Granulometric Size Distribution Research Articles

Statistics of the morphological pattern-spectrum moments for a random-grain model

The morphological pattern spectrum (granulometric size distribution) results from iteratively opening an image and at each step recording the area of the opened image. Owing to the manner in which the size distribution is normalized, it defines a probability distribution function and possesses moments. If a binary image is considered as a random process, then the moments of the pattern spectrum are random variables. It is these random moments that are employed as shape and texture signatures in image classification and segmentation. Consequently, the statistics (moments) of these moments are important, and in the present paper these are studied for a grain model that has been used in various applications. A numerical procedure is developed to obtain approximate moment distributions, and both exact and asympotic methods are developed to express the mean and variance of the pattern-spectrum mean and variance. The general methods are applied to both normal- and gamma-distributed grain sizes.