A NEW IMAGE ANALYSIS TECHNIQUE TO QUANTIFY PARTICLE

ANGULARITY

Tafesse Solomon1*

, Sun Wenjuan2, Fernlund Joanne

1, and Linbing Wang

2

1 Engineering Geology and Geophysics Research Group

Royal Institute of Technology (KTH)

Teknikringen 76, SE- 100 44

Stockholm, Sweden

*e-mail: tafesse@kth.se

Telephone: 0046-8-790-6807

2 Civil and Environmental Engineering

Virginia Tech, College of Engineering

Blacksburg, Virginia 24061

1

ABSTRACT 2

Angularity is a fundamental morphological descriptor of a particle; it determines the 3

aggregate performance in asphalt and concrete works. This paper introduces an innovative 4

matlab based image analysis technique to quantify the angularity of an aggregate. The 5

algorithm is based on application of two successive b-spline smoothing techniques around the 6

aggregate profile. The first b-spline smoothing curve is generated by joining the mid-points of 7

the adjacent segments; and the second smoothing curve is generated by a smoothing function 8

upon the first b-spline. Then the distribution of the perpendicular distance between these two-9

b-splines is evaluated, which provides an excellent estimate to the aggregate angularity. In 10

this paper the angularity index of six aggregate samples is determined using our new 11

technique. Then we compared the index obtained with an existing Aggregate Imaging 12

Measurement System (AIMS) and the measurement from the two methods revealed good 13

similarity. Therefore our new method can be considered as a useful alternative in the 14

aggregate industry for distinguishing the angularity of the samples obtained from different 15

sources. 16

Key words: angularity, aggregate, digital image analysis 17

INTRODUCTION 18

The shape distribution of granular particles is vital to both geologists and engineers. 19

Geologists are interested in the shape of granular particles, which is helpful to determine the 20

history of both transport and deposition of sediments. Engineers would pay attention to 21

aggregate shape properties, which have great influence on the strength and quality of 22

hydraulic cement concrete and asphalt concrete [7-9]. The shape of an aggregate can be 23

described in terms of three main morphological descriptors (Fig. 1): form, texture and 24

angularity [1-6]. Among the three shape descriptors, angularity (the irregularity of the 25

aggregate corners) is an important parameter. . Aggregate angularity is known to affect 26

workability, rheological properties, and interlocking strength of concrete joints for cement 27

concrete, and it also influences initial compaction and binder-aggregate bond for asphalt 28

concrete [9]. Thus it is essential to quantify the angularity characteristics of aggregates, and to 29

associate it with the performance of cement concrete and asphalt concrete. 30

Numerous measurement techniques have been developed for quantifying aggregate 31

angularity. These techniques can be broadly divided into manual and digital image analysis 32

methods. The manual methods are subjective, inaccurate and time consuming [10]; but the 33

image-based angularity indexes provide objective measurements [8, 11-22]. 34

Together with the advancement of digital image acquisition techniques and software 35

packages, the digital image analysis method is developing with a great variety. However the 36

image analysis principles and image acquisition setups used by the different researchers are 37

not comparable; and some of the algorithms used are complex, so that they require a longer 38

time for processing. 39

This paper describes a simple and faster image analysis algorithm developed in 40

Matlab program, to quantify the angularity of a particle from a digital image . The efficiency 41

of the new image analysis algorithm is tested on six aggregate samples from a wide range of 42

sources and the calculated angularity index is compared with the result obtained from the 43

existing Aggregate Image Measurement System (AIMS). 44

LITERATURE REVIEW: MEASUREMENT OF ANGULARITY 45

In general, there are three methods to determine aggregate angularity: manual measurement, 46

standard silhouette chart and digital image analysis. 47

Manual measurement 48

Manual measurement methods are easy to conduct, but they are considered as both subjective 49

and time consuming. Generally, they can be divided into two groups based on the analysis 50

concepts: namely direct method and indirect method. The direct method is performed by 51

counting the number of fractured faces on the particle surface [23]. The indirect method 52

determines aggregate angularity by calculating the uncompacted void content of a bulk 53

sample [24, 25], which is based on the assumption that samples with less angularity tends to 54

have smaller void content than angular aggregate samples. 55

Standard silhouette chart 56

The standard silhouette chart is used to estimate the aggregate angularity by visual 57

comparisons to the particle outline. In this method aggregate angularity is described by 58

different roundness value, which has a value ranging from 0.1 to 1.0 (Fig. 2). As shown in the 59

figure 2, a smaller value of roundness level represents the more angular aggregate. This 60

method is preferable than the manual measurement method for quick characterization of 61

aggregate angularity. 62

Digital Image Analysis 63

In general, the digital image analysis methods (DIAM) use different instrumental setups for 64

image acquisition and implement various mathematical algorithms to calculate the angularity 65

of particles [8, 11-16, 26, 27]. Since the mathematical algorithms used in the different DIAM 66

are various, the angularity indexes obtained from the different methods may not be 67

comparable to each other. 68

The most commonly used DIAM for aggregate angularity analysis are: Degree of angularity 69

(A), Gradient angularity index (GRAD), Radius angularity index (RAD), Angularity using 70

outline slope (AI), Surface erosion-dilation, Fractal dimension (FRCTL), and Fourier Power 71

Spectrum Analysis. These different techniques use different theories to calculate the 72

angularity. 73

Degree of angularity (A) 74

Lees (1964) quantified the angularity of a particle based on the ratio of the bounding edge 75

angles (a) and the distance of the edges from the center of the particle (x), which is defined by 76

the largest inscribed circle to the radius of the maximum inscribed circle (Fig. 3a): 77

(1) 78

where 79

= the angle bounding the edge 80

= distance from center of the maximum inscribed circle to the particle edges 81

= the radius of the maximum inscribed circle, assumed to be the center of the paricle 82

= the angularity of the particle edge 83

The total angularity (A) is given by the sum of all the Ai values, calculated from all 84

corners of the particle. 85

Gradient angularity index (GRAD) 86

In this method the gradient values for all the corners are calculated; then the angularity index 87

of the particle is determined as the average of the change in the angles of the gradient vectors 88

around the particle circumference [9, 10]. The direction of the gradient vector for angular 89

particle outline changes rapidly but the change is slow for the rounded outline (Fig.3b): 90

∑ | | (2) 91

where: 92

= the ith

pixel on the perimeter of the particle 93

N = the total number of pixels in the perimeter 94

= the orientation of the gradient at the given pixel 95

= number of pixels between gradients used in the calculations. 96

Radius angularity index (RAD) 97

Masad et. al. (2001) quantify the angularity as the sum of the distance difference between the 98

outline of a particle in certain direction to that of an equivalent ellipse. 99

∑| |

(3) 100

where 101

= radius of the particle at a directional angle 102

= radius of the equivalent ellipse at an angle of 103

AI = angularity index (the value is normalized by the ellipse dimension, to minimize 104

the effect of form on the angularity value). 105

Outline slope angularity 106

Rao et. al. (2002) measured the angularity of a particle as changes in the slope of the particle 107

outline. In this method the particle outline is approximated by an n-sided polygon (Fig. 3c). 108

The subtended angles at each polygon are measured and the frequency distribution of the 109

changes in the vertex angles is grouped in 10 degrees intervals. Then the magnitude and 110

number of occurrences of the subtended angles in a certain interval is related to the angularity 111

of the particle. 112

Surface erosion-dilation 113

Surface erosion-dilation is a basic morphological operation in image analysis. Erosion 114

removes pixels from an image and dilation adds pixel to the image. Masad and Button (2000) 115

and Rao et. al. (2000) have used this technique to quantify the angularity of a particle as the 116

area lost during the erosion-dilation process and named this difference as surface parameter 117

( ) (Fig. 3d), 118

(4) 119

where 120

= surface parameter 121

, = areas before and after applying the erosion-dilation operations (Fig. 3d). 122

Fractal dimension (FRCTL) 123

Masad et. al. (2000) measure the angularity of a particle based on fractal dimension methods 124

(Fig. 3e). Fractal behavior is the self-similarity exhibited by an irregular boundary of a 125

particle when captured at different magnification. Smooth boundaries erode or dilate at a 126

constant rate and show close similarities in shape, but angular boundaries do not. In this 127

method the eroded and dilated images are combined by the logical operator, “or”. The width 128

of the pixels retained on the final image, those removed during erosion and added during 129

dilation, would represent the particle angularity. 130

Fourier Power Spectrum Analysis 131

Wang et. al. (2005) used the Fourier transform to quantify the angularity of a particle. In this 132

method the particle profile is defined by the function , which can be analyzed using 133

Fourier series. 134

∑ [ ] (5) 135

where 136

= traces distance to the boundary from central point as a function of angle 137

and are the fourier coefficients. 138

Smoothing-Angularity Index (SAI) 139

In this section the principles used to represent aggregate angularity in our novel method will 140

be elaborated. Figure 4 summarizes the SAI technique in simplified flow chart. The new 141

program uses an image of a particle captured using a digital camera in JPG format. The 142

images were carefully captured, with sufficient contrast to easily recognize the aggregate 143

profiles from the image background. The analysis starts by converting the original gray level 144

digital image into a binary image, by applying an image segmentation algorithm. Then the 145

vertex of the binary image outline (polygon) is automatically identified by our program, 146

followed by two steps b-spline smoothing technique around the polygon (Fig. 5). The first 147

smoothing curve is generated by joining the mid-points of the adjacent edges of the polygon 148

(presented in green color); then the second smoothing curve (shown in red color) is generated 149

for the first b-spline smoothing curve. Finally the perpendicular distances between the two-b-150

spline smoothing curves calculated around each individual aggregate profile (Fig. 6). Then 151

both the distance distribution between the two smoothing curves and their mean are evaluated 152

and plotted together (Fig. 7). Thus in our smoothing angularity index (SAI) approach, we 153

defined the aggregate angularity index (SAI) as the average fluctuation of the perpendicular 154

distance around the calculated mean, Eq. (6). 155

∑ | |

(6) 156

where 157

= distance between the two smoothing curves at the ith

point 158

= mean of the distance between the two smoothing curves 159

= number of perpendicular segments between the two curves 160

= smoothing angularity index. 161

The smaller SAI value indicates that the distribution of the vertical distance between 162

the two curves is closer to the mean that would indicate the particle to have lower angularity 163

index. 164

RESULT AND DISCUSION 165

In order to examine the efficiency of our angularity analysis algorithm, SAI, we studied the 166

six samples, in the 1.9 – 2.54 cm size range, using both the SAI and AIMS methods. The 167

aggregate samples include: limestone, iron ore, glacial gravel rounded, glacial gravel crushed, 168

dolomite and copper ore. Except the glacial gravel rounded sample all the other five samples 169

are crushed aggregates. 170

Figure 8 plots the angularity index of the six samples in both histograms and cumulative 171

distributions. In general, the SAI value ranges from 0.15-0.45. As can be seen from the figure, 172

70% of the sample from the glacial gravel rounded aggregate have very low angularity index, 173

ranging from 0.2-0.25. However the iron ore predominantly has a higher angularity index 174

value, about 70% have SAI value between 0.25-0.3. The cumulative distribution show that 175

glacial gravel rounded aggregate has the smallest angularity index, indicating that it has the 176

least angular aggregates. Furthermore, it is worth noting that there are dramatic differences 177

between the crushed and natural aggregates, as glacial gravel rounded has the smallest 178

angularity index while glacial gravel crushed has a much greater angularity index. 179

The glacial gravel crushed aggregate sample has a wide range of SAI value, which is 180

0.226 (Table 1 and Figure 8); whereas the other aggregate samples have range less than 0.20. 181

Possible reason is that the glacial gravel crushed aggregates were originally rounded with 182

very small angularity. After crushing, some smooth aggregate surfaces are broken and 183

become angular aggregate surfaces with higher angularity index value, whereas some other 184

surfaces of aggregates remain uncrushed and keep as originally rounded with very small 185

angularity index. The existence of both crushed and uncrushed surfaces in captured images of 186

the glacial gravel crushed aggregate sample would lead to a wide range of angularity 187

distribution. 188

Figure 9 shows AIMS angularity distributions of the six samples. As can be seen from 189

the figure, glacial gravel rounded has the smallest angularity index value, which is less than 190

for 50% of the aggregates. In contrast only less than 10 % of iron ore aggregates have AIMS 191

angularity index of less than 2000. The cumulative curves revealed that both copper ore and 192

iron ore samples have the highest angularity index, followed by dolomite and limestone. 193

Glacial gravel rounded sample has the smallest AIMS angularity index, which is consistent 194

with the result obtained in SAI technique. 195

Table 1 shows the minimum, maximum, mean and range of the angularity index for 196

the six aggregate samples, calculated by using both the SAI and the AIMS methods. Based on 197

the mean angularity index value the samples are arranged in increasing rank order, from 198

smallest to the highest angularity. The ranking order is generally in agreement with unaided 199

eye visual judgment. Glacial gravel rounded has the smallest mean of the SAI value, whereas 200

copper ore has highest SAI value. The order of angularity ranking for glacial gravel rounded, 201

iron ore and copper ore samples are the same for both the SAI and AIMS. The major 202

difference lies in dolomite, which ranks the second-least angular sample using the SAI 203

method and the fourth-least angular using the AIMS method. Glacial gravel crushed ranked as 204

the third-least angular (followed by limestone) using the SAI method, and as the second-least 205

angular (followed by limestone) using the AIMS method. The difference in the ranking order 206

of the aggregate angularity obtained by the two methods could be possibly caused by the 207

difference in the particle orientation which may occur during the image acquisition. 208

In general it is interesting to note that the angularity index analysis in both methods 209

allowed the grouping of the aggregate samples in different angularity classes. The distribution 210

trend revealed some similarities but we have also observed some local differences (Fig. 8 and 211

9). Glacial gravel has the smallest angularity, whereas copper ore has the highest angularity 212

and iron ore ranks the second most angular sample. 213

CONCLUSION 214

The mathematical algorithm used in the SAI and AIMS methods is different. Therefore the 215

angularity index of the samples obtained by the two methods could not be directly compared 216

with each other. The SAI technique is used to quantify angularity of aggregates using an 217

algorithm developed in Matlab program. This method process the angularity of coarse particle 218

from a digital image. In the SAI approach we can take image of many aggregate at a time and 219

the mathematical algorithm used to process the image data is not complex. As a result the 220

speed of analysis is faster than the other existing methods. 221

In contrast the Aggregate Image Measurement System (AIMS) is an integrated system 222

comprised of the image acquisition hardware and a software package. The image acquisition 223

hardware includes expensive and complex equipments fitted with high resolution camera. The 224

software package provides a user-friendly interface to automatically capture images of 225

aggregates and analyze morphological characteristics of aggregates. But it allows acquiring 226

the images of few particles at a time and requires longer time to process aggregate angularity. 227

Unlike the erosion and dilation method, the SAI method does not remove any 228

information from captured images. The angularity result obtained using the SAI method is in 229

good agreement with visual judgment of the unaided eye. Furthermore, the cumulative 230

distribution of the angularity index from the SAI method shows considerable similarity to the 231

existing AIMS result. In general, the SAI method is able to distinguish angularity differences 232

for aggregate samples from a wide range of sources. This angularity difference among the 233

samples could be attributed to the variation in the crushing method used to produce the 234

aggregate samples. 235

The existing angularity analysis methods are based on different principles, to the 236

authors knowledge currently there is no standardized agreed-upon method for the angularity 237

determination. Therefore this novel morphological analysis method could be considered as a 238

useful alternative to study aggregate angularity. 239

ACKNOWLEDGEMENT 240

We thank Fredrik Bergholm who has assisted us to develop the algorithm for the SAI analysis 241

method.242

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TABLE 1 Ranking comparison based on the mean of the sample angularity obtained by the SAI and AIMS technique (No., Number of

Aggregate; min and max, Stands for the Minimum and Maximum Angularity Index)

SAI AIMS

sample name No. min max range mean sample name No. min max range mean

Glacial gravel rounded 18 0.156 0.311 0.155 0.228 Glacial gravel rounded 25 464.03 2991.33 2527.3 1582.67

Dolomite 30 0.191 0.375 0.184 0.252 Glacial gravel crushed 25 1181.91 3618.73 2436.82 2424.19

Glacial gravel crushed 24 0.185 0.411 0.226 0.259 Limestone 29 1574.52 4764.77 3190.25 2657.53

Limestone 29 0.204 0.315 0.111 0.262 Dolomite 29 1616.31 3987.84 2371.53 2721.88

Iron ore 21 0.215 0.354 0.139 0.273 Iron ore 30 1931.82 4754.79 2822.97 3065.38

Copper 25 0.225 0.359 0.134 0.274 Copper 30 2456.8 4145.36 1688.56 3150.80

Figure 1 Particle outline with its shape descriptors: form, angularity

and texture.

Figure 2 Silhouette chart, pebble images for roundness comparison.

(b) (a)

(c)

(d)

Area=A1 Area=A2

(e)

Erosion

Dilation

Area=A2

Area=A1

Effectivewidth

Figure 3 Illustration of the different techniques used for angularity measurement

(a) degree of angularity (Lees, 1964); (b) gradient angularity; (c) Outline slope

angularity; (d) erosion dilation; (e) fractal dimension.

Image

acquisition

Computing

particle

angularity

Boundary

detection

Calculate distance

between

smoothing curves

Two steps of

particle outline

smoothing

Figure 4 Flow chart of the new smoothing-angularity index (SAI)

determination.

pix

el

530 535 540 545 550 555 560 565

115

120

125

130

135

140

Figure 5 Two smoothing curves around the edge of a

particle. The first curve goes smoothly through every mid

points of the polygon segment. The second smoothing

curve is generated by sub sampling some points from the

first b-splines smoothing curve.

Particle edge

Firstsmoothing

curve

Second

smoothing curve

pixel

0 100 200 300 400 500 60050

100

150

200

250

300

350

400

450

500

Figure 6 Perpendicular segments between the two smoothing curves for the dolomite sample,

30 particles.

Pixel

pix

el

Figure 7 Diagrammatic representation of the distance distribution between the two smoothing

curves and mean of the distribution (m= 0.35093) for a particle from dolomite sample.

Number of perpendicular distances measured between the two curves

0 20 40 60 80 100 120 140 160 1800

0.2

0.4

0.6

0.8

1

1.2

1.4

Dis

tance

bet

wee

n t

he

two s

mooth

ing

curv

es

Copper ore Dolomite

Glacial gravel crushed Glacial gravel rounded

Iron ore Limestone

0.15 0.2 0.25 0.3 0.35 0.4 0.45

0

20

40

60

80

100

Copper oreDolomiteGlacial gravel

crushed

Glacial gravel

rounded

Iron oreLimestone

Pe

rce

nt d

istr

ibutio

n

GID angularity index

Figure 8 Smoothing Angularity Index (SAI)

measurement based on the distance between the two

smoothing curves.

copper ore Dolomite

Glacial gravel crushed Glacial gravel rounded

0

20

40

60

80

100

Copper oreDolomiteGlacial gravel

crushed

Glacial gravel

rounded

Iron oreLimestone

Pe

rce

nt d

istr

ibutio

n

AIMS Angularity index

Iron ore

0 1000 2000 3000 4000 5000

Limestone

Figure 9 AIMS angularity measurement based on the

gradient angularity index.