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Statistical methods to compare the texture features of machined surfaces
Pattern Recognition, Vol. 29, No. 9, pp. 1447 1459, 1996 Copyright © 1996 Pattern Recognition Society. Published by Elsevier Science Ltd. Printed in Great Britain 0031 3203/96 $15.00+.00
Pergamon
PII: S00031-3203(96)00008-8
STATISTICAL M E T H O D S TO C O M P A R E THE TEXTURE FEATURES OF M A C H I N E D SURFACES K. VENKAT RAMANA* and B. R A M A M O O R T H Y Manufacturing Engineering Section, Department of Mechanical Engineering, Indian Institute of Technology, Madras 600 036, India (Received 16 June 1995; in revised form 8 December 1995; received for publication 11 January 1996)
Abstract--Texture studies play a paramount role in many image processing applications. In this paper an attempt is made to study the textural features of machined surfaces (grinding, milling and shaping) using the most widely used statistical methods, viz. co-occurrence matrix approach, the amplitude varying rate statistical approach (AVRS) and the run length matrix approach. Textural features derived from these matrices are studied and analysed. A new matrix for the qualitative evaluation of surfaces, namely the gray-level difference-pixel distance matrix, is presented and its usefulness in texture analysis is analysed. The features calculated from these matrices are correlated with surface parameters, such as roughness, and the different features are studied for classification of these surfaces. Copyright © 1996 Pattern Recognition Society. Published by Elsevier Science Ltd. Textures
Machined surfaces
Co-occurrence
AVRM
images. The earliest approach towards higher-order
1. INTRODUCTION With growing emphasis of industrial automation in manufacturing, vision techniques play an important role in many applications. One of the important applications of image processing analysis is texture analysis. As different surfaces have different textures, the study of these textures form an important cue for the recognition of surfaces. Texture analysis is the predominant method that plays an important role in many image processing applications, such as classification, segmentation, pattern recognition, etc. As manufacturing involves machined surfaces, the study of textures of machined surfaces has become indispensable to the successful implementation of vision in manufacturing. Image texture can be quantitatively evaluated using the properties such as fineness, smoothness, coarseness, granulation, etc. Various statistical and structural methods have been developed to study these features. Statistical methods gained preference over structural methods as most image textures do not follow a specific grammar or rule, which is essential for the successful implementation of structural methods. The statistical methods followed are of different order based on the number of gray values considered for analysis and the type of relationship used. The statistical methods involves calculation of properties based on the gray tones of the specimens. The first-order statistics involves the computation and extraction of features such as mean, variance, standard-deviation, skewness and kurtosis from the histograms of the *Author for correspondence.
Run length
statistics was developed by Haralick et al. m They used the co-occurrence matrix approach for the calculation of various features based on the matrices and successfully employed it to the classification of images of landsat. Weszka and Rosenfeld t2) studied the application of texture analysis to materials inspection and deduced that the statistical approaches can be used to study materials, thus opening new avenues to the applications of texture analysis. Weszka et al. ~3~ compared the effectiveness of some of the statistical techniques used in terrain classification and deduced that spectrum methods fared poorly compared with statistical methods. Various texture methods developed and used in classification were reviewed by Haralick (4) and VanGoolJ 5) Unser ~6)proposed the sum and difference histogram approach, which was similar to the cooccurrence matrix approach, and deduced that the features computed from the developed approach gave results similar to that of the latter while occupying less memory and yielding greater computational speed. Galloway tT~ introduced the run length matrix approach. Textural features are defined to extract features from the image. Chu et al. ts~ supplemented the run length approach by introducing new parameters to that developed by Galloway. The importance of the new features are indicated by applying them to two sets of image data. Zhuang et al. ts) developed the amplitude varying rate statistical approach to texture analysis and compared them with co-occurrence matrices, while applying them to the study of Brodatz's textures. Dong chen He et al. ~1°) and Amasdusan et al. ~11~ studied the features extracted from textures and pro-
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K.V. RAMANA and B. RAMAMOORTHY
posed the optimization of these parameters for use in classification. In this paper the machined surfaces are analysed using both the first- and second-order statistics. In the second-order statistics the co-occurrence matrix approach, the amplitude varying rate statistical approach and the run length matrix approaches are considered for analysis. Various textural features from these matrices are calculated and presented. Some texture properties obtained are studied for their correlation with surface properties of machined components. A new matrix for the qualitative evaluation of surfaces is also presented.
2. E X P E R I M E N T A L P R O C E D U R E
The experiments were carried out by preparing flat specimens with different machining processes, such as grinding, milling and shaping. Surfaces with different textures are obtained by controlling the machining parameters of these processes. The images of the specimens are grabbed with a Matrox vision system on an Image-LC platform installed on an IBM PC-AT/486. The magnification of the input sensor [camera] is 10 X. The sample images of the specimens are shown in Fig. 1. The roughness values of the specimens are obtained with a stylus instrument. Table 1 shows the parameters used in the preparation of the specimens and the roughness values obtained. A small region is taken as a representative of the entire specimen (the texture of machined surfaces also has this property). Hence, the region of analysis is restricted to a pixel matrix of size 32 x 32. This will help in reducing the computer memory and time requirements. Also, it makes it possible to use the vision system as an on-line process. The input image is quantized to a five-bit gray scale. 3.
C O - O C C U R R E N C E MATRICES
The gray-tone spatial dependence matrices or the co-occurrence matrices and their texture features have been defined by Haralick et al. ~) The co-occurrence matrix is obtained by specifying a matrix of relative frequencies Pij, with which two neighboring resolution cells separated by distance d occur on the image, one with gray tone i and the other with gray tone j. In general, we obtain a series of matrices P0(i, jld), where 0 is the direction of evaluation with distance d. Here d ranges from 1 to dmax and i, j are taken over all gray levels. Generally, rather than using a single displacement one uses a set of displacements to obtain the desired property to which the textural feature corresponds. As machined surfaces have complex textures, it is very difficult to find a suitable distance "d" in the calculation of these matrices so as to obtain the desired texture properties. The texture properties of machined surfaces considered above are greatly influenced by the neighboring elements. Also, as a single light source is
Fig. 1. Photographs of the specimens: (a) grinding, (b) milling and (c) shaping.
used in this experimentation, it is felt that the texture discrimination is best obtained by considering the distance "d" to be 1. A constant light source is used for the grabbing of images. The ground specimens reflected more light, whereas the rougher shaped and milled specimens reflected relatively less light. This is clearly seen by the gray values of these specimens, which is shown in the histograms in Fig. 2 (the histograms are
Texture features of machined surfaces
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Table 1. Parameters used in the machining process Machining process
Speed
Grinding
593 rpm 684 813 500 500 500
Milling
280 rpm 280 280 280 280 280
Shaping
30 (mpm) 30 30 30 18 39
Depth of cut
Feed
Roughness (Ra pm)
-------------
0.80 1.06 1.01 1.09 1.17 1.29
0.4 mm 0.4 0.4 0.4 0.4 0.4
12.5 mm min x 31.5 80.0 100.0 200.0 250.0
1.31 1.53 3.18 3.30 2.80 3.70
0.5 mm 0.5 0.5 0.5 0.5 0.5
0.2 mm stroke- 1 0.4 0.6 0.8 0.2 0.4
30 pm 30 30 20 40 60
plotted on an eight-bit scale for the purpose of clarity). This can be explained by the fact that rougher surfaces scatter light, thus resulting in less light being collected by the sensor l-camera]. The reflection characteristics of milled surfaces is between that of ground and shaped specimens. This can also be verified by the roughness values obtained from these surfaces.
14.0 41.0 58.0 .... 12.0 37.0
information for the effective study of different properties. To remove these anomalies, a general AVRM is calculated where the neighbor relation is varied from 1 to 32. It is felt that with this relation the texture information of machined surfaces is better obtained. 5. RUN LENGTHMATRICES
4. AMPLITUDEVARYING RATE STATISTICAL APPROACH (AVRS)
In the AVRS approach, the distance between a point and a neighbor with the same gray level in given direction is examined. Its elements are the frequencies of distances "d" occurring in direction "0" between two pixels whose gray levels are "g". The distances between selected points in the image are measured and the frequency is accumulated in an array. The AVRM A0(g,d) is calculated by examining the profile of each scan line in a fixed direction and recording the frequencies of base line crossings for a fixed gray value"g". The elements of the matrix for a particular direction in a particular location indicate the number of times the gray value "g" is repeated with the particular distance threshold "d" in the scanned image. The two specific AVRM neighbor relations used in practice are denoted by A~ and A 2, respectively. In the former the first neighboring point is taken as the nearest neighbor to extract information on primitive properties, while in the latter the neighbor relation is taken as the second nearest neighbor to extract information on the periodicity of the placement of texture elements. As machined surfaces have complex surface characteristics, neither the A 1 nor the A 2 matrices give the specific surface details. Also, as the region of analysis is restricted, the A~ and A2 matrices do not give sufficient
In the run length matrix approach the gray-level runs are characterized by the gray tone of the run, the length of the run and the direction of the run. Let P(i, j) represent the run length matrix array, where the array consists of elements in which the gray tone "i" has a run length "j". A number of textural features are calculated from the array elements that are used to study the nature of image textures.
6. COMPARISON BETWEEN AVRM, CO-OCCURRENCE MATRICES AND R U N LENGTH MATRICES
In digital approximations of continuous images the neighbor of a pixel with gray level "g" may not necessarily lie on the sampling grid. In these cases, for calculation of texture descriptors, the distance is taken to be the length of the interval, including those points whose gray levels are in the same class when the image is threshold by "g'. This is an important difference between the AVRS approach and co-occurrence matrix approach. The AVR matrix is computed with an underlying neighbor relationship, but there is no such spatial relationship in the co-occurrence matrix. The other important difference is that in the AVRS approach the end points of the line segments may or may not be on the sample grid. However, in the co-occurrence method the end points are constrained
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Table 2. First-order statistics of the machining process Machining process
Mean
Variance
Standard deviation
Skewness
Kurtosis
Grinding
199.14 170.69 169.34 165.78 182.24 181.81
95.06 135.08 118.88 152.06 165.35 200.95
9.75 11.62 10.90 12.33 12.86 14.17
0.245 0.662 0.689 0.938 0.151 0.338
3.019 4.832 3.894 3.851 3.239 2.602
Milling
104.92 97.87 124.87 125.35 105.67 136.79
26.14 37.42 62.90 66.90 55.02 68.46
5.11 6.11 7.93 8.18 7.42 8.27
0.296 -0.430 0.704 0.485 0.656 0.121
3.617 3.431 3.113 2.825 3.362 3.609
Shaping
87.79 64.48 77.83 68.98 62.58 55.41
25.67 73.68 101.16 331.30 17.05 70.88
5.06 8.58 10.06 18.20 4.12 8.42
0.628 1.178 2.307 1.420 0.521 0.810
5.076 4.041 13.081 5.181 3.414 3.121
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to lie on the sample grid. Hence, any size of the image can be used to compute the AVR matrix, thus leading to better texture information within a given domain. The size of the AVR matrix can be varied, unlike the co-occurrence matrices where the size of the matrix is fixed to Q x Q, where Q is the number of quantized gray levels. The run length matrix approach differs from both the above approaches in that there is no spatial relationship between the gray values during the
computation of these matrices. Only the runs of the gray values are important with no emphasis on its placement with respect to other runs. The size of the matrix is extremely important here as texture details are completely lost if the matrix size chosen is smaller than the primitive element size. No detailed texture information can be obtained from these matrices, except for the type of texture element present, such as fine or coarse element. Also, noise greatly affects the matrix
Texture features of machined surfaces
1453
Table 3. Textural features calculated from the co-occurrence matrices MP
CON
COR
SOS
IDM
SA
SV
SE
ENT
DV
DE
COR1
COR2
G
0.00139 0.00152 0.00152 0.00132 0.00118 0.00222
1.3El0 8.6E09 1.6El0 1.5E10 1.8El0 2.2E10
8.892 6.832 6.406 5.464 7.081 5.125
2.7E-4 1.9E-4 1.3E-4 1.6E-4 2.3E-4 0.9E-4
0.1129 0.0952 0.0905 0.0858 0.0946 0.0988
35.929 27.329 21.627 28.740 28.323 20.505
1.5E-3 1.4E-3 0.9E-3 1.0E-3 1.3E-3 1.1E-3
1.5E-3 1.4E-3 0.9E-3 1.1E-3 1.4E-3 1.0E-3
6.6E-10 4.3E-10 1.5E-10 2.3E-10 5.5E-10 5.5E-11
4.5E-4 6.9E-4 4.1E-4 3.8E-4 4.1E-4 7.3E-4
-0.936 -0.923 -0.949 0.951 -0.957 -0.946
0.055 0.054 0.044 0.046 0.053 0.046
M
0.00062 0.00069 0.00354 0.00229 0.00181 0.00111
4.13E9 2.64E9 4.98E9 7.97E9 6.07E9 8.69E9
4.224 4.556 4.779 4.822 4.437 4.621
1.9E-4 3.1E-4 1.8E-4 2.1E-4 1.6E-4 2.1E-4
0.0773 0.0738 0.0787 0.0791 0.0801 0.0716
18.900 18.227 19.122 19.289 17.751 18.488
1.0E-3 1.5E-3 1.4E-3 1.4E-3 1.1E-3 1.2E-3
1.1E-3 1.5E-3 1.4E-3 1.4E-3 I.IE-3 1.2E-3
2.7E-10 8.0E-10 3.3E-10 4.3E-10 2.4E-10 4.4E-10
3.3E-4 3.7E-4 7.3E-4 5.9E-4 5.3E-4 3.7E-4
-0.931 -0.948 -0.912 -0.921 -0.913 -0.938
0.1)46 0.056 0.053 0.054 0.048 0.049
S
0.00159 0.00291 0.00125 0.01091 0.00111 0.00159
2.31E9 3.48E9 2.41E9 2.79E9 1.82E9 3.62E9
3.665 2.783 3.945 3.447 3.122 2.145
2.9E-4 2.1E-4 4.1E-4 2.7E-4 2.8E-4 2.1E-4
0.0698 0.0601 0.0710 0.0641 0.0687 0.0494
16.662 11.137 15.782 13.802 12.489 8.584
1.8E-3 1.4E-3 2.1E-3 1.6E-3 1.5E-3 1.2E-3
1.8E-3 1.4E-3 2.1E-3 1.7E-3 1.5E-3 1.2E-3
8.8E-10 3.4E-10 1.8E-09 7.7E-10 8.6E-10 3.6E-10
7.0E-4 5.9E-4 5.5E-4 6.8E-4 4.7E-4 4.2E-4
-0.921 -0.951 -0.950 -0.948 -0.932 -0.933
0.060 0.054 0.065 0.058 0.055 0.051
Table 4. Parameters obtained from AVR matrices Machining process
Regularity
Average size
Average primitive size
Average number of primitive intersections
Grinding
0.0532 0.0492 0.0595 0.0517 0.0571 0.0611
16.79 17.46 12.63 17.18 14.91 17.53
4.03 4.53 4.29 4.67 4.07 3.91
0.0632 0.0641 0.0571 0.0691 0.0735 0.0787
1.0834 1.0833 9.4864 0.6149 5.0688 0.3185
22.076 19.473 19.475 18.927 18.571 20.726
Milling
0.0753 0.0662 0.1304 0.1043 0.0565 0.0595
14.51 13.39 11.13 8.25 17.15 15.36
3.17 3.35 2.71 2.85 3.72 3.66
0.0982 0.0878 0.1121 0.0864 0.0883 0.0755
0.9994 1.5541 0.4801 2.0279 -1.7249 40.9405
10.574 9.381 14.421 14.263 10.802 14.886
Shaping
0.1017 0.0971 0.0699 0.0651 0.0991 0.1058
12.81 12.40 11.81 14.77 17.02 12.83
2.79 3.07 3.89 4.30 2.64 3.07
0.0894 0.1097 0.0571 0.0785 0.0914 0.1051
1.0952 -14.1671 -0.7943 1.8829 1.4462 3.4724
7.979 5.032 6.025 5.304 3.989 3.427
elements a n d texture properties as even a single noise pixel can c h a n g e the n u m b e r of elements of a particular gray value run.
7. GRAY-LEVEL DIFFERENCE VERSUS PIXEL DISTANCE MATRIX
T h e co-occurrence a n d A V R matrices are very useful in the study of m a c h i n e d surfaces, however, they d o n o t readily give the i n f o r m a t i o n o n surface finish, feed
Detail contrast
Rough contrast
etc. In this regard a new m a t r i x is p r o p o s e d in which the frequencies of gray-value differences with pixel distances are a c c u m u l a t e d in a n array. W i t h this, the surface quality c h a r a c t e r i z a t i o n is improved. T h e a m o u n t of light reflected by a surface being directly a measure of the surface finish, a m a t r i x which c o n t a i n s the frequencies of the gray-value difference with pixel distance is needed to evaluate the r o u g h n e s s of the surface. In such a matrix, if the frequencies of the gray-value difference of zero with m i n i m u m pixel dis-
1454
K.V. RAMANA and B. RAMAMOORTHY
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tance are higher, then the surface is smoother than a surface in which corresponding elements are lesser. Also, a matrix in which the frequencies are more for a larger gray-value difference and larger pixel distance, then the surface is regular than a surface of matrix with relatively fewer elements in the corresponding positions. These matrices are calculated for the specimen images.
8. RESULTSAND DISCUSSION The first-order statistics of the specimens are calculated and the properties obtained are given in Table 2. The plot of variance versus roughness is shown in Fig. 3. It is seen that a very good correlation of variance versus roughness is obtained for the specimens considered. The 3-D (three dimensional) plots of the co-occurrence matrices of the sample specimens
Texture features of machined surfaces
1455
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are shown in Fig. 4. The co-occurrence matrices are symmetrical, showing the accuracy of calculations. The parameters calculated from the co-occurrence matrices are given in Table 3. In this table the conventions used are as follows: M. P. : Machining Process; G: Grinding; M: Milling; S: Shaping; ASM: Angular Second Moment; 1DM: Inverse Difference Moment; ENT: Entropy; CON: 1, 2 -Contrast; COR: Correlation; SOS: Sum Of Squares; SA: Sum Average; SE:
Sum Entropy; SV: Sum Variance; DE: Difference Entropy; DV: Difference Variance. The following observations are made from the plots of these surfaces. In the 3-D plots of the co-occurrence matrices shown, the height of the element is proportional to the matrix element at the corresponding location. It is observed from the co-occurrence matrices of different surfaces that the relative positions and peaks varied with the machining process. The
1456
K.V. RAMANA and B. RAMAMOORTHY Table 5. Run-length parameters of the matrices
Machining process
Short-run emphasis
Long-run Gray-level emphasis Nonuniformity
Run-length nonuniformity
Grinding
0.5051 0.5382 0.5133 0.5759 0.6595 0.6755
9.1972 7.5217 8.9294 6.2629 5.0712 3.7616
86.723 88.991 83.333 89.052 92.804 94.697
112.7465 133.8696 123.6606 164.0438 228.5374 268.0499
0.4161 0.4492 0.4287 0.4902 0.5488 0.6064
0.001546 0.002077 0.002102 0.002192 0.001860 0.001858
654.561 491.896 484.581 467.177 549.067 551.230
Milling
0.5123 0.4777 0.7108 0.6144 0.4755 0.5675
9.6894 10.8578 3.8267 5.1143 9.3333 6.7361
145.381 117.485 172.754 136.705 110.831 121.192
115.9129 91.9302 298.6094 202.7023 102.4058 121.1922
0.4150 0.3779 0.6201 0.5381 0.4042 0.4775
0.005480 0.006281 0.003820 0.003785 0.005055 0.003256
185.178 162.824 266.111 269.125 202.224 312.447
Shaping
0.5061 0.6466 0.5193 0.6955 0.4667 0.6791
8.1213 6.8833 7.0956 4.2909 16.6117 3.8733
164.276 121.707 114.961 84.285 142.064 153.851
122.9371 206.3728 128.4652 272.0247 75.9000 267.1071
0.4345 0.5107 0.4492 0.5908 0.3320 0.6015
0.008014 0.013090 0.009387 0.012328 0.013915 0.015192
134.298 82.277 114.256 73.582 73.582 59.847
elements of the co-occurrence matrices tend to shift along the diagonal, with the smoother surfaces taking the far end of the principal diagonal. These matrices are found to be more sensitive to changes in surface finish than those calculated from the first-order statistics. The results obtained by the calculation of different parameters from the AVR matrices are listed in Table 4. The parameters average frequency, regularity, average size or period favoring both long and short lengths, average number of primitives, and rough contrast are calculated. Figure 5 gives the 3-D plots of the AVR matrices. From the study of the textural features calculated from the AVR matrices, the AVR matrices and the 3-D plots of these matrices, the following inferences are possible. (1)There is a clear distinction of the position of the elements based on manufacturing process and is as seen in the matrices. This variation of the positions based on the machining process considered is due to the fact that the reflectivity of light is directly dependent on the nature of the surface and smooth surfaces, such as grinding, reflecting more light than the relatively rougher surfaces, such as milling. Due to this, the elements of the matrices of the shaping process occupy relatively lower positions than those of the milling and grinding processes. (2) From the 3-D plots obtained it is clearly seen that the peaks shifted from top to bottom with an increase in the smoothness of the process. This is because smooth surfaces, such as grinding, reflected more light than rougher surfaces, such as milling or shaping. Hence, the AVR matrices for grinding contained elements with high gray values. For shaping, low gray
Run Low grayHigh graypercentage levelemphasis levelemphasis
values are obtained and in the case of milling they are in between the two. (3)In all the processes the immediate neighbor distance of d = 1 or 2 showed large values. This is due to the fact that an edge or any transition in texture is not immediate, but takes a certain pixel distance. The frequency of elements also gives in indication of the smoothness of the process. With grinding, the frequencies for high distance thresholds are higher compared with milling and shaping. In fact, in milling and shaping there are no entries at all in the AVRM. The 3-D plots of the run length matrices are shown in Fig. 6. The texture features computed from the run length matrices are given in Table 5. From the 3-D plots it can be seen that grinding specimens have larger runs than the milling and shaping specimens. This is explained by the fact that smooth surfaces have similar pixel values. The nature of the machining process determines the run of the gray-value, as runs are interrupted due to machining characteristics such as feed and speed. In grinding, the depth of cut being very low, the surfaces are smoother than in milling and shaping and hence these matrices have higher run length entries. The plots of the long run emphasis versus low gray-level emphasis and high gray-level emphasis versus low gray-level emphasis gives a clear distinction of the machining processes and thus shows the usefulness of the run length method. Figure 7 show these plots for the processes considered. A 3-D plot of the elements of the gray-value difference versus pixel distance matrices is shown in Fig. 8. From these matrices, the following conclusions are obtained. For smooth surfaces, such as grinding, the number of elements with low gray-value difference are considerably higher than with other matrices of mill-
Texture features of machined surfaces
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ing and shaping. Even with a gray-value difference of zero, the elements of the matrices are higher for large pixel distances for specimen matrices of shaping and milling, indicating a change in texture property, such as feed, etc. This is due to the fact the texture property, such as feed, is repetitive at regular periods of time, giving the same gray values at these positions. 9. CONCLUSIONS
With the co-occurrence, AVR and run length matrices it has been possible to study the textures of machined surfaces for possible classification of them
based on the plots of these processes as well some of the textural features calculated. The first-order parameter variance is found to give very good correlation with roughness, thus making it a possible feature that can be employed as an on-line parameter for the evaluation of roughness. The gray-level difference versus pixel distance matrices are very helpful in qualitatively comparing the roughness of the surfaces. They prove the point that they also form an effective tool in the classification of machined surfaces and this study of machined surfaces is particularly useful in the field of manufacturing. Efforts are on to calculate suitable parameters by which the machining process parameters can be better studied.
1458
K.V. RAMANA and B. RAMAMOORTHY
LO u
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Fig. 8. 3-D plots of the gray-value difference versus pixel distance: (a), (b) grinding; (c), (d) milling; (e), (f) shaping. Acknowledgement--The authors acknowledge the support given by CSIR, New Delhi, who have sponsored the project titled "Application of vision system for surface and dimensional inspection". The research work reported in this paper is part of the above project. REFERENCES
1. R.M. Haralick, K. Shanmugam and I. Dinstein, Textural features for image classification, IEEE Trans. Syst., Man Cybernet. 3, 610-621 (1973). 2. J. S. Weszka and A. Rosenfeld, An application of texture analysis to materials inspection, Pattern Recognition 8, 195 i99 (1976).
3. J. Weska, C. Dyer and A. Rosenfeld, A comparative study of texture measures for terrain classification, IEEE Trans. Syst., Man Cybernet. 6, 269-285 (1976). 4. R. M. Haralick, Statistical and structural approaches to texture, Proc. IEEE 67, 786-804 (1979). 5. L. Van Gool, P. Dewaele and A. Oosterlinck, Texture analysis anno 1983, Comput. l/is. Graphics Image Process. 29, 336-357 (1985). 6. M. Unser, Sum and difference histograms for texture classification, IEEE Trans. Pattern Anal. Mach. Intell. 8, 336-357 (1986). 7. M. M. Galloway, Texture analysis using gray level run lengths, Comput. 14s. Graphics linage Process. 4, 172-179 (t975).
Texture features of machined surfaces
8. A. Chu, C. M. Sehgal and J. F. GreenLeaf, Use of gray value distribution of run lengths for texture analysis, Pattern Recognition Lett. 11,415-420 (1990). 9. C. Zuang and S. Dunn, The amplitude varying rate statistical approach for texture classification, Pattern Recognition Lett. 11, 143-149 (1990).
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10. D.C. He, L. Wang and J. Guibert, Texture discrimination based on an optimal utilisation of texture features, Pattern Recognition 21, 141 146 (1988). 11. M. Amasdasun and R. King, Textural features corresponding to textural properties, 1EEE Trans. Syst., Man Cybernet. 19, 1264-1273 (1989).
About the Author--B. RAMAMOORTHY is currently an Associate Professor in the Manufacturing Engineering Section of the Department of Mechanical Engineering, Indian Institute of Technology, Madras, India. He completed his Ph.D from I. I. T Madras and has been engaged in teaching and research for the past decade. He has ca 25 research papers to his credit and his research areas are metrology and machine vision.
About the Author--K. VENKAT RAMANA is a research scholar at I. I. T. Madras currently doing an M. S.
Pergamon
PII: S00031-3203(96)00008-8
STATISTICAL M E T H O D S TO C O M P A R E THE TEXTURE FEATURES OF M A C H I N E D SURFACES K. VENKAT RAMANA* and B. R A M A M O O R T H Y Manufacturing Engineering Section, Department of Mechanical Engineering, Indian Institute of Technology, Madras 600 036, India (Received 16 June 1995; in revised form 8 December 1995; received for publication 11 January 1996)
Abstract--Texture studies play a paramount role in many image processing applications. In this paper an attempt is made to study the textural features of machined surfaces (grinding, milling and shaping) using the most widely used statistical methods, viz. co-occurrence matrix approach, the amplitude varying rate statistical approach (AVRS) and the run length matrix approach. Textural features derived from these matrices are studied and analysed. A new matrix for the qualitative evaluation of surfaces, namely the gray-level difference-pixel distance matrix, is presented and its usefulness in texture analysis is analysed. The features calculated from these matrices are correlated with surface parameters, such as roughness, and the different features are studied for classification of these surfaces. Copyright © 1996 Pattern Recognition Society. Published by Elsevier Science Ltd. Textures
Machined surfaces
Co-occurrence
AVRM
images. The earliest approach towards higher-order
1. INTRODUCTION With growing emphasis of industrial automation in manufacturing, vision techniques play an important role in many applications. One of the important applications of image processing analysis is texture analysis. As different surfaces have different textures, the study of these textures form an important cue for the recognition of surfaces. Texture analysis is the predominant method that plays an important role in many image processing applications, such as classification, segmentation, pattern recognition, etc. As manufacturing involves machined surfaces, the study of textures of machined surfaces has become indispensable to the successful implementation of vision in manufacturing. Image texture can be quantitatively evaluated using the properties such as fineness, smoothness, coarseness, granulation, etc. Various statistical and structural methods have been developed to study these features. Statistical methods gained preference over structural methods as most image textures do not follow a specific grammar or rule, which is essential for the successful implementation of structural methods. The statistical methods followed are of different order based on the number of gray values considered for analysis and the type of relationship used. The statistical methods involves calculation of properties based on the gray tones of the specimens. The first-order statistics involves the computation and extraction of features such as mean, variance, standard-deviation, skewness and kurtosis from the histograms of the *Author for correspondence.
Run length
statistics was developed by Haralick et al. m They used the co-occurrence matrix approach for the calculation of various features based on the matrices and successfully employed it to the classification of images of landsat. Weszka and Rosenfeld t2) studied the application of texture analysis to materials inspection and deduced that the statistical approaches can be used to study materials, thus opening new avenues to the applications of texture analysis. Weszka et al. ~3~ compared the effectiveness of some of the statistical techniques used in terrain classification and deduced that spectrum methods fared poorly compared with statistical methods. Various texture methods developed and used in classification were reviewed by Haralick (4) and VanGoolJ 5) Unser ~6)proposed the sum and difference histogram approach, which was similar to the cooccurrence matrix approach, and deduced that the features computed from the developed approach gave results similar to that of the latter while occupying less memory and yielding greater computational speed. Galloway tT~ introduced the run length matrix approach. Textural features are defined to extract features from the image. Chu et al. ts~ supplemented the run length approach by introducing new parameters to that developed by Galloway. The importance of the new features are indicated by applying them to two sets of image data. Zhuang et al. ts) developed the amplitude varying rate statistical approach to texture analysis and compared them with co-occurrence matrices, while applying them to the study of Brodatz's textures. Dong chen He et al. ~1°) and Amasdusan et al. ~11~ studied the features extracted from textures and pro-
1447
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K.V. RAMANA and B. RAMAMOORTHY
posed the optimization of these parameters for use in classification. In this paper the machined surfaces are analysed using both the first- and second-order statistics. In the second-order statistics the co-occurrence matrix approach, the amplitude varying rate statistical approach and the run length matrix approaches are considered for analysis. Various textural features from these matrices are calculated and presented. Some texture properties obtained are studied for their correlation with surface properties of machined components. A new matrix for the qualitative evaluation of surfaces is also presented.
2. E X P E R I M E N T A L P R O C E D U R E
The experiments were carried out by preparing flat specimens with different machining processes, such as grinding, milling and shaping. Surfaces with different textures are obtained by controlling the machining parameters of these processes. The images of the specimens are grabbed with a Matrox vision system on an Image-LC platform installed on an IBM PC-AT/486. The magnification of the input sensor [camera] is 10 X. The sample images of the specimens are shown in Fig. 1. The roughness values of the specimens are obtained with a stylus instrument. Table 1 shows the parameters used in the preparation of the specimens and the roughness values obtained. A small region is taken as a representative of the entire specimen (the texture of machined surfaces also has this property). Hence, the region of analysis is restricted to a pixel matrix of size 32 x 32. This will help in reducing the computer memory and time requirements. Also, it makes it possible to use the vision system as an on-line process. The input image is quantized to a five-bit gray scale. 3.
C O - O C C U R R E N C E MATRICES
The gray-tone spatial dependence matrices or the co-occurrence matrices and their texture features have been defined by Haralick et al. ~) The co-occurrence matrix is obtained by specifying a matrix of relative frequencies Pij, with which two neighboring resolution cells separated by distance d occur on the image, one with gray tone i and the other with gray tone j. In general, we obtain a series of matrices P0(i, jld), where 0 is the direction of evaluation with distance d. Here d ranges from 1 to dmax and i, j are taken over all gray levels. Generally, rather than using a single displacement one uses a set of displacements to obtain the desired property to which the textural feature corresponds. As machined surfaces have complex textures, it is very difficult to find a suitable distance "d" in the calculation of these matrices so as to obtain the desired texture properties. The texture properties of machined surfaces considered above are greatly influenced by the neighboring elements. Also, as a single light source is
Fig. 1. Photographs of the specimens: (a) grinding, (b) milling and (c) shaping.
used in this experimentation, it is felt that the texture discrimination is best obtained by considering the distance "d" to be 1. A constant light source is used for the grabbing of images. The ground specimens reflected more light, whereas the rougher shaped and milled specimens reflected relatively less light. This is clearly seen by the gray values of these specimens, which is shown in the histograms in Fig. 2 (the histograms are
Texture features of machined surfaces
1449
Table 1. Parameters used in the machining process Machining process
Speed
Grinding
593 rpm 684 813 500 500 500
Milling
280 rpm 280 280 280 280 280
Shaping
30 (mpm) 30 30 30 18 39
Depth of cut
Feed
Roughness (Ra pm)
-------------
0.80 1.06 1.01 1.09 1.17 1.29
0.4 mm 0.4 0.4 0.4 0.4 0.4
12.5 mm min x 31.5 80.0 100.0 200.0 250.0
1.31 1.53 3.18 3.30 2.80 3.70
0.5 mm 0.5 0.5 0.5 0.5 0.5
0.2 mm stroke- 1 0.4 0.6 0.8 0.2 0.4
30 pm 30 30 20 40 60
plotted on an eight-bit scale for the purpose of clarity). This can be explained by the fact that rougher surfaces scatter light, thus resulting in less light being collected by the sensor l-camera]. The reflection characteristics of milled surfaces is between that of ground and shaped specimens. This can also be verified by the roughness values obtained from these surfaces.
14.0 41.0 58.0 .... 12.0 37.0
information for the effective study of different properties. To remove these anomalies, a general AVRM is calculated where the neighbor relation is varied from 1 to 32. It is felt that with this relation the texture information of machined surfaces is better obtained. 5. RUN LENGTHMATRICES
4. AMPLITUDEVARYING RATE STATISTICAL APPROACH (AVRS)
In the AVRS approach, the distance between a point and a neighbor with the same gray level in given direction is examined. Its elements are the frequencies of distances "d" occurring in direction "0" between two pixels whose gray levels are "g". The distances between selected points in the image are measured and the frequency is accumulated in an array. The AVRM A0(g,d) is calculated by examining the profile of each scan line in a fixed direction and recording the frequencies of base line crossings for a fixed gray value"g". The elements of the matrix for a particular direction in a particular location indicate the number of times the gray value "g" is repeated with the particular distance threshold "d" in the scanned image. The two specific AVRM neighbor relations used in practice are denoted by A~ and A 2, respectively. In the former the first neighboring point is taken as the nearest neighbor to extract information on primitive properties, while in the latter the neighbor relation is taken as the second nearest neighbor to extract information on the periodicity of the placement of texture elements. As machined surfaces have complex surface characteristics, neither the A 1 nor the A 2 matrices give the specific surface details. Also, as the region of analysis is restricted, the A~ and A2 matrices do not give sufficient
In the run length matrix approach the gray-level runs are characterized by the gray tone of the run, the length of the run and the direction of the run. Let P(i, j) represent the run length matrix array, where the array consists of elements in which the gray tone "i" has a run length "j". A number of textural features are calculated from the array elements that are used to study the nature of image textures.
6. COMPARISON BETWEEN AVRM, CO-OCCURRENCE MATRICES AND R U N LENGTH MATRICES
In digital approximations of continuous images the neighbor of a pixel with gray level "g" may not necessarily lie on the sampling grid. In these cases, for calculation of texture descriptors, the distance is taken to be the length of the interval, including those points whose gray levels are in the same class when the image is threshold by "g'. This is an important difference between the AVRS approach and co-occurrence matrix approach. The AVR matrix is computed with an underlying neighbor relationship, but there is no such spatial relationship in the co-occurrence matrix. The other important difference is that in the AVRS approach the end points of the line segments may or may not be on the sample grid. However, in the co-occurrence method the end points are constrained
1450
K.V. RAMANA and B. RAMAMOORTHY
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Table 2. First-order statistics of the machining process Machining process
Mean
Variance
Standard deviation
Skewness
Kurtosis
Grinding
199.14 170.69 169.34 165.78 182.24 181.81
95.06 135.08 118.88 152.06 165.35 200.95
9.75 11.62 10.90 12.33 12.86 14.17
0.245 0.662 0.689 0.938 0.151 0.338
3.019 4.832 3.894 3.851 3.239 2.602
Milling
104.92 97.87 124.87 125.35 105.67 136.79
26.14 37.42 62.90 66.90 55.02 68.46
5.11 6.11 7.93 8.18 7.42 8.27
0.296 -0.430 0.704 0.485 0.656 0.121
3.617 3.431 3.113 2.825 3.362 3.609
Shaping
87.79 64.48 77.83 68.98 62.58 55.41
25.67 73.68 101.16 331.30 17.05 70.88
5.06 8.58 10.06 18.20 4.12 8.42
0.628 1.178 2.307 1.420 0.521 0.810
5.076 4.041 13.081 5.181 3.414 3.121
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1452
K.V. RAMANA and B. RAMAMOORTHY
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to lie on the sample grid. Hence, any size of the image can be used to compute the AVR matrix, thus leading to better texture information within a given domain. The size of the AVR matrix can be varied, unlike the co-occurrence matrices where the size of the matrix is fixed to Q x Q, where Q is the number of quantized gray levels. The run length matrix approach differs from both the above approaches in that there is no spatial relationship between the gray values during the
computation of these matrices. Only the runs of the gray values are important with no emphasis on its placement with respect to other runs. The size of the matrix is extremely important here as texture details are completely lost if the matrix size chosen is smaller than the primitive element size. No detailed texture information can be obtained from these matrices, except for the type of texture element present, such as fine or coarse element. Also, noise greatly affects the matrix
Texture features of machined surfaces
1453
Table 3. Textural features calculated from the co-occurrence matrices MP
CON
COR
SOS
IDM
SA
SV
SE
ENT
DV
DE
COR1
COR2
G
0.00139 0.00152 0.00152 0.00132 0.00118 0.00222
1.3El0 8.6E09 1.6El0 1.5E10 1.8El0 2.2E10
8.892 6.832 6.406 5.464 7.081 5.125
2.7E-4 1.9E-4 1.3E-4 1.6E-4 2.3E-4 0.9E-4
0.1129 0.0952 0.0905 0.0858 0.0946 0.0988
35.929 27.329 21.627 28.740 28.323 20.505
1.5E-3 1.4E-3 0.9E-3 1.0E-3 1.3E-3 1.1E-3
1.5E-3 1.4E-3 0.9E-3 1.1E-3 1.4E-3 1.0E-3
6.6E-10 4.3E-10 1.5E-10 2.3E-10 5.5E-10 5.5E-11
4.5E-4 6.9E-4 4.1E-4 3.8E-4 4.1E-4 7.3E-4
-0.936 -0.923 -0.949 0.951 -0.957 -0.946
0.055 0.054 0.044 0.046 0.053 0.046
M
0.00062 0.00069 0.00354 0.00229 0.00181 0.00111
4.13E9 2.64E9 4.98E9 7.97E9 6.07E9 8.69E9
4.224 4.556 4.779 4.822 4.437 4.621
1.9E-4 3.1E-4 1.8E-4 2.1E-4 1.6E-4 2.1E-4
0.0773 0.0738 0.0787 0.0791 0.0801 0.0716
18.900 18.227 19.122 19.289 17.751 18.488
1.0E-3 1.5E-3 1.4E-3 1.4E-3 1.1E-3 1.2E-3
1.1E-3 1.5E-3 1.4E-3 1.4E-3 I.IE-3 1.2E-3
2.7E-10 8.0E-10 3.3E-10 4.3E-10 2.4E-10 4.4E-10
3.3E-4 3.7E-4 7.3E-4 5.9E-4 5.3E-4 3.7E-4
-0.931 -0.948 -0.912 -0.921 -0.913 -0.938
0.1)46 0.056 0.053 0.054 0.048 0.049
S
0.00159 0.00291 0.00125 0.01091 0.00111 0.00159
2.31E9 3.48E9 2.41E9 2.79E9 1.82E9 3.62E9
3.665 2.783 3.945 3.447 3.122 2.145
2.9E-4 2.1E-4 4.1E-4 2.7E-4 2.8E-4 2.1E-4
0.0698 0.0601 0.0710 0.0641 0.0687 0.0494
16.662 11.137 15.782 13.802 12.489 8.584
1.8E-3 1.4E-3 2.1E-3 1.6E-3 1.5E-3 1.2E-3
1.8E-3 1.4E-3 2.1E-3 1.7E-3 1.5E-3 1.2E-3
8.8E-10 3.4E-10 1.8E-09 7.7E-10 8.6E-10 3.6E-10
7.0E-4 5.9E-4 5.5E-4 6.8E-4 4.7E-4 4.2E-4
-0.921 -0.951 -0.950 -0.948 -0.932 -0.933
0.060 0.054 0.065 0.058 0.055 0.051
Table 4. Parameters obtained from AVR matrices Machining process
Regularity
Average size
Average primitive size
Average number of primitive intersections
Grinding
0.0532 0.0492 0.0595 0.0517 0.0571 0.0611
16.79 17.46 12.63 17.18 14.91 17.53
4.03 4.53 4.29 4.67 4.07 3.91
0.0632 0.0641 0.0571 0.0691 0.0735 0.0787
1.0834 1.0833 9.4864 0.6149 5.0688 0.3185
22.076 19.473 19.475 18.927 18.571 20.726
Milling
0.0753 0.0662 0.1304 0.1043 0.0565 0.0595
14.51 13.39 11.13 8.25 17.15 15.36
3.17 3.35 2.71 2.85 3.72 3.66
0.0982 0.0878 0.1121 0.0864 0.0883 0.0755
0.9994 1.5541 0.4801 2.0279 -1.7249 40.9405
10.574 9.381 14.421 14.263 10.802 14.886
Shaping
0.1017 0.0971 0.0699 0.0651 0.0991 0.1058
12.81 12.40 11.81 14.77 17.02 12.83
2.79 3.07 3.89 4.30 2.64 3.07
0.0894 0.1097 0.0571 0.0785 0.0914 0.1051
1.0952 -14.1671 -0.7943 1.8829 1.4462 3.4724
7.979 5.032 6.025 5.304 3.989 3.427
elements a n d texture properties as even a single noise pixel can c h a n g e the n u m b e r of elements of a particular gray value run.
7. GRAY-LEVEL DIFFERENCE VERSUS PIXEL DISTANCE MATRIX
T h e co-occurrence a n d A V R matrices are very useful in the study of m a c h i n e d surfaces, however, they d o n o t readily give the i n f o r m a t i o n o n surface finish, feed
Detail contrast
Rough contrast
etc. In this regard a new m a t r i x is p r o p o s e d in which the frequencies of gray-value differences with pixel distances are a c c u m u l a t e d in a n array. W i t h this, the surface quality c h a r a c t e r i z a t i o n is improved. T h e a m o u n t of light reflected by a surface being directly a measure of the surface finish, a m a t r i x which c o n t a i n s the frequencies of the gray-value difference with pixel distance is needed to evaluate the r o u g h n e s s of the surface. In such a matrix, if the frequencies of the gray-value difference of zero with m i n i m u m pixel dis-
1454
K.V. RAMANA and B. RAMAMOORTHY
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tance are higher, then the surface is smoother than a surface in which corresponding elements are lesser. Also, a matrix in which the frequencies are more for a larger gray-value difference and larger pixel distance, then the surface is regular than a surface of matrix with relatively fewer elements in the corresponding positions. These matrices are calculated for the specimen images.
8. RESULTSAND DISCUSSION The first-order statistics of the specimens are calculated and the properties obtained are given in Table 2. The plot of variance versus roughness is shown in Fig. 3. It is seen that a very good correlation of variance versus roughness is obtained for the specimens considered. The 3-D (three dimensional) plots of the co-occurrence matrices of the sample specimens
Texture features of machined surfaces
1455
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are shown in Fig. 4. The co-occurrence matrices are symmetrical, showing the accuracy of calculations. The parameters calculated from the co-occurrence matrices are given in Table 3. In this table the conventions used are as follows: M. P. : Machining Process; G: Grinding; M: Milling; S: Shaping; ASM: Angular Second Moment; 1DM: Inverse Difference Moment; ENT: Entropy; CON: 1, 2 -Contrast; COR: Correlation; SOS: Sum Of Squares; SA: Sum Average; SE:
Sum Entropy; SV: Sum Variance; DE: Difference Entropy; DV: Difference Variance. The following observations are made from the plots of these surfaces. In the 3-D plots of the co-occurrence matrices shown, the height of the element is proportional to the matrix element at the corresponding location. It is observed from the co-occurrence matrices of different surfaces that the relative positions and peaks varied with the machining process. The
1456
K.V. RAMANA and B. RAMAMOORTHY Table 5. Run-length parameters of the matrices
Machining process
Short-run emphasis
Long-run Gray-level emphasis Nonuniformity
Run-length nonuniformity
Grinding
0.5051 0.5382 0.5133 0.5759 0.6595 0.6755
9.1972 7.5217 8.9294 6.2629 5.0712 3.7616
86.723 88.991 83.333 89.052 92.804 94.697
112.7465 133.8696 123.6606 164.0438 228.5374 268.0499
0.4161 0.4492 0.4287 0.4902 0.5488 0.6064
0.001546 0.002077 0.002102 0.002192 0.001860 0.001858
654.561 491.896 484.581 467.177 549.067 551.230
Milling
0.5123 0.4777 0.7108 0.6144 0.4755 0.5675
9.6894 10.8578 3.8267 5.1143 9.3333 6.7361
145.381 117.485 172.754 136.705 110.831 121.192
115.9129 91.9302 298.6094 202.7023 102.4058 121.1922
0.4150 0.3779 0.6201 0.5381 0.4042 0.4775
0.005480 0.006281 0.003820 0.003785 0.005055 0.003256
185.178 162.824 266.111 269.125 202.224 312.447
Shaping
0.5061 0.6466 0.5193 0.6955 0.4667 0.6791
8.1213 6.8833 7.0956 4.2909 16.6117 3.8733
164.276 121.707 114.961 84.285 142.064 153.851
122.9371 206.3728 128.4652 272.0247 75.9000 267.1071
0.4345 0.5107 0.4492 0.5908 0.3320 0.6015
0.008014 0.013090 0.009387 0.012328 0.013915 0.015192
134.298 82.277 114.256 73.582 73.582 59.847
elements of the co-occurrence matrices tend to shift along the diagonal, with the smoother surfaces taking the far end of the principal diagonal. These matrices are found to be more sensitive to changes in surface finish than those calculated from the first-order statistics. The results obtained by the calculation of different parameters from the AVR matrices are listed in Table 4. The parameters average frequency, regularity, average size or period favoring both long and short lengths, average number of primitives, and rough contrast are calculated. Figure 5 gives the 3-D plots of the AVR matrices. From the study of the textural features calculated from the AVR matrices, the AVR matrices and the 3-D plots of these matrices, the following inferences are possible. (1)There is a clear distinction of the position of the elements based on manufacturing process and is as seen in the matrices. This variation of the positions based on the machining process considered is due to the fact that the reflectivity of light is directly dependent on the nature of the surface and smooth surfaces, such as grinding, reflecting more light than the relatively rougher surfaces, such as milling. Due to this, the elements of the matrices of the shaping process occupy relatively lower positions than those of the milling and grinding processes. (2) From the 3-D plots obtained it is clearly seen that the peaks shifted from top to bottom with an increase in the smoothness of the process. This is because smooth surfaces, such as grinding, reflected more light than rougher surfaces, such as milling or shaping. Hence, the AVR matrices for grinding contained elements with high gray values. For shaping, low gray
Run Low grayHigh graypercentage levelemphasis levelemphasis
values are obtained and in the case of milling they are in between the two. (3)In all the processes the immediate neighbor distance of d = 1 or 2 showed large values. This is due to the fact that an edge or any transition in texture is not immediate, but takes a certain pixel distance. The frequency of elements also gives in indication of the smoothness of the process. With grinding, the frequencies for high distance thresholds are higher compared with milling and shaping. In fact, in milling and shaping there are no entries at all in the AVRM. The 3-D plots of the run length matrices are shown in Fig. 6. The texture features computed from the run length matrices are given in Table 5. From the 3-D plots it can be seen that grinding specimens have larger runs than the milling and shaping specimens. This is explained by the fact that smooth surfaces have similar pixel values. The nature of the machining process determines the run of the gray-value, as runs are interrupted due to machining characteristics such as feed and speed. In grinding, the depth of cut being very low, the surfaces are smoother than in milling and shaping and hence these matrices have higher run length entries. The plots of the long run emphasis versus low gray-level emphasis and high gray-level emphasis versus low gray-level emphasis gives a clear distinction of the machining processes and thus shows the usefulness of the run length method. Figure 7 show these plots for the processes considered. A 3-D plot of the elements of the gray-value difference versus pixel distance matrices is shown in Fig. 8. From these matrices, the following conclusions are obtained. For smooth surfaces, such as grinding, the number of elements with low gray-value difference are considerably higher than with other matrices of mill-
Texture features of machined surfaces
1457
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ing and shaping. Even with a gray-value difference of zero, the elements of the matrices are higher for large pixel distances for specimen matrices of shaping and milling, indicating a change in texture property, such as feed, etc. This is due to the fact the texture property, such as feed, is repetitive at regular periods of time, giving the same gray values at these positions. 9. CONCLUSIONS
With the co-occurrence, AVR and run length matrices it has been possible to study the textures of machined surfaces for possible classification of them
based on the plots of these processes as well some of the textural features calculated. The first-order parameter variance is found to give very good correlation with roughness, thus making it a possible feature that can be employed as an on-line parameter for the evaluation of roughness. The gray-level difference versus pixel distance matrices are very helpful in qualitatively comparing the roughness of the surfaces. They prove the point that they also form an effective tool in the classification of machined surfaces and this study of machined surfaces is particularly useful in the field of manufacturing. Efforts are on to calculate suitable parameters by which the machining process parameters can be better studied.
1458
K.V. RAMANA and B. RAMAMOORTHY
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Fig. 8. 3-D plots of the gray-value difference versus pixel distance: (a), (b) grinding; (c), (d) milling; (e), (f) shaping. Acknowledgement--The authors acknowledge the support given by CSIR, New Delhi, who have sponsored the project titled "Application of vision system for surface and dimensional inspection". The research work reported in this paper is part of the above project. REFERENCES
1. R.M. Haralick, K. Shanmugam and I. Dinstein, Textural features for image classification, IEEE Trans. Syst., Man Cybernet. 3, 610-621 (1973). 2. J. S. Weszka and A. Rosenfeld, An application of texture analysis to materials inspection, Pattern Recognition 8, 195 i99 (1976).
3. J. Weska, C. Dyer and A. Rosenfeld, A comparative study of texture measures for terrain classification, IEEE Trans. Syst., Man Cybernet. 6, 269-285 (1976). 4. R. M. Haralick, Statistical and structural approaches to texture, Proc. IEEE 67, 786-804 (1979). 5. L. Van Gool, P. Dewaele and A. Oosterlinck, Texture analysis anno 1983, Comput. l/is. Graphics Image Process. 29, 336-357 (1985). 6. M. Unser, Sum and difference histograms for texture classification, IEEE Trans. Pattern Anal. Mach. Intell. 8, 336-357 (1986). 7. M. M. Galloway, Texture analysis using gray level run lengths, Comput. 14s. Graphics linage Process. 4, 172-179 (t975).
Texture features of machined surfaces
8. A. Chu, C. M. Sehgal and J. F. GreenLeaf, Use of gray value distribution of run lengths for texture analysis, Pattern Recognition Lett. 11,415-420 (1990). 9. C. Zuang and S. Dunn, The amplitude varying rate statistical approach for texture classification, Pattern Recognition Lett. 11, 143-149 (1990).
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10. D.C. He, L. Wang and J. Guibert, Texture discrimination based on an optimal utilisation of texture features, Pattern Recognition 21, 141 146 (1988). 11. M. Amasdasun and R. King, Textural features corresponding to textural properties, 1EEE Trans. Syst., Man Cybernet. 19, 1264-1273 (1989).
About the Author--B. RAMAMOORTHY is currently an Associate Professor in the Manufacturing Engineering Section of the Department of Mechanical Engineering, Indian Institute of Technology, Madras, India. He completed his Ph.D from I. I. T Madras and has been engaged in teaching and research for the past decade. He has ca 25 research papers to his credit and his research areas are metrology and machine vision.
About the Author--K. VENKAT RAMANA is a research scholar at I. I. T. Madras currently doing an M. S.