Statistical Moments

Since a smooth region contains pixels with values close to each other and a rough region has wide variability in pixel values, statistical moments of the region histogram can be used as texture metrics. In an image with K gray levels, consider a region with mean value p, and histogram h(k) with k ranging from 0 to K — 1. The nth moment about the mean for this histogram is given by:

The second moment m2 or variance is a common texture measure; it correlates well with the visual roughness perception, and it is relatively fast to compute. The third and fourth moments, skewness and kurtosis, reflect respectively the asymmetry and uniformity of the histogram. Although these moments relate to the intensity variations within the region, they have to be used cautiously because they do not always correlate well with the visual texture interpretation. Nevertheless, they can be used as extracted features in pattern recognition applications where their potential value is explored with a quantitative analysis. The variance and kurtosis of three textures are illustrated with Fig. 13 and Table 1.

Statistical moments have been used for applications such as texture quantification in ultrasonic images of liver tissue [43]. Statistical moments do not contain spatial information because they are derived from the image histogram. Since the concept of roughness is often associated with the size of the grain in the object, texture measures that convey spatial information may be valuable.

FIGURE 11 A pixel representation of the Zhang and Suen thinning process. (a) Small section of an image. (b) Outcome of thinning with the algorithm, black pixels remain, and gray pixels are removed.

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