Discrimination of Textures using Texton Patterns

Table of contents

1. Introduction

nalysis of texture requires the identification of proper attributes or features that differentiate the textures in the image for segmentation, classification and recognition. Initially, texture analysis was based on the first order or second order statistics of textures [6,7,8,9,10]. Then, Gaussian Markov random field (GMRF) and Gibbs random field models were proposed to characterize textures [11,12,13,14,15,16]. Later, local linear transformations are used to compute texture features [17,18]. Then, texture spectrum technique was proposed for texture analysis [19]. The above traditional statistical approaches to texture analysis, such as co-occurrence matrices, second order statistics, GMRF, local linear transforms and texture spectrum are restricted to the analysis of spatial interactions over relatively small neighborhoods on a single scale. As a consequence, their performance is best for the analysis of micro textures only [20]. More recently, methods based on multi-resolution or multichannel analysis, such as Gabor filters and wavelet transform, have received a lot of attention [21,22,23,24,25,26,27,23,25]. From the literature survey, the present study found the Gray Level Co-occurrence Matrix (GLCM) is a benchmark method for extracting Haralick features (angular second moment, contrast, correlation, variance, inverse difference moment, sum average, sum variance, sum entropy, entropy, difference variance, difference entropy, information measures of correlation and maximal correlation coefficient) or Conners features [28] (inertia, cluster shade, cluster prominence, local homogeneity, energy and entropy). These features have been widely used in the analysis, classification and interpretation of remotely sensed data. Its aim is to characterize the stochastic properties of the spatial distribution of grey levels in an image.

The present paper is organized as follows. In he second section we have given clear information about grey level co-occurrence matrix information and the third section we discussed about textons. In fourth section we discussed deriving different Shape Descriptor Indexes (SDI). In the fifth section, proposed methodology is discussed and in sixth section results and discussions are given. Finally in last section we concluded about this paper.

2. II.

3. Gray Level Co-occurrence Matrix

One of the other most popular statistical methods used to measure the textural information of images is the Gray Level Co-occurrence Matrix (GLCM). The GLCM method gives reasonable texture information of an image that can be obtained only from two pixels. Grey level co-occurrence matrices introduced by Haralick [29] attempt to describe texture by statistically sampling how certain grey levels occur in relation to other grey levels. Suppose an image to be analyzed is rectangular and has N x rows and N y columns. Assume that the gray level appearing at each pixel is quantized to Ng levels. Let L x = {1,2,?,N x } be the horizontal spatial domain, L y = {1,2,?,N y } be the vertical spatial domain, and G= {0,1,2,?,N g -1} be the set of Ng quantized gray levels. The set L x × L y is the set of pixels of the image ordered by their row-column designations. Then the image I can be represented as a function of co-occurrence matrix that assigns some gray level in Lx × L y ; I: L x × L y ? G. The g ray level transitions are calculated based on the parameters, displacement (d) and angular orientation ( ?). By using a d istance of one pixel and angles quantized to 45 0 intervals, four matrices of horizontal, first diagonal, vertical, and second diagonal (0 0 , 45 0 , 90 0 and 135 0 degrees) are used. Then the un-normalized frequency in the four principal directions is defined by Equation (1).

where # is the number of elements in the set, (k, l) the coordinates with gray level i, (m, n) the coordinates with gray level j. The following Fig. 1 illustrates the above definitions of a co-occurrence matrix (d=1, ? = 0 0 ).

Even though Haralick extracted 24 parameters from co-occurrence matrix, the present paper used only energy, contrast, local homogeneity, and correlation as given in Equations ( 2) to (5).

Energy = ? ?ln??? ???? ? 2 ???1 ??,?? =0 (2)

Energy measures the number of repeated pairs and also measures uniformity of the normalized matrix.

Contrast = ? ??? ???? (i ? j) 2 ???1 ??,?? =0(3)

The contrast feature is a difference moment of the P matrix and is a standard measurement of the amount of local variations present in an image. The higher the value of contrast are, the sharper the structural variations in the image.

Local Homogenity = ? ? ?? ???? 1+(i?j) 2 ? ???1 ??,?? =0(4)

It measures the closeness of the distribution of elements in the GLCM to the GLCM diagonal. The converse of homogeneity results in the statement of contrast.

Correlation = ? ??? ???? (i??)(j??) (?) 2 ? ???1 ??,?? =0(5)

Where P ij is the pixel value in position (i, j) of the texture image, N is the number of gray levels in the image,

? is ? = ? i?? ???? N?1 i,j=0

mean of the texture image and (?) 2 is (?

) 2 = ? ?? ???? (i ? ?) 2 ???1 ??,?? =0

variance of the texture image. Correlation is the measure of similarity between two images in comparison. The measures mean (m), which represents the average intensity.

4. III. textons

Textons [30,31] are considered as texture primitives, which are located with certain placement rules. A close relationship can be obtained with image features such as shape, pattern, local distribution orientation, spatial distribution, etc. using textons. The textons are defined as a set of blobs or emergent patterns sharing a common property all over the image. The different textons may form various image features.

To have a precise and accurate texture classification, the present study strongly believes that one need to consider all different textons. That is the reason the present study considered all. There are several issues related with i) texton size ii) tonal difference between the size of neighbouring pixels iii) texton categories iv) expansion of textons in one orientation v) elongated elements of textons. By this sometimes a fine or coarse or an obvious shape may results or a pre-attentive discrimination is reduced or texton gradients at the texture boundaries may be increased. The present paper utilized the following five texton shades of 2×2 grid shown in Fig. 2. In Fig. 2 Blob shape (Index =5): TU 15 with all 1's represents a blob shape as shown in Fig. 8. The advantage of SDI is they don't depend on relative order of texture unit weights and can be given in any of the four forms as shown in Fig. 9 where the relative TU will change, but shape remains the same. 4 along with a bar graph shown in Fig. 19. The Table 5 compares discrimination rates of our earlier methods Texton based Cross Shape Descriptor Index (TCSDI) Texton based Diagonal Shape Descriptor Index (TDSDI) [ 2,4 ] with the current method TTSCM approach of this paper. The corresponding bar graph representation is shown in Fig. 20.

5. The

proposed TTSCM obtained high discrimination rate over our earlier TCSDI and TDSDI methods. This is because the TTSCM represent the SDI of the entire image instead of two separate or partial images of TCSDI and TDSDI.

Figure 1.
(a), the pixels are represented as d 1 , d 2 , d 3 and d 4 . The present paper considered texton shades if three or more pixels have the same intensity levels. This rule derives five texton shapes denoted as T 1 , T 2 , T 3 , T 4 and T 5 as shown in Fig.2.
Figure 2. Figure 1 :
1Figure 1: An example of Gray level co-occurrence matrix
Figure 3. Figure 2 :
2Figure 2 : Proposed 2×2 grid textons
Figure 4. Figure 3 :
3Figure 3 : Hole shape with SDI value 0 Dot shape (Index =1): The TU with 1, 2, 4 and 8 represents a dot shape. The dot shape will have only a single 1 as shown in Fig.4.
Figure 5. Figure 4 :
4Figure 4 : The four dot shapes with SDI value 1 Horizontal/Vertical line shape (Index =2): The two adjacent 1's results four different TU weights i.e. 3, 6, 9 and 12 and all of them represents a horizontal or vertical line as shown in Fig.5.
Figure 6. Figure 5 :
5Figure 5 : Representation of horizontal / vertical lines with SDI value 2. Diagonal Line shape (Index= 3): The other two adjacent 1's with TU values 5 and 10 represents diagonal lines as shown in Fig.6.
Figure 7. Figure 6 :
6Figure 6 : Representation of diagonal line with SDI value 3 Triangle shape (Index = 4): The three adjacent 1's with TU values 7, 11, 13 and 14 represents triangle shape as shown in Fig.7.
Figure 8. Figure 7 :
7Figure 7 : Representation of triangle shape with SDI value 4
Figure 9. Figure 8 :
8Figure 8 : Representation of blob shape with SDI value 5
Figure 10. Figure 9 :
9Figure 9 : Four different ways of assigning weights to TU
Figure 11. Figure 10 :Figure 11 :
1011Figure 10 : Representation of 3×3 neighborhood and its BDTUE and BCTUE
Figure 12. Figure 12 :
12Figure 12 : BDTUE in the form 2×2 grid and derived DSDI
Figure 13. Figure 14 :
14Figure 14 : Formation mechanism of TSDI image The Fig.15, 16 and 17 represents TSDI for Car, Water and Elephant images respectively.
Figure 14. Figure 15 :Figure 16 :
1516Figure 15 : (a) Car image (b) TSDI of (a)
Figure 15. Figure 17 :
17Figure 17 : (a) Elephant image (b) TSDI of (a)
Figure 16. Figure 18 :
18Figure 18 : Images of car, water and Eelephant textures
Figure 17. Figure 20 : 6 Global
206Figure 20 : Bar graph representation of proposed methods
Figure 18. Table 1 :
1
Figure 19. Table 2 :
2
Texture numbe r Contras t Correlat ion Energy Homog eneity
E_1 9.159 0.3525 0.032 0.4971
E_2 9.809 0.3369 0.0354 0.5044
E_3 9.129 0.3472 0.0375 0.5137
E_4 9.268 0.3631 0.0375 0.5165
E_5 8.801 0.3546 0.0387 0.5187
E_6 9.187 0.3343 0.0371 0.5156
E_7 7.254 0.2813 0.0474 0.5335
E_8 6.479 0.2645 0.0509 0.5414
E_9 12.69 0.4056 0.0324 0.5063
E_10 6.252 0.2921 0.0495 0.5478
Figure 20. Table 3 :
3
Texture numbe r Contras t Correlati on Energy Homog eneity
W_1 18.74 0.4686 0.0402 0.5306
W_2 16.83 0.3171 0.0327 0.4965
W_3 15.08 0.328 0.0352 0.5022
W_4 17.71 0.3615 0.0345 0.4859
W_5 18.45 0.4389 0.0301 0.5002
W_6 12.03 0.314 0.0359 0.5031
W_7 16.48 0.4387 0.0317 0.5013
W_8 15.26 0.5095 0.0408 0.5462
W_9 16.43 0.3591 0.0316 0.5024
W_10 19.39 0.3411 0.027 0.4851
Note: Algorithm 1: Discrimination algorithm using the proposed TTSCM method. Global Journal of C omp uter S cience and T echnology Volume XV Issue III Version I Year ( ) Figure 19 : Bar graph representation for Discrimination rates
Figure 21. Table 5 :
5
Methods Average discrimination rates (%)
TCSDI 84.33
TDSDI 88.66
TTSCM 93
Figure 22. Conclusion
Figure 23. Table 4 :
4
Texture Database Discrimination rate (%) TTSCM method
Elephant 93
Car 100
Water 86
Average Discrimination rate 93
original image one representing the cross and other
representing the diagonal features.
1
2

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Notes
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Date: 2015-01-15