CoOccurrence Matrix Measures

Several texture metrics that contain spatial information are based on the co-occurrence matrix, also known as spatial gray-level dependence matrix. Just as building the histogram is a preprocessing step that prepares the data for statistical moments, forming the co-occurrence matrices is an initial step that compiles spatial as well as statistical information for computing the texture metrics described below. The spatial information considered is the relative position of pairs of pixels, defined with distance d and orientation 6 that describe the location of the second pixel with respect to the first. A cooccurrence matrix is formed for each such position. In this manner, each co-occurrence matrix prepares the data to emphasize primarily structure or streaks in a given direction and a grain size that is at least as large as the selected distance. Typically, four values of 6, namely 0°, 45°, 90°, and 135°, cover the orientations, and the most common choice of distance is d = 1 when 6 is 0° or 90°, and d = V^ when 6 is 45° or 135°.

For an image with number of pixels P = 36, gray levels K = 4, and pixel values

FIGURE 13 Ultrasound image sections of normal liver (left), fatty liver (middle), and liver with cirrhosis (right).

TABLE 1 Some texture metrics obtained from the ultrasonic liver image sections shown in Fig. 13

Normal

Fatty

Cirrhosis

Statistical moments Variance Kurtosis

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