Construction

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Construction and Building Materials 21 (2007) 978–990

and Building

MATERIALS

Evaluation of image analysis techniques for quantifying aggregateshape characteristics

Taleb Al-Rousan a,*, Eyad Masad b,1, Erol Tutumluer c,2, Tongyan Pan c,2

a Department of Civil Engineering, The Hashemite University, P.O. Box 150459, Zarqa 13115, Jordanb Department of Civil Engineering, Texas A&M University, 3135 TAMU, College Station, TX 77843-3135, United States

c Department of Civil and Environmental Engineering, University of Illinois, Urbana, IL 61801, United States

Received 10 October 2005; accepted 8 March 2006Available online 19 May 2006

Abstract

Form, texture, and angularity are among the properties of aggregates that have a significant effect on the performance of hot-mixasphalt, hydraulic cement concrete, and unbound base and subbase layers. Imaging techniques have provided a good means to quantifyaggregate shape properties rapidly in spite of the fact that they might differ in the mathematical procedure and the instrumental setupthey utilize. The validity of the mathematical procedure is essential for the results to be useful in quantifying aggregate shape. Some ofthe most widely used aggregate shape analysis techniques were evaluated in this paper. The analysis results revealed that some of theavailable analysis methods are influenced by both angularity and form changes and, consequently, are not suitable to distinguish betweenthese two characteristics. Also, some of the analysis methods are quite adequate to measure both texture and angularity when changesare made to the image resolution and magnification level. The following analysis methods are recommended: wavelet analysis of grayimages for texture; both the gradient method and tracing the change in slope of a particle outline method for angularity; aspect ratiofor 2-dimensional form; and sphericity or the proportions of the three particle dimensions for 3-dimensional form.� 2006 Elsevier Ltd. All rights reserved.

Keywords: Aggregate; Shape; Image; Analysis

1. Introduction

The properties of coarse and fine aggregates used in hot-mix asphalt (HMA), hydraulic cement concrete, andunbound base and subbase layers have a significant influ-ence on the engineering properties of the pavement structurein which they are used [10,26c,20]. The form, angularity,and texture of fine and coarse aggregate particles influencetheir mutual interactions and interactions with any stabiliz-ing agents (e.g., asphalt, cement, and lime) and are related to

0950-0618/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.conbuildmat.2006.03.005

* Corresponding author. Tel.: +962 5 390 3333x4465; fax: +962 5 3826348.

E-mail addresses: taleb@hu.edu.jo (T. Al-Rousan), emasad@civil.tamu.edu (E. Masad), tutumlue@uiuc.edu (E. Tutumluer), tpan@uiuc.edu(T. Pan).

1 Tel.: +1 979 845 8308; fax: +1 979 845 0278.2 Tel.: +1 217 333 8637; fax: +1 217 333 1924.

durability, workability, shear resistance, tensile strength,stiffness, fatigue response, optimum stabilizer content,and, ultimately, performance of the pavement layer. There-fore, fundamental measurements of aggregate shape charac-teristics are essential for good quality control of aggregatesand for understanding the influence of these characteristicson the behavior of pavement structural layers.

There are currently no standard test methods fordirectly and objectively measuring aggregate angularityand surface texture. The current methods used in practicehave several limitations: They are laborious, subjective innature, and/or lack a direct relationship with the funda-mental parameters governing performance such as shearstrength and stiffness [7]. In addition, some of these meth-ods are limited in their ability to differentiate among aggre-gate characteristics (form, angularity, and texture). Theselimitations have various impacts on the quality of highwaypavements, as they impede the development of design

Table 1Analysis methods used in analyzing aggregate images

Method Analysis method label

Sphericity SPHRoundness ROUNDForm index FORMForm index (Fourier) FRFORMFlat and elongated ratio FERAspect ratio ASPTAngularity index (Fourier) FRANGSurface erosion–dilation STIFractal dimension FRCTLGradient angularity index GRADRadius angularity index RADAngularity using outline slope AITexture index (Fourier) FRTXTRWavelet analysis WVTXTR

T. Al-Rousan et al. / Construction and Building Materials 21 (2007) 978–990 979

methodologies and construction practices that requireaccurate, repeatable, and rapid measurements of aggregateproperties. Moreover, these limitations can lead to thedevelopment of specifications that in some cases overem-phasize the need for superior aggregate properties or allowthe use of marginal aggregates without a clear relationshipto performance.

Limitations of available test methods have directedresearchers toward seeking new technologies to accuratelyand rapidly measure aggregate shape. Motivated byadvancements in digital vision and the availability of low-cost, powerful, and fast image processing software, newtechniques for directly measuring aggregate shape proper-ties have been developed. These systems operate based ondifferent concepts such as image analysis techniques, laserscanning, and physical measurements of aggregate dimen-sions [8,27,15,11]. These newly developed direct measure-ment methods have the potential to objectively quantifyaggregate characteristics. However, some of these methodsdiffer significantly in their experimental setups, analysisprocedures, and the shape properties they measure [1].Therefore, it becomes crucial to determine the methodsand the mathematical procedures that are more valid, accu-rate, and sensitive in quantifying and differentiating aggre-gate shape properties. Knowing the best mathematicalprocedures is essential for the results to be useful in quan-tifying aggregate shape, and especially very significant inmaking a rational recommendation for incorporating a testmethod or methods in aggregate specifications. The pri-mary objective of this paper is to evaluate the most widelyused available image analysis techniques that are used tomeasure aggregate shape properties.

2. Image analysis methods for characterizing aggregate

shape

Al-Rousan [1] discussed the image analysis techniquesused by most of the available imaging systems that utilizedifferent mathematical procedures for the analysis of aggre-gate shape characteristics. In this section, a brief descrip-tion is provided on some of the most widely used analysistechniques (listed in Table 1) for characterizing form, angu-larity, and texture properties of aggregate particles.

2.1. Analysis of form

2.1.1. Sphericity (SPH)

To properly characterize the form of an aggregate parti-cle, information about three dimensions of the particle isnecessary (longest dimension [dl], intermediate dimension[di] and shortest dimension, [ds]). Sphericity [12] is amonga number of indices that have been proposed for measuringthe form in terms of the three dimensions.

Sphericity ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffids � d i

d2l

3

sð1Þ

2.1.2. Roundness (ROUND)

Roundness is a widely used measure of form in twodimensions, and expressed by the following equation:

Roundness ¼ p2

4pAð2Þ

where p and A are the perimeter and area of the 2-dimen-sional projection of an aggregate particle, respectively. Acircular object will have a roundness value of 1.0 and othershapes will have roundness values greater than 1.0.

2.1.3. Form indexForm index was proposed by Masad et al. [19] to describe

form in 2-dimensional. It uses incremental changes in theparticle radius. The length of a line that connects the centerof the particle to the boundary of the particle is termedradius. Form index is expressed by the following equation:

Form index ¼Xh¼360�Dh

h¼0

jRhþDh � RhjRh

ð3Þ

where h is the directional angle and R is the radius in dif-ferent directions. By examining Eq. (3), it will be notedthat, if a particle was a perfect circle, the form index wouldbe zero. Although the form index is based on 2-dimen-sional measurements, it can easily be extended to analyzethe 3-dimensional images of aggregates.

2.1.4. Form index using Fourier series (FRFORM)Fourier series can be used to analyze the form, angular-

ity, and texture of aggregate shape. Each aggregate profile,defined by the function R(h), can be analyzed using Fourierseries coefficients as follows:

RðhÞ ¼ a0 þX1n¼1

½an cosðnhÞ þ bn sinðnhÞ� ð4Þ

where an and bn are the Fourier coefficients. The functionR(h) traces out the distance to the boundary from a centralpoint as a function of the angle h, 0� < h < 360�. Obviously,R(h) is a periodic function. These coefficients can be evalu-ated using the following integrals:

980 T. Al-Rousan et al. / Construction and Building Materials 21 (2007) 978–990

a0 ¼1

2p

Z 2p

0

RðhÞ dh ð5Þ

an ¼1

p

Z 2p

0

RðhÞ cosðnhÞ dh n ¼ 1; 2; 3; . . . : ð6Þ

bn ¼1

p

Z 2p

0

RðhÞ sinðnhÞ dh n ¼ 1; 2; 3; . . . : ð7Þ

If R(h) is only known numerically at a discrete number ofangles, the above integrals can be written using summa-tions as follows:

a0 ¼1

2p

X2p�Dh

h¼0

Rðhþ DhÞ þ RðhÞ2

� �ð8Þ

an ¼1

p

X2p�Dh

h¼0

Rðhþ DhÞ þ RðhÞ2

� �ðsin nðhþ DhÞ � sin nhÞ

ð9Þ

bn ¼1

p

X2p�Dh

h¼0

Rðhþ DhÞ þ RðhÞ2

� �ð� cosðhþ DhÞ þ cos nhÞ

ð10Þ

where R(h) is measured only at predefined increments, andh takes on values from 0 to (2p � Dh) with an increment Dhof about 4�. The higher the value of n used in Eq. (5), thebetter the actual particle profile is reproduced. Wang et al.[30] formulated a form signatures using the an and bn coef-ficients as follows:

as ¼X4

j¼1

an

a0

� �2

þ bn

a0

� �2" #

ð11Þ

The shape parameters (form, angularity, and texture)can all be represented by the same function in Eq. (11)and at the same time can be differentiated by the frequencymagnitudes of the harmonics used to capture a particleboundary. Form is captured using harmonics with lowerfrequency than texture and angularity.

2.1.5. Flat and elongated ratio (FER)

In 3-dimensional analysis of a particle form, particleflatness is measured by the ratio of the intermediate dimen-sion to the shortest dimension, and elongation is measuredby the ratio of the longest dimension to the intermediatedimension. Another way of presenting the form of a parti-cle is by using the flat and elongated ratio, which representsthe ratio between the longest dimension and the shortestdimension of a particle.

2.1.6. Aspect ratio (ASPT)

Aspect ratio, which is similar to flat and elongated ratiobut usually used for 2-dimensional projections, is also usedto describe the form of particles. It is the ratio of the majoraxis to minor axis of the ellipse equivalent to the object,which is a particle image in this case. The equivalent ellipsehas the same area, first degree moment, and second degreemoment as the particle image. Aspect ratio is always equal

to or greater than 1.0 since it is defined as (major axis/minor axis).

2.2. Analysis of angularity

Analysis methods for angularity have used mainly blackand white images of 2-dimensional projections of aggre-gates. The assumption here is that the angularity elementsin 2-dimensional are a good measure of the 3-dimensionalangularity. It should be noted that the image resolutionrequired for angularity analysis can easily be achievedusing automated systems for capturing images. Masadet al. [19] specified that an image resolution with a pixel sizeless than or equal to 1% of the particle diameter is requiredfor angularity analysis.

2.2.1. Angularity using fourier analysis (FRANG)

As mentioned earlier in the previous section, Fourierseries analysis can be used to analyze angularity of aggre-gates. The angularity signature as formulated by Wanget al. [30] is given by:

ar ¼X25

j¼5

an

a0

� �2

þ bn

a0

� �2" #

ð12Þ

where a0, an, and bn are found using Eqs. (8)–(10). Angular-ity is captured using harmonics with frequencies that arehigher than form and lower than texture.

2.2.2. Surface erosion–dilation (STI)

The erosion–dilation technique has been used to capturefine aggregate angularity and even surface texture [17]. ero-sion–dilation is well known in image processing, where it isused both as a smoothing technique [26a] and a shape clas-sifier [2]. Erosion is a morphological operation in whichpixels are removed from the image according to the num-ber of pixels surrounding it with different color [3,18].

Dilation is the opposite of the erosion in which pixels areadded to the image. An image could change due to the ero-sion–dilation cycles because surface angularities that arelost under erosion and will not be all restored during dila-tion [31,5]. Aggregate particle angularity is measured bythe area lost during the erosion–dilation process and isexpressed as a percentage of the total area of the originalparticle, which is described by the following expression:

Surface parameter ¼ A1 � A2

A1

� 100% ð13Þ

where A1 and A2 are the area of the object before and afterapplying the erosion–dilation operations, respectively(Fig. 1). A particle with more angularity would lose morearea than that of a smooth one; therefore, the surfaceparameter would be higher. Masad and Button [17] usedthis parameter to analyze angularity of a particle in low-resolution images and to analyze surface texture of a parti-cle at higher resolutions. Also, Rao et al. [23] implementedthe parameter is Eq. (13) to analyze aggregate texture.

Fig. 1. Illustration of the erosion–dilation and fractal behavior methods (after [19]).

T. Al-Rousan et al. / Construction and Building Materials 21 (2007) 978–990 981

2.2.3. Fractal dimension (FRCTL)

In its simplest form, fractal behavior is defined as theself-similarity exhibited by an irregular boundary whencaptured at different magnifications. Fractal behavior hasmany applications in science [14]. Smooth boundarieserode (or dilate) at a constant rate. However, irregular orfractal boundaries have more pixels touching opposite-color neighbors, and, hence, they do not erode (or dilate)uniformly [26b]. This effect has been used to estimate frac-tal dimensions, and, consequently, angularity along theobject boundary. This procedure was used by Masadet al. [18] to characterize the angularity of a wide rangeof aggregates used in asphalt mixes. The procedure isdepicted in Fig. 1.

The first step is to apply a number of erosion and dila-tion operations on the original image as shown inFig. 1(a), (b), and (d). Then, the eroded and dilated imagesare combined using the logical operator (Ex-OR). Usingthis operator, the two images (b and d) are comparedand pixels that have black color representing aggregateand are at the same location on both images are removed,

as shown in 1(e). By doing so, the pixels retained on thefinal image (Fig. 1(e)) are only those removed during ero-sion and added during dilation. These pixels form a bound-ary, which has a width proportional to the number oferosion–dilation cycles and surface angularity (Fig. 1(e)).

The procedure continues by varying the number of ero-sion–dilation cycles and measuring the increase in the effec-tive width of the boundary (total number of pixels dividedby boundary length and number of cycles) [26b]. Then, theeffective width is plotted versus the number of erosion–dila-tion cycles on a log–log scale. For a smooth boundary, theeffective width to number-of-cycles relationship shows notrend; that is, the effective width remains constant at differ-ent numbers of cycles. However, for a boundary with angu-larity, the graph would show a linear variation, where theslope gives the fractal length of the boundary.

2.2.4. Gradient angularity index (GRAD)The main idea behind this method is that at sharp cor-

ners of the surface of a particle image, the direction ofthe gradient vector for adjacent points on the surface

982 T. Al-Rousan et al. / Construction and Building Materials 21 (2007) 978–990

changes rapidly. On the other hand, the direction of thegradient vector for rounded particles change slowly foradjacent points on the surface.

The gradient-based method for measuring angularityconsists of the following steps. The acquired image is firstthreshold to get a binary image. This is followed by theboundary-detection step. Next, the gradient vectors at eachsurface point are calculated, using a Sobel mask that oper-ates at each point on the surface and its eight nearest neigh-bors [4].

The Sobel operator performs a 2-dimensional spatialgradient measurement on an image and emphasizes regionsof high spatial gradient that are located at the surface. TheSobel operator picks up the horizontal (Gx) and vertical(Gy) running edges in an image. These can then be com-bined to find the absolute magnitude of the gradient ateach point and the orientation of the gradient. The angleof orientation of the edge (relative to the pixel grid) thatresults in the spatial gradient is given by:

hðx; yÞ ¼ tan�1 Gx

Gy

� �ð14Þ

For the angularity analysis, the angle of orientation val-ues of the edge points (h) and the magnitude of the differ-ence in these values (Dh) for adjacent points on the edge arecalculated to describe how sharp or how rounded the cor-ner is. Fig. 2, illustrates the method of assigning angularityvalues to a corner point on the edge. The angularity valuesfor all the boundary points are calculated and their sumaccumulated around the edge to finally form a measureof angularity, which is denoted the gradient index (GI) [4]:

GI ¼XN�3

i¼1

jhi � hiþ3j ð15Þ

where i denotes the ith point on the edge of the particle andN is the total number of points on the edge of the particle.

2.2.5. Radius angularity index (RAD)

Masad et al. [19] proposed the radius angularity index,which is described by the following equation:

Radius angularity index ¼Xh¼360�Dh

h¼0

jRPh � REEhjREEh

ð16Þ

Fig. 2. Illustration of the difference in gradient between particles (after[4]).

where RPh is the radius of the particle at a directional angle,h, and REEh is the radius of an equivalent ellipse at thesame h. The index relies on the difference between the ra-dius of a particle in a certain direction and a radius of anequivalent ellipse taken in the same direction as a measureof angularity. By normalizing the measurements to the el-lipse dimensions, the effect of form on angularity is mini-mized [19].

2.2.6. Angularity using outline slope (AI)

Based on analyses of coarse aggregate images capturedby the University of Illinois Aggregate Image Analyzer(UIAIA), a quantitative angularity index (AI) was devel-oped [23]. The AI methodology is based on tracing thechange in slope of the particle image outline obtained fromeach of the top, side, and front images. Accordingly, the AIprocedure first determines an angularity index value foreach 2-dimensional image. Then, a final AI is establishedfor the particle by taking a weighted average of its angular-ity determined for all three views.

To determine the angularity for each 2-dimensional pro-jection, coordinates of an image outline that is based onaggregate camera view projection are first extracted. Next,the outline is approximated by an n-sided polygon asshown in Fig. 3. The angle subtended at each vertex ofthe polygon is then computed. Relative change in slopeof the n sides of the polygon is subsequently estimated bycomputing the change in angle (a) at each vertex withrespect to the angle in the preceding vertex. The frequencydistribution of the changes in the vertex angles is estab-lished in 10� class intervals. The number of occurrencesin a certain interval and the magnitude are then relatedto the angularity of the particle profile.

Eq. (17) is used for calculating angularity of each pro-jected image. In this equation, e is the starting angle valuefor each 10� class interval and P(e) is the probability thatchange in angle a has a value in the range e to (e + 10)

Angularity ¼ A ¼X170

e¼0

e� P ðeÞ ð17Þ

The AI of a particle is then determined by averaging theangularity values calculated from all three views whenweighted by their areas as given in the following equation:

n = 1

2

3

n=24

4

α1

α2

α3

αn

n-1

Fig. 3. Illustration of an n-sided polygon approximating the outline of aparticle (after [23]).

AI ¼ AðfrontÞ �AreaðfrontÞ þ AðtopÞ �AreaðtopÞ þ AðsideÞ �AreaðsideÞAreaðfrontÞ þAreaðtopÞ þAreaðsideÞ ð18Þ

T. Al-Rousan et al. / Construction and Building Materials 21 (2007) 978–990 983

The final AI value for the entire sample is simply anaverage of the angularity index values of all the particlesweighted by the particle weight, which measures overalldegree changes on the boundary of a particle.

2.3. Analysis of texture

The analysis of texture is commonly performed usingblack and white and gray images. The main disadvantageof using black and white images is the high-resolutionrequired for capturing images, which makes it difficult touse automated systems. In addition, the majority of texturedetails are lost when a gray image is converted to black andwhite. The analysis of gray images has the advantage ofanalyzing more texture data at the surface of a particle,leading to detailed information about texture. However,

Fig. 4. Illustration of the wavel

the main challenge facing this technique is the influenceof natural variation of color on gray intensities and, conse-quently, texture analysis. Some image analysis techniqueshave the potential to separate the actual texture from colorvariations. This section discusses some of the techniquesused to analyze the texture of aggregates.

2.3.1. Texture using Fourier series (FRTXTR)As mentioned in the previous section, Fourier series

analysis can be used to analyze texture of aggregates. Thetexture signature, as formulated by Wang et al. [30], isgiven by:

at ¼X180

j¼26

an

a0

� �2

þ bn

a0

� �2" #

ð19Þ

et decomposition (after [4]).

984 T. Al-Rousan et al. / Construction and Building Materials 21 (2007) 978–990

where a0, an, and bn are found using Eqs. (8)–(10). Textureis captured using harmonics with frequencies that are high-er than angularity and form.

2.3.2. Wavelet analysis (WVTXTR)

Texture in an image is represented by the local variationin the pixel gray intensity values. Wavelet theory offers amathematical framework for multi-scale image analysis oftexture [13]. This is advantageous to determine the texturescale or a combination that has the most influence on theaggregate performance in pavement layers.

The wavelet transform works by mapping an image ontoa low-resolution image and a series of detailed images. Anillustration of the method is presented here with the aid ofFig. 4. The original image is shown in Fig. 4(a). It isdecomposed into a low-resolution image (Image 1 inFig. 4(b)) by iteratively blurring the original image. Theremaining images contain information on the fine intensityvariation (high frequency) that was lost in Image 1. Image2 contains the information lost in the y-direction, Image 3has the information lost in the x-direction, and Image 4contains the information lost in both x- and y-directions.Image 1 in Fig. 4(b) can be further decomposed similarlyinto the first iteration, which gives a multi-resolutiondecomposition and facilitates quantification of texture atdifferent scales. An image can be represented in the waveletdomain by these blurred and detailed images. The textureparameter used is the average energy on Images 2, 3, and4 at each level. Texture index is taken at a given level asthe arithmetic mean of the squared values of the detailcoefficients at that level (level 6 is used):

Texture indexn ¼1

3N

X3

i¼1

XN

j¼1

ðDi;jðx; yÞÞ2 ð20Þ

where N denotes the level of decomposition and i takes val-ues 1, 2, or 3, for the three detailed images of texture, and j

is the wavelet coefficient index. More details on this methodcan be found in previous studies [13,6,4]. Owing to the multi-resolution nature of the decomposition, the energy signa-ture, or equivalently, the texture content has a physicalmeaning at each level. Energy signatures at higher levelsreflect the ‘‘coarser’’ texture content of the sample, whilethose at lower levels reflect the ‘‘finer’’ texture content.

3. Evaluation procedure

To evaluate the analysis techniques listed in Table 1, thefollowing procedure was adopted:

1. Analysis of diagrams of sediments with different shape

characteristics. These diagrams were developed by geol-ogists in the past to describe and quantify the 2-dimen-sional form and angularity of sediments. They wereplotted based on actual observations of sediments andmanual measurements of their form and angularity. Thisapproach is used to determine whether the analysis

methods are capable of identifying clear differencesbetween particle projections. Also, this task was helpfulto determine if an analysis method is able to separate thedifferent characteristics of shape (form, angularity, andtexture).

2. Analysis of the uniqueness of analysis methods. It is nec-essary to evaluate the correlations among different anal-ysis methods to identify which methods are able tocapture the same characteristics.

3. Comparison between visual rankings of texture and angu-

larity of aggregates by experienced individuals and results

of analysis methods. This is useful to identify analysismethods that are not capable of discriminating aggre-gates with extreme angularity and texture characteristics(e.g., uncrushed river gravel vs. crushed gravel, uncru-shed river gravel vs. crushed granite).

4. Analysis and results

4.1. Comparison with geological projections

The 2-dimensional image analysis methods listed inTable 1 were used to analyze the particle projections shownin Fig. 5. Fig. 5(a) was developed by Rittenhouse [25] tomeasure 2-dimensional form. This method is based onthe one developed earlier by Wadell [28,29], which is con-sidered a standard and accurate method for evaluatingform [24,22]. Fig. 5(b) was developed by Krumbein [12]to evaluate angularity. This method is also based on theone proposed by Wadell [28,29].

Correlations between analysis method parameters andvisual numbers by Rittenhouse [25] and Krumbiem [12]are shown in Tables 2 and 3, respectively. The Pearsoncoefficient (r) is given by:

r ¼Pn

i¼1ðxi � �xÞðyi � �yÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPni¼1ðxi � �xÞ2

Pni¼1ðyi � �yÞ2

q ð21Þ

where x and y represent two p-dimensional observations(items) x = [x1,x2, . . . ,xp] and y = [y1,y2, . . . ,yp]. x repre-sents the values measured by the image analysis methodson the projections, and y represents the visual numbers as-signed to the projections in Fig. 5 a and b. The Spearmancoefficient is defined exactly as the Pearson coefficient inEq. (21), but x and y represent the rankings of the imageanalysis results and visual numbers, respectively, insteadof the actual values. The use of Spearman coefficient is use-ful with the form of the x–y relationship (e.g., linear,power, and exponential) that varies among the differenttests. Examples of the correlations of image analysis meth-ods with angularity visual numbers are shown in Figs. 6and 7.

Rittenhouse [25] and Krumbein [12] projections can beused to identify analysis methods capable of capturingchanges in form and angularity, respectively. The correla-tion results in Tables 2 and 3 suggest that:

Fig. 5. Charts used by geologists in the past for visual evaluation of granular materials.

Table 2Pearson and Spearman correlation coefficients of Rittenhouse sphericity

Analysis methodparameter

Pearsoncorrelationcoefficient

Spearmancorrelationcoefficient

Applicability

GRAD 0.458 �0.54 NRAD �0.868 �0.894 Ya

FORM �0.98 �0.991 Ya

FRFORM �0.918 �0.993 YFRANG �0.814 �0.99 Ya

FRTXTR �0.858 �0.999 Ya

FER �0.938 �0.993 YAI �0.388 �0.368 NSTI 0.273 0.425 NASPT �0.938 �0.995 YFRCTL 0.256 �0.322 NROUND �0.941 �0.996 Ya

a Method correlates with two characteristics.

Table 3Pearson and Spearman correlation coefficients of Krumbein roundness

Analysis methodparameter

Pearsoncorrelationcoefficient

Spearmancorrelationcoefficient

Applicability

GRAD �0.886 �0.983 YRAD �0.964 �0.967 Ya

FORM �0.958 �0.967 Ya

FORM �0.016 �0.033 NFRANG �0.908 �0.883 Ya

FRTXTR �0.942 �0.967 Ya

FER 0.486 �0.317 NAI �0.959 �0.983 YSTI �0.957 �0.983 YASPT �0.414 0.317 NFRCTL �0.869 �0.867 YROUND �0.959 �0.967 Ya

a Method correlates with two characteristics.

T. Al-Rousan et al. / Construction and Building Materials 21 (2007) 978–990 985

R2 = 0.92

0

100

200

300

400

500

600

700

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

AI

Krumbein Visual Number

R2 = 0.94

0

1000

2000

3000

4000

5000

6000

0 0.2 0.4 0.6 0.8 1

GR

AD

Krumbein Visual Number

(a)

(b)

Fig. 6. Examples of the correlations of image analysis methods with visualnumbers of angularity.

Fig. 7. Examples of the correlations of image analysis methods with visualnumbers of form (sphericity).

986 T. Al-Rousan et al. / Construction and Building Materials 21 (2007) 978–990

� The following methods can be used only to describeform without being affected by angularity of a particle:(a) Flat and Elongated Ratio (FER) used by Universityof Illinois test method [27]; (b) Form index measuredusing Fourier Series (FRFORM); and (c) Aspect Ratiomeasured using Image Pro software (ASPT).� The following methods can be used to describe angular-

ity without being affected by form: (a) Gradient Angu-larity (GRAD) used in the Aggregate Imaging System(AIMS) [16]; (b) Angularity Index (AI) used by the Uni-versity of Illinois test method [23]; (c) Fractal technique(FRCTL).� Roundness (ROUND) and Texture Index using Fourier

(FRTXTR), Angularity Index using Fourier (FRANG),Form index (FORM) used in the AIMS system, andRadius Angularity (RAD) have good correlation withRittenhouse sphericity numbers and Krumbein round-ness numbers. This indicates that these methods arenot as unique as the other methods in distinguishingbetween angularity and form of particles. The Angular-ity Index (AI) and Texture Index (STI) have high corre-lations with each other. This could be attributed to thenature of the projections in Fig. 5b as they might have

been created to have the same levels of surface irregular-ities at the angularity and texture scales at differentmagnifications.

4.2. Uniqueness of test methods based on aggregate

clustering

This task was performed to examine the uniqueness ofthe analysis methods in capturing aggregate characteristics.A simple setup of a camera and a microscope was used tocapture images of 50 randomly selected coarse particles(12.5–9.5 mm; 1/2–3/8 in.), and 50 fine particles (2.36–1.18 mm; sieve #8–#16) of each aggregate type, listed inTable 4, at specified magnification. The aggregates wereselected to cover a wide spectrum of origin, rock type,and shape characteristics. The setup was equipped withtop lighting to capture gray images for texture analysisand a backlighting to capture black and white images forangularity analysis. The resulting images were analyzedusing standard image analysis techniques listed in Table 1.

Using the capabilities of SPSS statistical software, theanalysis results from the 50 images of the coarse aggregatesize of each aggregate type were used to cluster the analysismethods. The analysis methods were clustered using

Table 4Aggregates used in uniqueness evaluation

Label Source Aggregate description

CA-1 Montgomery, AL Uncrushed River GravelCA-2 Montgomery, AL Crushed River GravelCA-3 Childersburg, AL LimestoneCA-4 Auburn, AL DolomiteCA-5 Birmingham, AL SlagCA-6 Brownwood, TX LimestoneCA-7 Fairfield, OH Crushed Glacial GravelCA-8 Fairfield, OH Uncrushed Glacial GravelCA-9 Forsyth, GA GraniteCA-10 Ruby, GA GraniteCA-11 Knippa, TX TraprockCA-12 San Antonio, TX LimestoneCA-13 Augusta, GA Granite

T. Al-Rousan et al. / Construction and Building Materials 21 (2007) 978–990 987

Ward’s Linkage method. Clustering is a widely used pat-tern recognition method for grouping data and variables.Grouping is done on the basis of similarities or distances.In many areas of engineering and science, it is importantto group items into natural clusters. Basic references aboutclustering methods include most applied multivariate sta-tistical texts (e.g., [9,21]). All clustering methods start froma choice of a metric (a distance or closeness among objects)and a choice of a method for grouping objects. When items(units or cases) are clustered, proximity is usually indicatedby some sort of distance. On the other hand, variables areusually grouped on the basis of correlation coefficients orlike measure of association [9].

Two types of similarities were used. Pearson correlationcoefficient, given by Eq. (21), is used as a measure of prox-imity when variables are grouped. The second measure ofsimilarity was the Euclidean distance, given by Eq. (22),which is used to cluster cases. The Pearson correlationcoefficient is defined earlier in Eq. (21), and the Euclideandistance is given by:

dðx; yÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXp

i¼1

ðxi � y iÞ2

sð22Þ

Table 5Clustering of analysis methods based on Pearson correlation

Analysis method Aggregate

CA-1 CA-2 CA-3 CA-4 CA-5 CA-6

WVTXTR 1 1 1 1 1 1GRAD 2 2 2 2 2 2RAD 2 2 3 2 2 3FORM 2 2 2 2 2 3SPH 3 3 3 3 3 1FER 4 4 4 4 4 4AI 4 4 4 4 4 4STI 4 4 4 4 4 4FRFORM 2 2 2 2 2 3FRANG 2 2 2 2 2 3FRTXTR 2 2 2 2 2 3ASPCT 2 2 2 2 2 3FRCTL 2 2 3 2 2 3ROUND 2 2 2 2 2 3

where x and y represent two p-dimensional observations(items) x = [x1,x2, . . . ,xp] and y = [y1,y2, . . . ,yp].

Ward’s Linkage method forces to make the similarity orsum of squares of distance measures within groups as smallas possible. In this sense, it makes an ANOVA F-testamong the clusters as large as possible. Or, in other words,Ward’s method groups clusters whose combination resultsyields the smallest increase in the sum of squared devia-tions from the cluster mean.

Ward’s Linkage method with Pearson correlation prox-imity measure was applied to the analysis results. This typeof analysis was needed in order to identify clusters of anal-ysis methods. The results of the cluster analysis are shownin Table 5. For each aggregate type, the test methods thathave the same number (1, 2, 3, or 4) indicate that thesemethods are clustered, or they are more correlated witheach other than with other test methods. For example,the data from WVTXTR analysis of CA-1 is statisticallydifferent than the data from all the other test methods, indi-cating that this analysis method captures an aggregatecharacteristic different than what is captured by all theother methods. The percentage of aggregates for which atest method is clustered with other test methods is shownin Table 6. For example, the WVTXTR method is clusteredalone in 54% of aggregates, clustered with another methodin 31% of aggregates, and so on. In other words, anincrease in percentage in the cells toward the left of thetable is an indication of an increase in the uniqueness ofthe characteristic measured using this method. Based onthe results in Tables 5 and 6, WVTXTR is the most uniqueamong the texture parameters, GRAD and AI are the mostunique among the angularity parameters, and SPH is themost unique among the form parameters.

4.3. Comparison with visual rankings of texture and

angularity

Ward’s Linkage method was used to cluster aggregatesbased on their angularity and texture measured using each

CA-7 CA-8 CA-9 CA-10 CA-11 CA-12 CA-13

1 1 1 1 1 1 12 2 2 2 1 2 22 1 2 3 2 3 32 1 2 3 2 3 33 3 3 1 3 1 44 3 4 4 4 4 14 2 4 4 4 4 24 2 4 4 4 4 12 1 2 3 2 3 32 1 2 3 2 3 32 4 2 3 2 3 32 1 2 3 2 3 33 1 2 3 2 3 32 1 2 3 2 3 3

Table 7Coarse aggregates in texture classes estimated using ward’s linkage

Method Class 1 Class 2 Class 3 Class 4

WVTXTR 1, 2, 12 3, 5, 10, 11, 13 4, 6, 7, 8 9STI 1, 8 2, 3, 7, 10, 11, 13 4, 6, 9, 12 5FRTXTR 1, 7, 9, 10, 12 2, 4 3, 5, 6, 11, 13 8FRACTL 1, 4, 9, 10, 12 2, 3, 6, 11, 13 5, 7 8

Table 8Coarse aggregates in angularity classes estimated using ward’s linkage

Method Class 1 Class 2 Class 3 Class 4

GRAD 1, 8 2, 4, 6, 7, 12 5, 9, 10 3, 11, 13RAD 1, 2, 9 3, 4, 11, 13 5, 6, 7, 10, 12 8AI 1 2, 6, 9 3, 4, 5, 7, 10,

11, 12, 138

FRANG 1, 2, 3, 6,9, 11, 12

4, 5, 7, 10 8 13

FRACTL 1, 4, 9, 10, 12 2, 3, 6, 11, 13 5, 7 8ROUND 1, 2, 6, 12 3, 4, 5, 7, 9,

10, 118 13

Table 6Percentage of clustered aggregates for each analysis method

Analysis method Number of methods to cluster with

0 1 2 6 7 8

WVTXTR 54% 31% 8% 8%GRAD 23% 15% 8% 8% 8% 38%RAD 8% 54% 38%FORM 8% 54% 38%SPH 54% 38% 8%FER 8% 92%AI 8% 92%STI 100%FRFORM 8% 54% 38%FRANG 8% 54% 38%FRTXTR 8% 8% 46% 38%ASPCT 8% 54% 38%FRCTL 8% 8% 46% 38%ROUND 8% 54% 38%

988 T. Al-Rousan et al. / Construction and Building Materials 21 (2007) 978–990

of the analysis methods. The results of four clusters areshown in Tables 7 and 8. This analysis is useful to identifythose inaccurate methods that cluster aggregates with dis-tinct characteristics.

As shown in Table 7, both the FRTXTR and FRACTLparameters show aggregates CA-1 (uncrushed gravel) andaggregates CA-9 and CA-10 (both granite) in the samecluster. This finding indicates the inability of these methodsto detect significant differences between aggregates. STI

Table 9Characteristics of methods used in analyzing aggregate images

Method Description Features

Sphericity SPH � Separates aggrega� Captures unique c

Roundness ROUND � Separates angular� Clusters aggregate

different image resForm Index FORM � Captures 2-dimenForm Index (Fourier) FRFORM � Separates form fro

� Clusters aggregateolutions are used.

Flat and Elongated Ratio FER � Capable of separa� Capable of separa

Aspect Ratio ASPT � Separates angularAngularity Index (Fourier) FRANG � Does not separate

� Clusters aggregateolutions are used.

Surface erosion–dilation STI � Capable of separa� Clusters aggregate

used.Fractal Dimension FRCTL � Separates angular

� Clusters aggregatedifferent image res

Gradient angularity index GRAD � Capable of separa� Separates angular

Radius angularity index RAD � Captures angulariAngularity using outline slope AI � Capable of separa

� Separates angularTexture Index (Fourier) FRTXTR � Clusters aggregate

olutions are used.Wavelet Analysis WVTXTR � Capable of separa

� Most unique amo

shows both aggregates CA-2 (crushed gravel) and CA-10(granite) in the same texture cluster.

The results in Table 8 show that RAD, FRANG,FRTXTR, and ROUND methods cluster the uncrushed(CA-1) and crushed gravel (CA-2) in the same group. Thisresult indicates the inability of these methods to capturethe influence of crushing on angularity. Recall that these

tes with different form characteristics.haracteristics of aggregates.ity from form.s with distinct characteristics in the same group. This can be improved ifolutions are used.

sional form but it is not capable of separating form from angularity.m angularity.

s with distinct characteristics. This can be improved if different image res-

ting aggregates with different form characteristics.ting form from angularity.ity from form.angularity from form.

s with distinct characteristics. This can be improved if different image res-

ting aggregates with different aggregate characteristics.s similar to AI. This can be improved if different image resolutions are

ity from form.s with distinct characteristics in the same group. This can be improved ifolutions are used.ting aggregates with different angularity characteristics.ity from form.ty but it is not capable of separating 2-dimensional form from angularity.ting aggregates with different angularity characteristics.ity from form.s with distinct characteristics. This can be improved if different image res-

ting aggregates with different texture characteristics.ng the texture parameters.

T. Al-Rousan et al. / Construction and Building Materials 21 (2007) 978–990 989

methods are also not unique in distinguishing betweenangularity and form when used to analyze the geologicalprojections. Table 9 presents a summary of the findingsabout the analysis methods.

5. Conclusions

Shape properties of coarse and fine aggregates used inhot-mix asphalt, hydraulic cement concrete, and unboundbase and subbase layers are very important to the perfor-mance of the pavement system in which they are used in.Aggregate characteristics can be quantified using three inde-pendent parameters: form, angularity, and texture. Currentmethods used in practice for measuring these characteristicshave several limitations; they are laborious, subjective,often visual based classifications and not standardized, lackdirect relation with performance parameters, and limited intheir ability to distinguish individual characteristics ofform, angularity and surface texture. Imaging techniques,a strongly emerging technology, have proven to be capableof objectively quantifying these shape characteristics. Thevalidity of the analysis techniques and mathematical proce-dures employed by these methods is essential for the resultsto be useful in quantifying aggregate morphologies.

Accuracy of the analysis methods used in the currentlyavailable imaging systems was assessed in this paper byanalyzing some particle projections that have been usedby geologists for visual evaluation of particle shape. Also,all analysis methods were used to analyze images of aggre-gate particles in order to identify the ability of these meth-ods to accurately rank aggregates and capture uniquecharacteristics of aggregates. The analysis results revealedthat some of the available analysis methods were influencedby changes in both form and angularity characteristics and,consequently, were not suitable to distinguish betweenthese two characteristics. Also, some of the analysis meth-ods were not capable of distinguishing between changes intexture and angularity without considering image resolu-tion and magnification level. The following analysis meth-ods are recommended:

� Texture: Wavelet analysis of gray images of particle sur-face (WVTXTR);� Angularity: The gradient method (GRAD) and the

angularity changes in the slope of a particle outline (AI);� Shape: Sphericity (SPH) or the proportions of the three

particle dimensions for computing flatness and elonga-tion (FER).

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