Computer-Aided Civil and Infrastructure Engineering 22 (2007) 197–209

Three-Dimensional Surface Texture Characterizationof Portland Cement Concrete Pavements

Ala Abbas∗

The University of Akron, Department of Civil Engineering, Akron, OH, USA

M. Emin Kutay, Haleh Azari

Turner-Fairbank Highway Research Center, 6300 Georgetown Pike, HRDI-11, McLean, VA, USA

&

Robert Rasmussen

The Transtec Group, 1012 East 38 Street, Austin, TX, USA

Abstract: This article investigates the effectiveness ofdifferent mathematical methods in describing the three-dimensional surface texture of Portland cement concrete(PCC) pavements. Ten PCC field cores of varying surfacetextures were included in the analysis. X-ray ComputedTomography (CT) was used to scan the upper portionof these cores, resulting in a stack of two-dimensionalgrayscale images. Image processing techniques were uti-lized to isolate the void pixels from the solid pixels andreconstruct the three-dimensional surface topography.The resulting three-dimensional surfaces were reduced totwo-dimensional “map of heights” images, whereby thegrayscale intensity of each pixel within the image repre-sented the vertical location of the surface at that pointwith respect to the lowest point on the surface. The “mapof heights” images were analyzed using four mathemati-cal methods, namely the Hessian model, the Fast Fouriertransform (FFT), the wavelet analysis, and the power spec-tral density (PSD). Results obtained using these methodswere compared to the mean profile depth (MPD) com-puted in accordance with ASTM E1845.

∗To whom correspondence should be addressed. E-mail: abbas@uakron.edu.

1 INTRODUCTION

Significant changes in the Portland cement concrete(PCC) pavement texturing practices took place duringthe late 1940s and early 1950s due to the high rate of wet-weather related accidents and fatalities resulting from in-creases in traffic volumes and vehicle speeds (Hoerner etal., 2003). Efforts to increase surface friction to addresssafety concerns resulted in some cases in objectionabletire-pavement noise emissions, which encouraged theneed to better understand the relationship between thepavement surface texture and the interior (on the com-muter) and exterior (on the surrounding environment)noise levels. It was recognized that a tradeoff existed be-tween surfaces with higher friction and tire-pavementnoise (Hoerner et al., 2003).

Nowadays, PCC pavements are textured using variousmethods such as longitudinal, skewed, and transversetining that are applied before the concrete is cured,and diamond grinding, diamond grooving, and abrad-ing (shotblasting) that are applied on hardened con-crete (Hoerner et al., 2003). The inclusion of uniformlyspaced transverse tines often resulted in an uncomfort-able sound commonly referred to as “whining,” which

C© 2007 Computer-Aided Civil and Infrastructure Engineering. Published by Blackwell Publishing, 350 Main Street, Malden, MA 02148, USA,and 9600 Garsington Road, Oxford OX4 2DQ, UK.

198 Abbas, Kutay, Azari & Rasmussen

could be eliminated by randomizing the tine spacing(Saad et al., 2000). Longitudinal and skewed tines werereported to produce less noise than transverse tines; andpavements of wide and deep grooves were reported tobe the noisiest (Jaeckel et al., 2000).

Several parameters have been suggested to character-ize the pavement surface texture. The most traditionalparameter is the mean texture depth (MTD) measuredusing the sand patch test (ASTM E965). Other parame-ters include the outflow time (OFT) measured using theoutflow meter (ASTM E2380), the mean profile depth(MPD) measured using the circular track meter (CT-Meter; ASTM E2157), and the international friction in-dex (IFI) that requires at least one friction measurementand one macrotexture measurement, such as the MTDor the MPD. High correlation among these parametershas been reported for nonporous pavements (Abe et al.,2001; Flintsch et al., 2003). Poor correlation, however,was found between these parameters and certain pave-ment surface characteristics such as tire-pavement noise(Sandberg and Ejsmont, 2002). Therefore, there is a needto better understand the macrotextural characteristics ofpavement surfaces.

This study aims at improving the three-dimensionalsurface texture characterization of PCC pavementsthrough the use of advanced mathematical methods. TenPCC field cores of varying surface textures were includedin the analysis. X-ray computed tomography (CT) wasused to scan the upper portion of these cores, resultingin a stack of two-dimensional grayscale images. Imageprocessing techniques were utilized to isolate the voidpixels from the solid pixels and reconstruct the three-dimensional surface topography. The resulting three-dimensional surfaces were reduced to two-dimensional“map of heights” images, whereby the grayscale intensityof each pixel within the image represented the verticallocation of the surface at that point with respect to thelowest point on the surface. The “map of heights” im-ages were analyzed using four mathematical methods,namely the Hessian model, the Fast Fourier transform(FFT), the wavelet analysis, and the power spectral den-sity (PSD). The Hessian model is a simple geometricmodel that relates the texture of the surface of interestto the curvature at each point along that surface. The re-maining three methods are signal processing techniquesthat have extensively been used in the literature in ana-lyzing different types of signals. Results obtained usingthese methods were compared to the mean profile depth(MPD) computed in accordance with ASTM E1845.

2 IMAGE ACQUISITION USING X-RAY CT

The X-ray CT technique is a nondestructive visualizationtool capable of identifying the various density phases

Fig. 1. Illustration of a typical X-ray CT system.

within the scanned object. An illustration of a typical X-ray CT system is shown in Figure 1. It consists of an X-raysource and a detector with the test specimen placed inbetween. The source emits X-rays of known intensitiestoward the specimen and the detector records the inten-sities after passing through the specimen. The intensityvalues are recorded while the specimen rotates. Once afull rotation is completed, the specimen is shifted verti-cally by a fixed amount equivalent to the slice thicknessand another scan is performed. This process is repeateduntil the end of the specimen is reached. The intensityvalues are used to calculate the distribution of the linearattenuation coefficient within the specimen, which aremapped into grayscale CT scan images. The grayscale in-tensity of each pixel ranging from 0 (black) to 255 (white)in the image is directly related to the density of the spec-imen at that point. Each image represents a slice of thespecimen of a known thickness. Its position in the stackcorresponds to its vertical location.

In this study, the X-ray CT technique was utilized toscan the upper portion of ten PCC specimens. A photo-graph of these specimens is presented in Figure 2. The

Fig. 2. A photograph of the PCC specimens used in theanalysis.

Three-dimensional surface texture characterization 199

Table 1Description of the surface texture of the PCC specimens used in the analysis

Specimen name Specimen description

DC-1 Nominal uniform 5/8 tiningDC-2 Nominal uniform 3/4 tining (significant variability in as-constructed)DC-3 (1423) Drag texture (possible rough float)DC-4 (1079) Nominal uniform 1/2 tiningDC-5 Bottom of core with embedded aggregate particles from base courseDC-6 Porous concrete with 1/4 to 1/2 aggregates1492 (SHRP 204053) Nominal uniform 3/4 tining1522 (SHRP 133007) Nominal uniform 1/2 tining1562 (SHRP 195046) Nominal random tining (1.00, 0.90, 0.60, 0.75, 0.90, 1.10 on core)2605 (SHRP 485035) Drag texture (possible rough float)

description of these specimens is given in Table 1. Eachspecimen—measuring 150 mm (6 inch) in diameter—was scanned using a spatial resolution of 0.303 mm/pixeland a slice thickness of 0.4 mm. The total thickness of thescanned portion was selected large enough to exceed themaximum texture depth of the scanned specimen. Ac-cordingly, more slices were acquired for specimens ofdeep grooves or large exposed aggregates as comparedto those of shallow grooves or relatively flat surfaces.

3 IMAGE PROCESSING

The grayscale images, obtained using the X-ray CT tech-nique, were converted to black and white images bythresholding. The selection of an appropriate thresholdvalue was facilitated by the relatively high resolution em-ployed in the X-ray CT scanning, which resulted in aclear distinction between the solid and the void phases.Grayscale intensities below the threshold value wereconverted to 0 (black) and those above were convertedto 255 (white).

The three-dimensional surface texture of the PCCspecimens was reconstructed using the black and whiteimages. Image analysis was utilized to identify the solidpixels constituting the PCC surface texture and assigna height parameter (δz) to each of the surface pixelsmeasured from the lowest point on the surface. To en-sure the quality of the resulting surfaces, each spec-imen represented by a stack of processed black andwhite images was rendered using a commercial three-dimensional visualization tool called 3D Constructor asshown in Figure 3. The similarity between the three-dimensional renderings and the actual specimens pre-sented in Figure 2 is noticeable. The three-dimensionalrenderings were then reduced to two-dimensional “map

Fig. 3. Three-dimensional renderings of the PCC specimensshown in Figure 2.

Fig. 4. Schematic of the “map of heights” image creation.

of heights” images. The creation of the “map of heights”images is illustrated in Figure 4. As noticed in this figure,the grayscale intensity of each pixel in the “map ofheights” images is no longer indicative of the materialcomposition, but rather representative of the vertical

200 Abbas, Kutay, Azari & Rasmussen

Fig. 5. Two-dimensional “map of heights” images of the PCCspecimens.

location of the surface at that point with respect to thelowest point on the surface. To enhance the visual qualityof these images, each slice was represented by a grayscaleintensity increment of 5; thus, allowing a maximum tex-ture depth of (255/5) × 0.4 mm = 20.4 mm, which wasnot exceeded by any specimen. The resulting “map ofheights” images are depicted in Figure 5. Based on thisfigure, the PCC specimens can be classified into threegroups:

� Group-A: Specimens of relatively flat surfaces, as ev-ident in the uniformity in color of their “map ofheights” images. This group includes specimens DC-3and 2605.

� Group-B: Specimens with an average texture depthof about 7 mm. This group includes specimens DC-4,1492, DC-1, 1562, DC-2, and 1522.

� Group-C: Specimens of relatively rough surface tex-ture. This group includes specimens DC-5 (exposed

aggregate) and DC-6 (porous concrete). The maxi-mum texture depths of these specimens are 17.0 mmand 13.5 mm, respectively.

4 MATHEMATICAL CHARACTERIZATIONOF THE SURFACE TEXTURE

Four mathematical methods were used to analyze the“map of heights” images presented in Figure 5 for thepavement surface texture, namely the Hessian model,the FFT, the wavelet analysis, and the PSD. Each methodis covered separately in the following subsections.

4.1 Hessian model

The Hessian model, suggested by Alvarez and Morel(1994), is a simple geometric model based on the curva-ture (i.e., second derivative) of the surface. The curvatureof each point on the surface, defined by its Cartesiancoordinates (x and y), is described using the followingmatrix:

H(x, y) =(

r s

s t

)(1)

where r, s, and t are defined as:

r = ∂2 I(x, y)∂x2

, s = ∂2 I(x, y)∂x∂y

, t = ∂2 I(x, y)∂y2

(2)

where I(x, y) is the grayscale intensity of the pixel lo-cated at the coordinates x and y; ∂x and ∂y are the pixeldimensions. Hence, r, s, and t are expressed in grayscaleintesity/pixel2.

The minimum and maximum curvatures at the point(x, y) are respectively equal to the minimum and max-imum eigenvalues of the matrix presented in Equation(1):

β1 = 12

(r + t −

√(r − t)2 + 4s2

)(3)

and

β2 = 12

(r + t +

√(r − t)2 + 4s2

)(4)

The Hessian model was used by Khoudeir et al. (2004)in investigating the wearing of the pavement surface tex-ture due to traffic. The following criterion was suggestedin describing the surface texture:

Texture Index = average of |β1|variance in |β1| (5)

In this study, the matrix elements r, s, and t werecalculated using the discrete numerical differentiation

Three-dimensional surface texture characterization 201

Fig. 6. Average of Iβ1I obtained using the Hessian model forall specimens.

functions in Matlab for each of the ten PCC speci-mens presented in Figure 5. Two functions were usedfor this purpose, namely the discrete Laplacian func-tion “del2” and the discrete gradient function “gra-dient”. It was noticed that the Texture Index givenin Equation (5) did not yield realistic texture mea-sures. This was attributed to the high variance in|β1| noticed for some specimens. It was found, how-ever, that the average of |β1| resulted in more con-sistent measures when compared to the visual surfacetexture observations. The β1 values calculated usingEquation (3) were converted from grayscale inten-sity/pixel2 to the actual horizontal and vertical scales bysuccessively multiplying them by (1 pixel/0.303 mm)2 and(0.4 mm/5 grayscale intensities). Hence, the converted β1

values hold the unit of mm−1. Figure 6 presents the av-erage of|β1| values for all specimens sorted in ascendingorder. As expected, the lowest texture measures wereobtained for Group-A, while the highest texture mea-sures were obtained for Group-C. Group-B specimenswere in the middle range.

4.2 FFT

The fast Fourier transform (FFT) is a method used todecompose a series, y, of N data points into a sum ofsinusoids of various frequencies, f i, amplitudes, ai, andphases, ϕi. The FFT method is mathematically expressedas follows:

y(xn) =N/2∑i=0

ai sin(2π fi xn + ϕi )(n = 1, 2, . . . , N) (6)

where, xn is the nth data point of the independentvariable x in the space or the time domain, y (xn) isthe FFT prediction at x = xn, fi = i

N/2 × 12 × 1

�x ; i =0, 1, . . . , N/2, �x is the sampling interval, and 1/�x is the

sampling frequency. At each frequency, f i, the amplitude,ai, is related to the magnitude of the FFT complex vec-tor, while the phase, ϕi, is equal to the angle betweenthat vector and the real axis. The higher the amplitudeis, the higher is the contribution of the correspondingfrequency to the series.

The FFT analysis was accomplished using the com-mercial image analysis software Image Pro Plus (IPP)(IPP, 2002). Upon the application of the FFT on a 2Dgrayscale image, amplitudes and phases are calculatedfor the grayscale intensity values of individual lines pass-ing through the center of the image at angles rangingfrom –180◦ to 180◦, where 0◦, –180◦, and 180◦ denotehorizontal lines passing though the center of the imageand –90◦ and 90◦ denote vertical lines passing throughits center. The amplitude and phase results are summa-rized in graphical form using two additional grayscaleimages, namely the FFT-amplitude image and the FFT-phase image. In these images, the grayscale intensity ofeach pixel reflects the magnitude of the correspondingamplitude or phase, while the distance from the im-age center represents the frequency (reciprocal of pe-riodicity or wavelength). Due to the symmetry of theFFT results at opposite angles, only half of the FFT isrequired.

Example FFT-amplitude images for four specimens(DC-1, 1562, DC-3, and DC-6) are presented in Figure 7.As indicated in Table 1, these specimens representedsurfaces of uniform tines, random tines, drag texture,and porous concrete, respectively. The following obser-vations are noted about this figure. First, the direction-ality of the surface texture of specimens DC-1 and 1562is apparent in the alignment of the dominant frequen-cies in the direction of the tines. Second, specimen DC-1 of the uniform tines has distinctive dominant peaksalong the direction of the tines, whereas specimen 1562of the random tines lacks this characteristic. Third, nopreferred orientation for the dominant frequencies isobserved for either DC-3 or DC-6, which indicates anisotropic texture orientation. Fourth, a scattered spec-trum is noticed for the rough DC-6 specimen as com-pared to the smooth DC-3 specimen, which indicatesthat specimen DC-6 has more dominant frequencies thanspecimen DC-3. The fourth observation (i.e., the disper-sal of the spectrum) was utilized by Masad et al. (2001)in studying the asperity distribution along the surfaceof fine aggregates. The number of amplitude pixels inthe FFT-amplitude image having a magnitude greaterthan 5% of the peak amplitude was suggested as a crite-rion for the surface texture of these aggregates. As ex-pected, smooth aggregates were reported to have fewerdominant peaks than rough aggregates. Analysis resultsobtained using this criterion (i.e., the FFT index) are

202 Abbas, Kutay, Azari & Rasmussen

Fig. 7. Example “map of heights” images and theircorresponding FFT-amplitude images for specimens DC-1,

1562, DC-3, and DC-6.

presented in Figure 8. It can be noticed that specimensDC-5 and DC-6 attained the highest values primarily dueto the large number of dominant frequencies observedin their texture. Furthermore, lower FFT indices wereobtained for surfaces of uniformly spaced tines due tothe presence of the dominant peaks (e.g., 1522 and DC-1) as opposed to those of randomly spaced tines (e.g.,1562 and DC-2). Therefore, it is concluded that the FFTindex is primarily useful in capturing the orientation

Fig. 8. FFT index obtained by counting the number ofamplitude pixels in the FFT-amplitude image having a value

greater than 5% of the peak amplitude.

and spacing of the tines in the pavement surfacetexture.

4.3 Wavelet analysis

The FFT method discussed previously decomposes a sig-nal into sine functions that repeat themselves from minusinfinity to plus infinity. Hence, this method is suitable forperiodic signals that are not changing much over time(or space). Signals that do not exhibit such character-istic can be analyzed using different types of functionscalled wavelets. As opposed to the sine functions, thesewavelets have limited duration with an average value ofzero.

A wide range of wavelet functions is available in theliterature including but not limited to the Daubechies(db), the Symlets (sym), and the Coiflets (coif) familyfunctions (Matlab, 2004). This decomposition techniquerepresents a signal, f(x) in time (or space) domain, x,as a linear combination of scaling functions, ϕ (x), andwavelet functions, ψ (x), that are assigned shift and scalefactors for the various segments composing the signal.Therefore, they are capable of capturing not only themagnitude of the different frequencies but also theirchange over time (or space).

A one-dimensional signal, f(x), can be analyzed intotwo components—a coarse approximation component(i.e., low frequency) and a detail component (i.e., highfrequency)—using the inverse wavelet transform, whichcan be expressed as follows (Erlebacher et al., 1996):

f (x) =∑k∈Z

s Jk ϕ J

k (x) +J∑

j=1

∑k∈Z

d jkψ

jk (x) (7)

where the integer k represents the translational shift inthe time (or space) domain, the integer j represents the

Three-dimensional surface texture characterization 203

shift in spectrum (or frequency), ϕ (x) is the scaling func-tion, ψ(x) is the wavelet function, s denotes the scal-ing coefficients obtained by applying a low-pass filter onthe discrete data points of the signal, and d denotes thewavelet coefficients obtained by applying a high-pass fil-ter on the discrete data points of the signal.

The wavelet analysis approach was used by Wei andFwa (2004) in an effort to characterize pavement rough-ness. The pavement profile was decomposed into sevenfrequency subbands using the “db3” wavelet function(from the Daubechies wavelet family), and the waveletenergy for each subband was used as a quantitative mea-sure for roughness. The “db3” wavelet was chosen be-cause of its good resolution in the range of both spa-tial and frequency domains of interest in road roughnessanalysis. The wavelet energy, E, was calculated as fol-lows:

E =N∑

i=1

s2(i)� (8)

where s(i) is the signal of the frequency subband, � isthe sampling interval of the roughness data, and N is thetotal number of data points.

Based on the previous discussion, the most challengingtask in the wavelet decomposition is the selection of anappropriate wavelet function and decomposition level.In this study, the “map of heights” images presented inFigure 5 were analyzed using the wavelets “db1” through“db6” to cover a wide range of spatial and frequencydomains. Each grayscale image was decomposed intotwo frequency subbands using the discrete wavelet trans-form. In comparison with one-dimensional signals, whichare decomposed into an approximation component anda detail component, two-dimensional signals are decom-posed into four components, one approximation compo-

Fig. 9. Example two-level decomposition of a grayscale image (left) into one approximation and six detail images (right) usingthe wavelet function “db3.”

nent and three detail components (horizontal, vertical,and diagonal). An example two-level wavelet decompo-sition of a grayscale image is depicted in Figure 9. Asshown in this figure, the original grayscale image couldbe expressed as the sum of one approximation and six de-tail images, each of which could be defined by its energy,E, expressed as follows:

E =Nj∑j=1

Ni∑i=1

s2(i, j)�x�y (9)

where, s(i, j) is the two-dimensional signal of the fre-quency subband; �x and �y are the horizontal and verti-cal sampling intervals, respectively; and Ni and Nj are thenumber of data points along the horizontal and verticaldirections, respectively.

The energies of the approximation and the detail sig-nals were calculated using Equation (9) for each of the 10PCC specimens analyzed. To facilitate the comparison,the energies of the three detail signals at each decom-position level (horizontal, vertical, and diagonal) weresummed. Figures 10–12 present the energies of the detaillevel-1, detail level-2, and approximation level-2 images,respectively. The following points are noted about thesefigures. Similar energy trends are noticed in Figures 10and 11 for decomposition levels 1 and 2, respectively.The energy of the detail images decreased with the de-crease in the wavelet order number, while it remainedalmost constant for the approximation image regardlessof the wavelet order number used in the analysis. Thehighest energy levels were obtained for specimen DC-6, followed by specimens DC-2, DC-3, DC-4, and DC-5,and then by specimens 1492, 1522, 1562, 2605, and DC-1.The lowest energy levels for the detail images were ob-tained for specimens 2605 and DC-1 and for the approx-imation images for specimens 1522 and 2605. Specimen

204 Abbas, Kutay, Azari & Rasmussen

Fig. 10. Summation of the detail signals’ energies (horizontal, vertical, and diagonal) at level-1 decomposition.

Fig. 11. Summation of the detail signals’ energies (horizontal, vertical, and diagonal) at level-2 decomposition.

DC-3 of the relatively flat surface was in the middle rangein terms of energies.

4.4 PSD

The power spectral density (PSD) is a well-knownmethod for the interpretation of complex signals con-taining a variety of wavelengths and amplitudes (Hayes,1996). In this study, the PSD analysis was accomplished

using the signal processing toolbox in Matlab (Matlab,2004). Profile signals in a direction perpendicular to thetines were extracted from the “map of heights” imagesand stitched together, creating much longer signals thanthe 150-mm diameter of the specimen. The PSD of theseprofile signals was calculated using the pwelch algorithm,which estimates the PSD using the Welch’s averagedmodified periodogram method of spectral estimation(Hayes, 1996). In this method, the signal is divided into

Three-dimensional surface texture characterization 205

Fig. 12. Energy of the approximation signal at level-2 decomposition.

a number of segments, Ns, of equal sizes, each with 50%overlap. Each segment is windowed with a Hammingwindow that has the same length as the segment. Then,the FFT is applied to the windowed data and the peri-odogram of each windowed segment is computed. Theset of modified periodograms is averaged to form thespectrum estimate. The resulting spectrum estimate isscaled to compute the PSD (Hayes, 1996).

A tradeoff exists in the selection of Ns; increasing Ns

decreases the longest wavelength that can be analyzedusing this technique and decreasing Ns increases the scat-ter and thus, the accuracy of the PSD values. Followinga series of trials, an Ns equal to 8 was found to be the op-timum number of segments for the least scatter withoutsacrificing the analysis wavelength range.

Figure 13a shows the PSD values for all 10 PCC spec-imens. The distinction between the specimens at differ-ent wavelengths can easily be observed. As expected,Group-A specimens exhibited the lowest PSD values(i.e., surface irregularities), whereas Group-C specimensexhibited the highest PSD values. The PSD values ofGroup-B specimens were generally in between Group-A and Group-C. A closer examination of the powerspectrum is presented in Figure 13b, where the entirewavelength range was divided into three discrete inter-vals ((i) 0.2–2 mm, (ii) 2–10 mm, and (iii) 10–80 mmrepresenting short, medium, and long wavelengths, re-spectively) and an average PSD value was calculatedfor each interval. In the short wavelength range, Group-A specimens exhibited smaller amplitudes as comparedto Groups B and C. As the wavelength increased

(>10 mm), the difference in the PSD values betweenthe specimens decreased, which implies a dominant tex-ture in the short wavelength range. Finally, Figure 13bpresents an example on how the PSD analysis can beused to capture local extremes in the surface texture; ajump in the PSD values is noticed in the long wavelengthrange (10–80 mm) for specimen DC-5, which has a largeexposed aggregate.

5 CONVENTIONAL MACROTEXTUREMEASURES

As mentioned previously, the most conventional param-eter for characterizing the pavement surface macrotex-ture is the mean texture depth (MTD) measured usingthe sand patch test (ASTM E965). In this test, a knownamount of sand (or glass beads) is spread evenly overthe pavement surface to form a circle, and the MTDvalue is calculated by dividing the volume of the sandfilling the pavement surface voids by the area of theresulting circle. Due to the subjective nature of thistest, several new parameters have recently emerged. Inparticular, the mean profile depth (MPD) is increas-ingly gaining popularity. This parameter is measured us-ing a device called the circular track meter (CTMeter).The experimental procedure for measuring the MPDusing the CTMeter is documented in ASTM E2157.According to this method, the pavement surface macro-texture is measured using a laser-displacement sensormounted on a rotating arm having a diameter of 284 mm

206 Abbas, Kutay, Azari & Rasmussen

Fig. 13. Power spectral density plots of the specimens: (a) continuous PSD and (b) average PSD in the given intervals.

(11.2 inch). The surface profile of the resulting circulartrack is divided into eight segments, and the MPD foreach segment is measured in accordance with ASTME1845. The average of the eight MPD values is used asa measure of the pavement macrotexture.

In this study, the MPD was computed in accor-dance with ASTM E1845 using cross sections extractedfrom the “map of heights” images. Perpendicular cross-sections to the direction of the tines were used for thetined specimens, while random cross sections were usedfor the rest of the specimens. To suppress the effect of thespecimen inclination (i.e., slope), a linear trend line wasfitted to the surface profile and later subtracted from thecorresponding profile data; thus, creating a zero-meanprofile. The corrected profile was divided into two equalsegments and the mean segment depth (MSD) was com-puted by averaging the profile peaks in each segment.The MPD was calculated as the average of the MSD val-ues for all segments. Furthermore, an estimated texturedepth (ETD) was predicted from the MPD using thefollowing transformation equation suggested by ASTM1845: ETD = 0.2 + 0.8 times; MPD. The variations inthe computed MPD and the predicted ETD values for

all ten PCC specimens analyzed in this study are shownin Figure 14. As noticed from this figure, the MPD valuesranged from 0.65 to 7 mm, while the ETD values rangedfrom 0.7 to 5.5 mm.

Fig. 14. Mean profile depth (MPD) and estimated texturedepth (ETD) values of the specimens.

Three-dimensional surface texture characterization 207

Fig. 15. Correlation of: (a) FFT Index and MPD, (b) average of Iβ1I and MPD, (c) Ed1 and MPD, and (d) PSD and MPD.

6 CORRELATION OF MATHEMATICAL TOCONVENTIONAL MACROTEXTURE

MEASURES

Figure 15 presents the correlation of different mathe-matical parameters explored in this study to the MPD.The highest correlation was obtained between the MPDand both the Hessian model (i.e., average of |β1|) andthe PSD with R2 values of 0.71 and 0.89, respectively.The long wavelength (10–80 mm) PSD value for speci-men DC-5 was treated as an outlier and hence, was re-moved from the analysis. As mentioned previously, theprimary reason for specimen DC-5 to exhibit such highPSD within that range was the presence of a relativelylarge exposed aggregate particle. Therefore, it shouldbe noted that the correlation between the PSD and theMPD is valid only when there are no abrupt changes inthe texture causing large PSD values at certain wave-lengths. Correlation of the MPD to other macrotexturemeasures such as the FFT index and wavelength energy(Ed1) was weak with observed R2 values of 0.57 and 0.59,

respectively. It should be noted, however, that these R2

values are highly influenced by a single specimen thatis specimen DC-6 (porous concrete). Therefore, as dis-cussed next, better correlations can be obtained by in-cluding more specimens in the analysis.

7 ANALYSIS LIMITATIONS ANDRECOMMENDED FUTURE WORK

The major limitations of this study are:

� A limited number of specimens were analyzed in thisstudy.

� X-ray CT scanning was conducted using a spatial res-olution of 0.303 mm/pixel and a vertical resolution of0.4 mm/slice. Hence, a peak or valley on the surfacewith a height less than 0.4 mm cannot be detected bythe acquired CT images. Accordingly, this shortcom-ing is more pronounced in the case of relatively flator smooth surfaces.

208 Abbas, Kutay, Azari & Rasmussen

� X-ray CT scanning artifacts, which can be isolated atthe image processing stage.

� Inherent limitations in the mathematical methodsused in the analysis.

Most of these limitations can be addressed by usinghigh-resolution laser profilers to define the 3D surfaceof the scanned specimens. The 3D data can then be trans-formed into grayscale “map of heights” images and ana-lyzed using the mathematical methods presented in thisarticle. Recommended future work also includes com-parison between the suggested texture measures andphysical surface properties such as roughness, noise, andfriction.

8 SUMMARY AND CONCLUSIONS

Image analysis techniques were utilized to reconstructthe three-dimensional surface texture of ten PCC spec-imens from two-dimensional grayscale images acquiredusing the X-ray CT technique. The resulting three-dimensional surfaces were reduced to two-dimensional“map of heights” images, whereby the grayscale intensityof each pixel within the image represented the verticallocation of the surface at that point with respect to thelowest point on the surface. The “map of heights” im-ages were analyzed using four mathematical methods,namely the Hessian model, the Fast Fourier transform,the Daubechies family of wavelets, and the power spec-tral density. Results obtained using these methods werecompared to the mean profile depth computed in accor-dance with ASTM E1845.

The following conclusions were drawn based on theanalyses provided in this article:

� The Texture Index suggested by Khoudeir et al. (2004)did not yield realistic texture measures. This was at-tributed to the high variance in |β1| noticed for somespecimens. However, it was found that the numeratorof the Texture Index equation (i.e., average of |β1|)was more meaningful in discriminating between thePCC specimens based on texture.

� Lower FFT indices were obtained for smooth surfaces(e.g., DC-3) as compared to rough surfaces (e.g., DC-6). Therefore, it is concluded that the FFT index is ca-pable of discriminating between these surfaces basedon texture.

� Furthermore, lower FFT indices were obtained forsurfaces of uniformly spaced tines due to the pres-ence of the dominant peaks (e.g., 1522 and DC-1) asopposed to those of randomly spaced tines (e.g., 1562and DC-2). Therefore, it is concluded that the FFTindex is primarily useful in capturing the orientation

and spacing of the tines in the pavement surface tex-ture.

� Similar results were obtained using the Daubechiesfamily of wavelets regardless of the wavelet order.The wavelet energy was incapable of discriminatingbetween specimens based on texture.

� A slight increase in the PSD spectrum is noticed inthe wavelength range of 0.6 to 10 mm followed byan abrupt increase until the 13-mm wavelength, af-ter which the spectrum becomes almost constant. Itis worth pointing out, however, that the effect ofthe X-ray scanning resolution (0.303 mm/pixel res-olution) is expected to be more pronounced on smallwavelengths (less than 1.0 mm) and that the effect ofthe specimen diameter (150 mm) is expected to bemore pronounced on large wavelengths (greater than10 mm).

� The PSD was able to identify local anomalies in thesurface texture. This was clear in specimen DC-5 (ex-posed aggregate).

� Finally, the highest correlation was obtained betweenthe MPD and the Hessian model (i.e., average of |β1|)and the PSD indices with R2 values ranging from 0.71to 0.89, and the lowest correlation was observed be-tween the MPD and the FFT Index and the Wave-length energy index (Ed1) with R2 values of 0.57 and0.59, respectively.

ACKNOWLEDGMENT

The authors would like to thank Mr. Tom Harman andMr. Richard Meinenger of the Federal Highway Admin-istration (FHWA) for their cooperation. They would liketo extend their thanks to Dr. Eyad Masad of the Depart-ment of Civil Engineering at Texas A&M University andMr. Ted Ferragut, the president of TDC Partners, LTDfor their valuable comments.

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