128.

[Cover] [Contents] [Index]

Page 212

of the power spectrum have a diagonal (bottom-left to top-right) orientation. This is because the geological patterns in the image have a NW/SE direction (recall that the direction of features on the power spectrum is perpendicular to the direction of image patterns in the spatial domain).

Figure 5.14b shows a texture image generated by applying a ring filter within the frequency range [30, 100] on Figure 5.14a. It can be seen that the original image has become blurred, because only low frequency information is preserved. Figure 5.14c shows an image derived by a wedge filter with a horizontal direction with angles θ₁ and θ₂ defined by −22.5° and 22.5°, respectively, and the resulting patterns have a vertical orientation.

5.3 Grey level co-occurrence matrix (GLCM)

This section describes the texture feature extraction technique based on the grey level co-occurrence matrix (GLCM), sometimes called the grey-tone spatial-dependency matrix. The principal concept of GLCM is that the texture information contained in an image is defined by the adjacency relationships that the grey tones in an image have to one another. In other words, it is assumed that the texture information is specified by values f_ij within the GLCM, where f_ij denotes the frequency of occurrence of two cells of grey tone i and j, respectively, separated by distance d with a specific direction on the image. Values of f_ij can be calculated for any feasible direction and distance d. Generally, only four directions corresponding to angles of 0°, 45°, 90° and 135° are used.

5.3.1 Introduction to the GLCM

Consider Figure 5.15a, which represents a 4×4 image with four grey levels. Figure 5.15b displays the general form of the corresponding GLCM. For example, the value contained in cell (2, 3) represents the number of times that grey levels 2 and 3 occur with a specific direction and distance, d. Figure 5.15c−f presents the results for four directions given above with d=1, while ‘H’, ‘V’, ‘LD’ and ‘RD’ each denotes cell number calculation for angles 0° (horizontal), 90° (vertical), 135° (left diagonal), and 45° (right diagonal), respectively, as indicated by the arrows.

Instead of using the frequency values in a GLCM directly, it is common practice to normalise them to the range [0, 1] to avoid scaling effects. The normalisation procedure for each cell inside the matrix can be easily calculated. For the horizontal direction, with d=1, there will be 2×(number of columns–1) pairs in each row. Consequently, the total number of nearest neighbour pairs can be obtained by the expression 2×(number of columns−1)×(number of rows). For instance, in the case of Figure 5.15a, the total number of pairs of horizontal direction is computed by 2·(4 – l)·4=24. It can be easily verified that the sum of the entries in

[Cover] [Contents] [Index]