characterization of roughness.Possible topics for further research include an investigation ofother roughness characterization methods and the developmentof new roughness measures that are robust against noise.

References

[1] Rosser NJ, Petley DN, Lim M, Dunning SA, Allison RJ. Terrestrial laser scanningfor monitoring the process of hard rock coastal cliff erosion. Q J Eng GeolHydrogeol 2005;38:363–75.

[2] Dewez T, Gebrayel D, Lhomme D, Robin Y. Quantifying morphologicalchanges of sandy coasts by photogrammetry and cliff coasts by lasergram-metry. In: Proceedings of the conference on new approaches of coastal risks.Paris: Soc Hydrotechnique France; 2008. p. 32–7.

[3] Huang RQ, Dong XJ. Application of three-dimensional laser scanning andsurveying in geological investigation of high rock slope. J China Univ Geosci2008;19:184–90.

[4] Sturzenegger M, Stead D. Quantifying discontinuity orientation and persistenceon high mountain rock slopes and large landslides using terrestrial remotesensing techniques. Nat Hazards Earth Syst Sci 2009;9:267–87.

[5] Oppikofer T, Jaboyedoff M, Blikra L, Derron MH, Metzger R. Characterizationand monitoring of the Aknes rockslide using terrestrial laser scanning.Nat Hazards Earth Syst Sci 2009;9:1003–19.

[6] Slob S, van Knapen B, Hack R, Turner K, Kemeny J. A method for automateddiscontinuity analysis of rock slopes with 3D laser scanning. In: Proceedingsof the 84th annual meeting on transport research board, Washington, DC;2005. p. 187–94.

[7] Sturzenegger M, Stead D. Close-range terrestrial digital photogrammetry andterrestrial laser scanning for discontinuity characterization on rock cuts.Eng Geol 2009;106:163–82.

[8] Lanaro F. A random field model for surface roughness and aperture of rockfractures. Int J Rock Mech Min Sci 2000;37:1195–210.

[9] Feng Q, Fardin N, Jing L, Stephansson O. A new method for in-situ non-contactroughness measurement of large rock fracture surfaces. Rock Mech Rock Eng2003;36:3–25.

[10] Fardin N, Feng Q, Stephansson O. Application of a new in situ 3D laserscanner to study the scale effect on the rock joint surface roughness.Int J Rock Mech Min Sci 2004;41:329–35.

[11] Rahman Z, Slob S, Hack R. Deriving roughness characteristics of rock massdiscontinuities from terrestrial laser scan data. In: Proceedings of the 10thIAEG congress, Nottingham; 2006.

[12] Haneberg W. Directional roughness profiles from three-dimensional photo-grammetric or laser scanner point clouds. In: Eberhardt E, Stead D, Morrison T,

K. Khoshelham et al. / International Journal of Rock Mechanics & Mining Sciences 48 (2011) 1215–1223 1223

editors. Proceedings of the first Canadian/US rock mechanics symposium,Vancouver. London: Taylor & Francis; 2007. p. 101–6.

[13] Poropat GV. Remote characterisation of surface roughness of rock disconti-nuities. In: Proceedings of the first southern hemisphere international rockmechanics symposium, Perth; 2008. p. 447–58.

[14] Poropat GV. Measurement of surface roughness of rock discontinuities.In: Proceedings of the rock engineering 09, Toronto, paper 3976; 2009.

[15] Tatone BSA, Grasselli G, Cottrell B. Accounting for the influence of measure-ment resolution on discontinuity roughness estimates. In: Proceedings of theEurock 2010, Lausanne; 2010.

[16] Ladanyi B, Archambault G. Simulation of the shear behavior of a jointed rockmass. In: Proceedings of the 11th US rock mechanics symposium. New York:ASCE; 1969. p. 105–25.

[17] Patton FD. Multiple modes of shear failure in rock. In: Proceedings of the firstinternational congress on rock mechanics, Lisbon; 1966. p. 509–13.

[18] Fecker E, Rengers N. Measurement of large scale roughnesses of rock planesby means of profilograph and geological compass. In: Proceedings of theinternational symposium on rock fracture, Nancy, France; 1971.

[19] Barton N. A relationship between joint roughness and joint shear strength.In: Proceedings of the international symposium on rock fracture, Nancy,France; 1971.

[20] Brown ET. Rock characterisation testing and monitoring: ISRM suggestedmethods. Oxford: Pergamon; 1981.

[21] Barton N, Choubey V. The shear strength of rock joints in theory and practice.Rock Mech 1977;10:1–54.

[22] Grasselli G. Shear strength of rock joints based on quantified surfacedescription. PhD thesis, Ecole Polytechnique Federale de Lausanne; 2001.

[23] Reeves MJ. Rock surface roughness and frictional strength. Int J Rock MechMin Sci 1985;22:429–42.

[24] Sande Cvd, Soudarissanane S, Khoshelham K. Assessment of relative accuracyof AHN-2 laser scanning data using planar features. Sensors 2010;10:8198–214.

[25] Dorninger P, Nothegger C, Pfeifer N, Molnar G. On-the-job detection andcorrection of systematic cyclic distance measurement errors of terrestriallaser scanners. J Appl Geodesy 2008;2:191–204.

[26] Borah DK, Voelz DG. Estimation of laser beam pointing parameters in thepresence of atmospheric turbulence. Appl Opt 2007;46:6010–8.

[27] Soudarissanane S, Lindenbergh R, Menenti M, Teunissen P. Incidence angleinfluence on the quality of terrestrial laser scanning points. In: Proceedings ofthe ISPRS workshop laser scanning, Paris; 2009.

[28] Bitenc M, Lindenbergh R, Khoshelham K, van Waarden AP. Evaluation of aLIDAR land-based mobile mapping system for monitoring sandy coasts.Remote Sensing 2011;3:1472–91.

[29] Lichti DD. Error modelling, calibration and analysis of an AM-CW terrestriallaser scanner system. ISPRS-J. Photogramm. Remote Sens. 2007;61:307–24.

[30] Kulatilake PHSW, Um J. Requirements for accurate quantification of self-

affine roughness using the roughness-length method. Int J Rock Mech Min Sci1999;36:5–18.

[31] Gonzalez RC, Woods RE. Digital image processing. New York: Addison-Wesley; 1992.

[32] Malinverno A. A simple method to estimate the fractal dimension of a self-affine series. Geophys Res Lett 1990;17:1953–6.

[33] Hardle W, Kerkyacharian G, Picard D, Tsybakov A. Wavelets, approximationand statistical applications. Berlin: Springer; 1998.

[34] Strang G, Nguyen T. Wavelets and filter banks. Wellesley, MA: Wellesley-Cambridge Press; 1996.

[35] Faro. Laser Scanner LS 880 Techsheet, 2009. p. Accessed September 2009/http://faro.com/FaroIP/Files/File/Techsheets%20Download/UK_LASER_SCANNER_LS.pdf.PDFS.

[36] Jolliffe IT. Principal component analysis. 2nd ed. New York: Springer; 2002.[37] Grasselli G, Wirth J, Egger P. Quantitative three-dimensional description of a

rough surface and parameter evolution with shearing. Int J Rock Mech MinSci 2002;39:789–800.

[38] Tatone BSA, Grasselli G. A method to evaluate the three-dimensional rough-ness of fracture surfaces in brittle geomaterials. Rev Sci Instrum 2009;80:

125110 [10 p].[39] Kulatilake PHSW, Um J, Panda BB, Nghiem N. Development of a new peak

shear strength criterion for anisotropic rock joints. J Eng Mech 1999;125:1010–7.

[40] Oppenheim AV, Schafer RW. Discrete-time signal processing. 2nd ed. UpperSaddle River, NJ: Prentice-Hall; 1999.

[41] Li ZL, Khoshelham K, Ding X, Zheng D. Empirical mode decomposition

transform for spatial analysis. In: Li ZL, Zhou Q, Kainz W, editors. Advancesin spatial analysis and decision making. Lisse: Swets & Zeitlinger; 2004.

p. 19–29.[42] Donoho DL, Johnstone IM. Adapting to unknown smoothness via wavelet

shrinkage. J Am Stat Assoc 1995;90:1200–24.[43] Donoho DL, Johnstone IM. Ideal spatial adaptation by wavelet shrinkage.

Biometrika 1994;81:425–55.[44] Birge L, Massart P. From model selection to adaptive estimation. In: Pollard D,

Torgersen E, Yang GL, editors. Festschrift for Lucien Le Cam: research papers

in probability and statistics. New York: Springer; 1997. p. 55–87.[45] Donoho DL. De-noising by soft-thresholding. IEEE Trans Inf Theory 1995;41:

613–27.