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: [email protected]
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.
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