Appendixes to NCHRP Report 555: Test Methods for Characterizing Aggregate Shape, Texture, and Angularity (2007)

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C-1 APPENDIX C IMAGE ANALYSIS METHODS FOR CHARACTERIZING AGGREGATE SHAPE PROPERTIES

C-2 IMAGE ANALYSIS METHODS FOR CHARACTERIZING AGGREGATE SHAPE PROPERTIES Several investigations have been conducted on the use of imaging technology to quantify aggregate shape properties and relate them to the performance of pavement layers. Some of these studies focused on developing procedures to describe shape (1, 2, 3, 4, 5, 6, 7, 8), angularity (9, 10, 11, 12, 13, 14, 15), and surface texture (14, 16, 17, 18, 19, 20, 21). This section describes, in general terms, most of the image analysis methods used to characterize particle shape, angularity, or texture. The discussion provided in this section on the analysis methods is largely taken from Masad (14), Fletcher (22) , and Chandan et al. (21). Typical Analysis of Shape Sphericity In order to properly characterize the shape of an aggregate particle, information about three dimensions of the particle is necessary {longest dimension, [dl], intermediate dimension, [di], and shortest dimension, [ds]). A number of indices have been proposed for measuring shape that relate the ratio of two dimensions, such as elongation and flatness. Sphericity and shape factor are indices that are expressed in terms of three dimensions (23). Sphericity = 3 2 * l is d dd (C-1) Shape Factor = il s dd d * (C-2)

C-3 Form Factor Form factor is widely used measure of shape in two-dimensions (2-D) and is expressed by the following equation: Form Factor = 2 4 P Aπ (C-3) where P and A are the perimeter and area of a particle, respectively. Form factor is equal to unity for a circular-shaped particle. Roundness The inverse of the form factor, Equation (C-3), which is known as roundness (ROUND) can also be used. Some analysis systems use other tems to describe form factor. The Camsizer system, for example, uses the term sphericity (SPHT) to describe this same term (roundness). As in shape factor, a circular object will have a roundness value of 1.0, and other shapes will have roundness values greater than 1.0. Form Index Form index was proposed by Masad et al., (24) to describe shape (or form) in 2-D. It uses incremental changes in the particle radius. The length of a line that connects the center of the particle to the boundary of the particle is termed radius. Form index is expressed by the following equation: Form Index = ∑Δ−= = Δ+ −θθ θ θ θθθ360 0 R RR (C-4) where θ is the directional angle and R is the radius in different directions. By examining Equation (C-4), it will be noted that, if a particle was a perfect circle, the form index would be

C-4 zero. Although the form index is based on 2-D measurements, it can easily be extended to analyze the 3-D images of aggregates. Form Index (Fourier Series) Fourier series can be used to analyze the shape, angularity, and texture of aggregates. Each aggregate profile, defined by the function R(θ), can be analyzed using Fourier series coefficients as follows: [ ]∑∞ = ++= 1 )sin()cos()( n nn nbnaaR θθθ o (C-5) where na and nb are the Fourier coefficients. The function R(θ) traces out the distance to the boundary from a central point as a function of the angle θ, 0o < θ < 360o. Obviously, R(θ) is a periodic function. These coefficients can be evaluated using the following integrals: ( )dθ θR 2π 1 2π 0 ∫=oa (C-6) ( )∫= π θθθπ 2 0 cos)(1 dnRa n n = 1, 2, 3, …. (C-7) ( )∫= π θθθπ 2 0 )sin(1 dnRbn n = 1, 2, 3, …. (C-8) If R(θ) is only known numerically at a discrete number of angles, the above integrals can be written using summations as follows: ∑Δ− = ⎟⎠ ⎞⎜⎝ ⎛ +Δ+= θπ θ θθθ π 2 0 2 )()( 2 1 RRa o (C-9) ( )( )θθθθθθπ θπ θ nnRRa n sinsin2 )()(1 2 0 −Δ+⎟⎠ ⎞⎜⎝ ⎛ +Δ+= ∑Δ− = (C-10)

C-5 ( ) ( )θθθθθθπ θπ θ nRRbn cos)cos(2 )(1 2 0 +Δ+−⎟⎠ ⎞⎜⎝ ⎛ +Δ+= ∑Δ− = (C-11) where R(θ) is measured only at predefined increments, and θ takes on values from 0 to (2π - Δθ) with an increment Δθ of about 4o. The higher the value of n used in Equation (C-5), the better the actual particle profile is reproduced. Wang et al., (25) formulated shape signatures using the an and bn coefficients as follows: Form Signature: n ≤ 4 ∑ = ⎥⎥⎦ ⎤ ⎢⎢⎣ ⎡ ⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛+⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛= 4 1 2 0 2 0j nn s a b a aα (C-12) The characteristics (shape, angularity, and texture) can all be represented by the same function and at the same time can be differentiated by the frequency magnitudes of the harmonics used to capture a particle boundary. Shape (or form) is captured using harmonics with lower frequency than texture and angularity. Flat and Elongated Ratio Another way of presenting the shape of a particle is by using flat and elongated ratio (FER). FER represents the ratio between the longest dimension and the shortest dimension of a particle which is perpindicular to the longets dimension. Aspect Ratio Aspect ratio (ASPCT), which is similar to FER ratio but usually used for 2-D projections, is used to describe the shape of particles. It is the ratio of the major axis to minor axis of the ellipse equivalent to the object, which is a particle image in this case. The equivalent ellipse is

C-6 supposed to have the same area as the particle image and first and second degree moment. Aspect ratio is always equal to or greater than 1.0, since it is defined as (major axis/minor axis). Breadth to Width Ratio Breadth to width ratio can be used to describe the shape of aggregate particles. The Camziser system uses the following equation to calculate this ratio: Ratio of Breadth to Width = )max( )min( / Fe c x x lb = (C-13) Where, xc is the maximum chord, and xFe is the Feret diameter, both determined from up to 32 directions for each particle. Feret diameter is the distance between two tangents placed 90o to the measuring direction and touching the particle. Symmetry Symmetry is another term that some imaging systems use to describe aggregate shape. Symmetry of an aggregate particle can be given by: Symmetry = ⎥⎦ ⎤⎢⎣ ⎡ ⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛+ 2 1min1 2 1 r r (C-14) where r1 and r2 are the distances of the center of gravity to the edge in a given direction, i.e., maximum diameter = r1 + r2. Typical Analysis of Angularity Analysis methods for angularity have used mainly black and white images of 2-D projections of aggregates. The assumption here is that the angularity elements in 2-D are a good measure of the 3-D angularity. It should be noted that the image resolution required for

C-7 angularity analysis can easily be achieved using automated systems for capturing images. Masad et al., (24) specified that an image resolution with a pixel size less than or equal to 1% of the particle diameter is required for angularity analysis. Fourier Series Analysis of Angularity As mentioned earlier in the previous section, Fourier series analysis can be used to analyze angularity of aggregates. The shape signature for angularity as formulated by Wang et al. (25) is given by: Angularity Signature: 5 ≤ n ≤ 25 ∑ = ⎥⎥⎦ ⎤ ⎢⎢⎣ ⎡ ⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛+⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛= 25 5 2 0 2 0j nn r a b a aα (C-15) where a0, an, and bn are found using Equations (C-9 through C-11). Angularity is captured using harmonics with frequencies that are higher than form and lower than texture. Surface Erosion-Dilation Technique The erosion-dilation technique has been used to capture fine aggregate angularity and even surface texture (18). Erosion-dilation is well known in image processing, where it is used both as a smoothing technique (26) and a shape classifier (27). Erosion is a morphological operation in which pixels are removed from the image according to the number of pixels surrounding it with different color (24). Erosion can be visualized as a fire burning inward from the periphery of an object, in order to shrink the object to a skeleton or a point (28). Layer-by- layer erosion tends to smooth a particle surface.

C-8 Dilation is the opposite of the erosion. A layer of pixels is added around the periphery of the eroded image to form a simplified version of the original object. An image does not necessarily need to be restored to its original state after a number of erosion and dilation cycles (29). Surface angularities may be lost under erosion and will not be restored during dilation since there is no seed pixel from which the dilation can build (30). Following this logic, one can state that the area of the object lost after erosion and dilation is “proportional” to the angularity of the particle, assuming that no particles are lost during the procedure. Aggregate particle angularity is measured by the area lost during the erosion-dilation process and is expressed as a percentage of the total area of the original particle, which is described by the following expression: Surface Parameter = %100* 1 21 A AA − (C-16) where A1 and A2 are the area of the object before and after applying the erosion-dilation operations, respectively (Figure C-1). A particle with more angularity would lose more area than that of a smooth one; therefore, the surface parameter would be higher. Masad and Button (18) found that this parameter correlated to angularity of a particle at low resolutions and to surface texture of a particle at higher resolutions. Fractal Behavior Technique In its simplest form, fractal behavior is defined as the self-similarity exhibited by an irregular boundary when captured at different magnifications. Fractal behavior has many applications in science (31), particularly for describing the shape of natural objects (e.g., clouds, body organs, rocks, etc.). Smooth boundaries erode (or dilate) at a constant rate. However, irregular or fractal boundaries have more pixels touching opposite-color neighbors, and, hence, they do not erode (or dilate) uniformly. This effect has been used to estimate fractal dimensions,

C-9 and, consequently, angularity along the object boundary. The basic idea for measuring a fractal dimension by image analysis came from the Minkowski definition of a fractal boundary dimension (32). This procedure was used by Masad et al., (12) to characterize the angularity of a wide range of aggregates used in asphalt mixes. The procedure is depicted in Figure C-1. The first step is to apply a number of erosion and dilation operations on the original image as shown in Figure C-1(a), (b), and (d). Then, the eroded and dilated images are combined using the logical operator (Ex-OR). Using this operator, the two images (b and d) are compared and pixels that have black color representing aggregate and are at the same location on both images are removed, as shown in Figure C-1(e). By doing so, the pixels retained on the final image (Figure C-1(e)) are only those removed during erosion and added during dilation. These pixels form a boundary, which has a width proportional to the number of erosion-dilation cycles and surface angularity (Figure C-1 (e)). The procedure continues by varying the number of erosion-dilation cycles and measuring the increase in the effective width of the boundary (total number of pixels divided by boundary length and number of cycles). Then, the effective width is plotted versus the number of erosion- dilation cycles on a log-log scale. For a smooth boundary, the effective width to number-of- cycles relationship shows no trend; that is, the effective width remains constant at different numbers of cycles. However, for a boundary with angularity, the graph would show a linear variation, where the slope gives the fractal length of the boundary.

C-10 Erosion Dilation Area = A1 Area = A2 Ex-Or Effective width Erosion - Dilation Technique Fractal Behavior Technique Dilation (d) (e) (a) (b) (c) Figure C-1. Illustration of the Erosion-Dilation and Fractal Behavior Method (after (24)).

C-11 Hough Transform Hough Transform is another technique used to recognize co-linearity in pixels that form the particle outline (33). This technique has been successfully implemented in the medical field and in the analysis of aerial images. By detecting and measuring the length of any straight lines in a 2-D image and the angle between them, angularity of a particle can easily be determined. Wilson et al., (34) used the Hough Transform to develop an index for quantifying aggregate angularity. This transform was used to determine the longest line on the outline of particle images at each possible direction A(θ). Then, the length of the longest line, AMax, in all directions and the average length of the line, A, which also corresponds to the longest line on the edge of the particle are computed. Angularity is then quantified by the index: Hough Transform Shape Index = MaxA A−1 (C-17) Wilson and Klotz (10) noted that, if only one or two lines dominated the particle, the value approached 1.0. However, if the particle was rounded or irregular, then all of the straight lines are short and close to the average and the index approached 0.0. Therefore, the index approaches 0.0 for rounded particles and is typically greater than 0.6 for angular particles. Gradient Method The main idea behind this method is that, at sharp corners of the surface of a particle image, the direction of the gradient vector for adjacent points on the surface changes rapidly. On the other hand, the direction of the gradient vector for rounded particles changes slowly for adjacent points on the surface. The gradient-based method for measuring angularity consists of the following steps. The acquired image is first thresholded to get a binary image. This is followed by the boundary-

C-12 detection step. Next, the gradient vectors at each surface point are calculated, using a Sobel mask that operates at each point on the surface and its eight nearest neighbors (21). The Sobel operator performs a 2-D spatial gradient measurement on an image and emphasizes regions of high spatial gradient that are located at the surface. The Sobel operator picks up the horizontal (Gx) and vertical (Gy) running edges in an image. These can then be combined to find the absolute magnitude of the gradient at each point and the orientation of the gradient. The angle of orientation of the edge (relative to the pixel grid) that results in the spatial gradient is given by: ⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛= − y x G Gyx 1tan),(θ (C-18) For the angularity analysis, the angle of orientation values of the edge points (θ) and the magnitude of the difference in these values (Δθ) for adjacent points on the edge are calculated to describe how sharp or how rounded the corner is. Figure C-2 illustrates the method of assigning angularity values to a corner point on the edge. The angularity values for all the boundary points are calculated, and their sum is accumulated around the edge to finally form a measure of angularity, which is denoted the gradient index (GI) (21): ∑− = +−= 3 1 3 N i iiGI θθ (C-19) where i denotes the ith point on the edge of the particle, and N is the total number of points on the edge of the particle.

C-13 Figure C-2. Illustration of the Difference in Gradient between Particles (after (21)).

C-14 Direct Measurements of Particle Dimensions Kuo and Freeman (13) (2000) proposed an angularity parameter, which is expressed by the following equation: Angularity Parameter = 2 ellipse convex P P ⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛ (C-20) where Pellipse is the perimeter of an equivalent ellipse (i.e., an ellipse with the same longest and shortest axes of a particle), and Pconvex is the perimeter of the bounding polygon. Angularity Index Masad et al,. (24) proposed the angularity index, which is described by the following equation: Angularity Index = ∑Δ−= = −θθ θ θ θθ360 0 EE EEP R RR (C-21) where RPθ is the radius of the particle at a directional angle, θ. REEθ is the radius of an equivalent ellipse at the same θ. The index relies on the difference between the radius of a particle in a certain direction and a radius of an equivalent ellipse taken in the same direction as a measure of angularity. By normalizing the measurements to the ellipse dimensions, the effect of form on angularity is minimized (24). Outline Slope Method Based on image analysis from the images captured by the University of Illinois Aggregate Imaging Analyzer (UIAIA), a quantitative angularity index (AIUI) was developed (15). The AIUI methodology is based on tracing the change in slope of the particle image

C-15 outline obtained from each of the top, side, and front images. Accordingly, the AIUI procedure first determines an angularity index value for each 2-D image. Then, a final AIUI is established for the particle by taking a weighted average of its angularity determined for all three views. To determine angularity for each 2-D projection, an image outline based on aggregate camera view projection and its coordinates are first extracted. Next, the outline is approximated by an n-sided polygon, as shown in Figure C-3. The angle subtended at each vertex of the polygon is then computed. Relative change in slope of the n sides of the polygon is subsequently estimated by computing the change in angle (β) at each vertex with respect to the angle in the preceding vertex. The frequency distribution of the changes in the vertex angles is established in 10o class intervals. The number of occurrences in a certain interval and the magnitude are then related to the angularity of the particle profile. Equation (C-22) is used for calculating angularity of each projected image. In this equation, e is the starting angle value for each 10o class interval, and P(e) is the probability that change in angle α has a value in the range e to (e+10). ∑ = == 170 0 )(* e ePeAAngularity (C-22) The UIAI of a particle is then determined by averaging the angularity values (see Equation C-23) calculated from all three views when weighted by their areas as given in the following equation: )()()( )(*)()(*)()(*)( sideAreatopAreafrontArea sideAreasideAtopAreatopAfrontAreafrontAUIAI ++ ++= (C-23) The final UIAI value for the entire sample is simply an average of the angularity index values of all the particles weighted by the particle weight, which measures overall degree changes on the boundary of a particle.

C-16 n = 1 2 3 n=24 4 α1 α2 α3 αn n-1 Figure C-3. Illustration of an n-Sided Polygon Approximating the Outline of a Particle (after (15)).

C-17 Convexity Convexity is another parameter that can used to describe angularity of aggregate particles. Convexity can be calculated using the following formula: Convexity = Convex Particle A A Conv = (C-24) Where AParticle is the area of the real projection of the particle, and AConvex is the area of the convex particle’s projection. Minimum Average Curve Radius This method is described by Maerz (35) and illustrated in Figure C-4. In this method, aggregate angularity is defined as the minimum average curve radius of the individual particles. Maerz (35) described the following procedure to calculate the minimum average curve radius: The radius of a circle containing three points on the profile is calculated from the array of x, y points, each point separated by 10 pixels. An instantaneous curve radius is determined for each point on the profile in this manner, creating an array of curve radii. Then the array of curve radii values are smoothed by a moving average filter. A 5-point Gaussian low-pass filter is used (see Figure C-5). The array of smoothed curve radii is examined to find local minimal in the curve radius function. A test is performed to ensure that a corner of the aggregate piece does not result in more than one local minimum. Then the list of local minimum curve radii is ordered from smallest to largest. The averages of the four smallest curve radii are averaged to produce the minimum average curve radius of the individual piece.

C-18 Figure C-4. Average Minimum Curve Radius Calculations. Left: Rounded Aggregate. Right: Angular Aggregate. Bottom: Aggregate Profile with Inscribed Curve Radii (after (35)). 0 5 10 15 20 25 30 35 1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151 161 171 181 191 201 211 221 Position on Perimeter C ur ve R ad iu s (p ix el s) Raw Values Smoothed Values Figure C-5. Curve Radius Measurements around the Profile of the Rounded Particle in Figure C-4; Raw and Smoothed Values (after (35)).

C-19 Typical Analysis of Texture The analysis of texture has been performed using both black and white images and gray images. The main disadvantage of using black and white images is the high resolution required for capturing images, which makes it difficult to use automated systems. In addition, the majority of texture details are lost when a gray image is converted to black and white. The analysis of gray images has the advantage of analyzing more texture data at the surface of a particle, leading to detailed information about texture. However, the main challenge facing this technique is the influence of natural variation of color on gray intensities and, consequently, texture analysis. Some image analysis techniques have the potential to separate the actual texture from color variations. This section discusses some of the techniques used to analyze the texture of aggregates. Fourier Series Analysis of Texture As mentioned in the previous section, Fourier series analysis can be used to analyze texture of aggregates. The shape signature for texture, as formulated by Wang et al. (25), is given by: Texture Signature: 26 ≤ n ≤ 180 ∑ = ⎥⎥⎦ ⎤ ⎢⎢⎣ ⎡ ⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛+⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛= 180 26 2 0 2 0j nn t a b a aα (C-25)

C-20 where a0, an, and bn are found using Equations C-9 to C-11. Texture is captured using harmonics with frequencies that are higher than angularity and shape. Intensity Histogram Method An intensity histogram evaluates the variation in the gray intensity of the gray- scale image over the entire image. The mean and standard deviation of the variations are the output from the intensity histogram. There is a correlation between the standard deviation of gray intensity and the surface texture of the particle (24). Standard deviations are typically much lower for smooth particles than for rough particles. Figure B-6 shows images of smooth and rough particles and their intensity histograms. Fast Fourier Transform Method This is a well-known method in the sciences for converting data from the time or spatial domain to the frequency domain. Dominant frequencies become apparent when a Fast Fourier Transform (FFT) is applied to a gray-scale image. Frequency is a measure of reoccurrence of a distinct gray level intensity in the image. The resulting FFT image consists of points of different gray levels, where the distance of a point from the center represents the frequency and the gray level in the FFT image corresponds to the peak intensity at a given frequency (32). The number of dominant peaks in the FFT has been found to be a measure of the surface texture (24) (Figure C-6).

C-21 (a) Smooth texture (b) Rough texture (c) FFT of smooth texture (d) FFT of rough texture (e) Histogram of smooth texture (f) Histogram of rough texture Figure C-6. Images of Smooth-and Rough-Textured Aggregates and their Fast Fourier Transforms and Histograms (after (24)).

C-22 Wavelet Analysis Texture in an image is represented by the local variation in the pixel gray intensity values. Although there is no single scale that represents texture, the histogram and FFT analyses of texture capture only a single scale. Wavelet theory offers a mathematical framework for multi-scale image analysis of texture (36). This is advantageous to determine the texture scale or a combination of them that has the most influence on the aggregate performance in pavement layers The wavelet transform works by mapping an image onto a low-resolution image and a series of detail images. An illustration of the method is presented here with the aid of Figure B-7. The original image is shown in Figure C-7(a). It is decomposed into a low-resolution image (Image 1 in Figure C-7(b)) by iteratively blurring the original image. The remaining images contain information on the fine intensity variation (high frequency) that was lost in Image 1. Image 2 contains the information lost in the y- direction, Image 3 has the information lost in the x-direction, and Image 4 contains the information lost in both x- and y-directions. Image 1 in Figure C-7(b) can be further decomposed similar to the first iteration, which gives a multi-resolution decomposition and facilitates quantification of texture at different scales. An image can be represented in the wavelet domain by these blurred and detailed images. The texture parameter used is the average energy on Images 2, 3, and 4 at each level. Texture index is taken at a given level as the arithmetic mean of the squared values of the detail coefficients at that level (level 6 is used):

C-23 (a) (b) Figure C-7. Illustration of the Wavelet Decomposition (after (21)). Image 3 Image 1 Image 2 Image 4

C-24 ( )( )23 , 1 1 1 , 3 N n i j i j Texture Index D x y N = = = ∑∑ (C-26) where N denotes the level of decomposition and i takes values 1, 2, or 3, for the three detailed images of texture, and j is the wavelet coefficient index. More details on this method can be found in other references (19, 21, 36), Owing to the multi-resolution nature of the decomposition, the energy signature, or equivalently, the texture content has a physical meaning at each level. Energy signatures at higher levels reflect the “coarser” texture content of the sample, while those at lower levels reflect the “finer” texture content. Direct Measurements of Particle Dimensions Kuo and Freeman (13) proposed the texture parameter, which is expressed as follows: Texture Parameter = 2 convexP P ⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛ (C-27) Where, P is the perimeter of a particle measured on a black and white image, and Pconvex is the perimeter of a bounding polygon.

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