Texture Classification - IEEE Xplore

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Ju Hyun Kim, Soo Chang Kim, Tae Jin Kang. Intelligent Textile System Research Center and School of Materials Science and Engineering. Seoul National ...
Fractal Dimension Co-occurrence Matrix Method for Texture Classification Ju Hyun Kim, Soo Chang Kim, Tae Jin Kang Intelligent Textile System Research Center and School of Materials Science and Engineering Seoul National University, Sillim-9-dong, Gwanak-gu, Seoul, Korea 151-744 Phone: +82-2-880-7197, Fax: +82-2-885-1748, Email: [email protected]

Abstract - The fractal dimension co-occurrence matrix (FDCM) method, incorporating with fractal dimension and the gray level co-occurrence matrix (GLCM) method, is presented for texture classification. 12 Brodatz's natural texture images were classified by the GLCM method, sub-band domain cooccurrence matrix (SBCM) method and the FDCM method. The FDCM method showed the highest classification rate among the compared methods. Keywords - Texture classification, gray level co-occurrence matrix, fractal dimension, box counting method, wavelet fractal

method

I.

INTRODUCTION

Texture analysis is one of the important applications of image-processing. Several approaches to texture analysis have been developed over the past three decades. At the beginning, many researches by the statistical approach and model-based method have been attempted. Recently, signal processing methods such as the wavelet transform and Gabor transform have been noted since they could provide multi-scale analysis for texture [1]. Gray level co-occurrence matrix (GLCM) is the most popular method among statistical methods in texture analysis. Texture features can be simply extracted using the GLCM in image application. However, the GLCM shows relatively low accuracy and lack speed performance. To improve the accuracy, methods combining the GLCM with other methods have been studied. Latif-Amet et al. [1] proposed the sub-band domain co-occurrence matrix (SBCM), which combines concepts from wavelet theory and GLCM, for the fabric defect detection. Texture analysis methods incorporating the properties of both GLCM and texture spectrum was also investigated by Al-Janobi [2]. Clausi and Deng [3] developed a design-based method to fuse Gabor filter and GLCM for improved texture recognition. In the biomedical field, fractal dimension (FD) and GLCM were estimated for the texture segmentation of electron micrograph images [4]. In this study, a new method combining concepts of the FD and the GLCM method, namely the fractal dimension cooccurrence matrix (FDCM) method, is presented for texture classification. Generally, the box-counting method (BCM) is used as an appropriate method of FD estimation for images [5]. Consi and Proen,a [6] developed a fractal image analysis

1-4244-0549-1/06/$20.00 (2006 IEEE.

system for fabric inspection based on the BCM. However, the BCM is computationally expensive and is well known to coincide with the theoretical FD only in a small range. Kang et al. [7] proposed a wavelet-fractal method (WFM) to calculate accurate FD of surface, and demonstrated that the WFM is more accurate and faster than the BCM. In this study, this approach and the BCM were adopted to calculate the FD. The FD was calculated to lines of the image, while GLCM and SBCM focus on pixels. In contrast to those methods, the FDCM focuses on patterns of gray levels on the line of the image. The experimental results showed that the FDCM method was more effective than GLCM and SBCM methods for the texture classification. II. METHODOLOGY

A. Gray level co-occurrence matrix and sub-band domain co-occurrence matrix The GLCM is constructed from the image by estimating the probability that two pixels with a specified separation have the specified difference of gray levels as P(i, j, d, 0) =# {(x1, Y1), (X2 Y2 )I f(x1,y1 ) i (1) f(x2,y2) = i,l (XIY1)-(X2Y2)1= d, o} Z((X1,yI),(X2,Y2))= where # denotes the number of occurrences inside the window sizes where the intensity level of a pixel pair changes from i to j, d is a displacement between two pixels, and is the angle between the two pixels [1-3]. The method to be developed for improving accuracy of the GLCM is the SBCM method, which combined the discrete wavelet transform (WT) and the GLCM method [1]. The WT is used to determine the frequency bands carrying the most information about the texture by decomposing images into multiple frequency bands and computing the band energies. Then the SBCM is computed from the filtered images through theWT. Haralick features [8] are extracted from GLCM and SBCM. In this study, we used the following 8 features. ASM = Z P(i, j, d, 0)2, (2) i

j

j,d,f9), ZiP(i, i j 2 = ,E (f J=ZZ(i_P~)2pwdo)' ( ,c (,j, d, 09) u

(3)

=

'J'

Cont = ZZ(i - j)2 P(i,j, d, 6),

(6)

Diss = E E (i - j)P(i, j, d, 6),

(7)

i

Z

where

(i - )( -A)P(i, j,d,0)2

Corr =

2N-j

(4)

I

j

i

E d =E

j

d*

n=l

dj,n

2 -j(a+0.5)

Practically, when

(13)

d* is plotted

i~ ~ lote against j on a double logarithmic scale, the linear regression with a slope can be obtained using a least-square fit algorithm. Therefore the FD of a 2-D profile is i N-j 2

.

FD = 2.5+ slope

(14)

J

Ent = ,IP(i, j,d,0)logP(i, j,d,0)'

(8)

P(i,j,d,O),

IDM=ZZ 1+(i

(9)

j)

Fractal Dimension Co-occurrence Matrix Figure 1 illustrates the overall procedures of the FDCM method. The histogram-equalized image is converted into NxN matrix by computing the absolute average deviation from the mean (ADD) [9] of each pixel as an energy definition.

where ASM, /1, Corr, Cont, Diss, Ent, IDM are angular second moment, mean, variance, correlation, contrast, dissimilarity, entropy, and inverse difference moment, respectively. U,

B. Fractal Dimension.

Fractal designates a rough or fragmented geometric shape that can be subdivided into parts, each of which is similar to a reduced-size copy of the whole. The FD is defined as 1 = NrrFD or FD = (10) log(1/ r) where Nr is the number of non-overlapping copies, r is a ratio. To calculate the FD, we used the box counting method [5, 6] and wavelet-fractal method [7] in this study.

log(NJ)

,

Box counting method (BCM) The BCM uses the process of estimating the probability that interested points lie in the box. Numbers of boxes which contain points are obtained as the size of box decreases and the linear regression equation is obtained by Equation (10). The FD is the slope at the equation. To obtain the FD from the line of gray level image, total number of boxes (Nr) is estimated as nr (i)=int(Gmax

/r)-int(Gmin/r) + 1,

(11)

(12) Nr = nr(') where int( ) is the integer part of a division, Gmax and Gmin are the maximum gray level and the minimum gray level in the grid (i). Wavelet-fractal method (WFM) The WFM is more accurate and faster than the BCM in the computation of the FD [7]. If qVjn(x) is a Daubechies wavelet base with a vanishing moment 2, and continuous and bounded function f(x) C- (a is the exponent Holder continuous complex space) and Em,n < E, the first norms of {dj7,1} have the E

equation

Figure 1. Overall procedures of the FDCM method

Then the FDs for each row and column of the matrix are calculated by the BCM and the WFM. Through this process, we could obtain FD vectors (FD(i)) for rows and columns, respectively. FD vector = [FD (i): 1 < FD (i) < 2] (15)

The elements of the FD vectors are changed to integer in order to construct the co-occurrence matrix by the following equation. NFD (i) = round{(FD (i) - 1) x I00 + 1}, (16) where round{t} rounds off to the nearest integer. The FDCM is derived from NFD(i) as shown in Figure 2 and equation (17). The FDCM means the probability that two lines with a specified separation have the specified difference of FD. Because the range of NFD(i) is 1 to 101, the FDCM becomes 101 x 101 matrix. FDCM, (p, q) (17) =

[(i, i + d): NFD(i) =p,NFD(i + d) =q],

where a is row or column, d is a displacement between elements of the NFD(i). Haralick features are calculated from the FDCM. Therefore, the final features are obtained by adding features from the row FDCM and features from the column FDCM. ND (i+d)

101

NFD)

Figure 3. 12 Brodatz's natural images.

classifi-cation using only values of mean and variance of the FD values as features. Because the FD is only information on the pattern of gray values on row or column of the image, the classification rates were low (about 60%). The features by the GLCM method and the SBCM method reflect the relation between pixels. On the other hand, the

101 Figure 2. Constructing the FDCM from NFD(i).

III. RESULTS AND DISCUSSION

12 Brodatz's natural texture images shown in Figure 3 were chosen for samples [10] and Bayes classifier was used for the texture classification. Table I summarizes the results of texture classification by the GLCM method, the SBCM method, methods using the only FD, and the FDCM methods. Relative accuracies of methods are shown in Figure 4. In case of the fabric defect detection, accuracy using the SBCM method was better than that using the GLCM method in the literature [1]. However, it was found from the Table 1 that the results could vary by samples. In the case of the SBCM method, accuracy could be fallen because smaller images decomposed by WT are dealt with. To investigate the effect of the FD as a texture feature, we performed the texture

100 VV|

FD(BCM) r 90 E FD(WFM) I 80

1 GLCM a SBCM |EFDCM(BCM) I

40

30 20

Training

Figure 4. Comparison of texture classification rates of the GLCM method, the SBCM method, the FD methods, and the FDCM methods.

features by the FDCM method represent the relation between patterns of the line. Therefore, it can be said that the features by the FDCM method have more information on texture. As a result, the texture classification accuracies when using features

from the FDCM were better than the others. In general, the FDCM method using the BCM showed more accurate results, but required more computational time. On the other hands, when the WFM was used for the FD calculation, the execution speed was even faster than the BCM and the accuracy was about l100%.

this research through SRC/ERC (RI 1-2005-065).

of MOST/KOSEF

REFERENCES [1] [2]

[3]

IV. CONCLUSIONS

[4]

A new texture feature extraction method, namely the fractal dimension co-occurrence matrix (FDCM) method, has been developed. Texture classification with 12 Brodatz's natural texture images was performed and the proposed method was compared with the GLCM method and the SBCM method. The texture classification accuracies by the FDCM method were even better than the others. The FDCM method with the WFM saved the computational time and achieved the similar results as that with the BCM.

[5]

[6] [7]

[8] [9]

ACKNOWLEDGMENT

The authors of this paper would like to thank the Korea Science and Engineering Foundation (KOSEF) for sponsoring

program

[10]

A. Latif-Amet, A. Ertuzun and A. Ercil, "An Efficient Method for Texture Defect Detection: Sub-Band Domain Co-Occurrence Matrices," Image and Vision Computing, vol. 18, pp. 543-553, 2000. A. Al-Janobi, "Performance Evaluation of Cross-Diagonal Texture Matrix Method of Texture Analysis," Pattern Recognit., vol. 34, pp. 171-180, 2001. D. A. Clausi and H. Deng, "Design-Based Texture Feature Fusion Using Gabor Filters and Co-Occurrence Probabilities," IEEE Trans. Image Process., vol. 14, no. 7, pp. 925-936, 2005. K. L. Chan, "Quantitative Characterization of Electron Micrograph Image Using Fractal Feature," IEEE Trans. Biomedical Engineering, vol. 42,no.10,1995. K. Foroutan-Pour, P. Dutilleul and D. L. Smith, "Advances in the Implementation of the Box-Counting Method of Fractal Dimension Estimation," Applied Mathematics and Computation, vol. 105, pp. 195210,1999. A. Conci and C. B. Proenca, "A Fractal Image Analysis System for Fabric Inspection Based on a Box-Counting Method," Computer Networks andISDNSystems, vol. 30, pp. 1887-1895, 1998. T. J. Kang, S. C. Kim, I. H. Sul, J. R. Youn and K. Chung, "Fabric Surface Roughness Evaluation Using Wavelet-Fractal Method, Part I: Wrinkle, Smoothness and Seam Pucker," Textile Res. J., vol. 75, no. 11, pp. 751-760, 2005. R. Haralick, "Textural Features for Image Classification," IEEE Trans. Syst. Man. Cybern., vol.3, no. 6, pp. 610-621, 1973. M. Acharyya, R. K. De and M. K. Kundu, "Extraction of Features Using M-Band Wavelet Packet Frame and Their Neuro-Fuzzy Evaluation for Multitexture Segmentation," IEEE Trans. Pattern Anal. Mach. Intell., vol. 25, no. 12, pp. 1639-1644, 2003. P. Brodatz, Texture - A Photographic Album for Artists and Designers, Dover, New York, 1966.

TABLE I. Accuracies of four methods for the texture classification.

Class GLCM Training GLCM Test SBCM Train SBCM Test FD Train, BCM FD Test, BCM FD Train, WFM FD Test, WFM FDCM Train, BCM FDCM Test, BCM FDCM Train, WFM

1 100 87.5 100 90.63 43.75 71.88 75 43.75 100 100 100

2 43.75 65.63 100 81.25 28.13 50 53.13 50 100 100 100

FDCMTest, WFM

100

100

3 100 100 100 100 53.13 84.38 65.63 100 100 100 100 100

4 96.88 100 100 87.5 59.38 96.88 34.38 96.88 100 100 100

100

5 96.88 100 100 100 53.13 81.25 53.13 62.5 100 100 100 100

Accuracy (0) 6 7 93.75 100 100 96.88 100 100 100 96.88 46.88 87.5 71.88 0 37.5 93.75 43.75 62.5 100 100 100 100 100 100 100 100

8 93.75 87.5 100 56.25 87.5 0 100 18.75 100 100 100 100

9 100 96.88 100 100 62.5 37.5 96.88 25 100 100 100

Io100T

10 100 87.5 100 93.75 40.63 28.13 96.88 28.13 100 100 100

96.88

11

1

100 96.88 100 100 84.38 46.88 43.75 59.38 100 100 100

12 93.75 40.63 100 56.25 100 25 43.75 53.13 100 100 100

Total 97.92 82.81 100 74.22 58.85 52.88 65.1 54.69 100 100 100

100

100

99.74