Morphological granulometric simulation: distribution of the pattern-spectrum mean and variance for binary images with overlapping elements
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Several studies have discussed how the granulometric pattern-spectrum moments can provide good texture discrimination within images. Because textural images are modeled as random processes, the moments of an image's pattern spectrum are random variables, and knowledge of their distributions is key to the classification procedure. Both exact and asymptotic descriptions of the mean and variance distributions have previously been found under the assumption that the texture elements are nonoverlapping. The present study employs computer simulations to address the situation where the elements are not disjoint. The image is generated by Monte Carlo techniques with the predefined set of primitives, openings are calculated, and the pattern spectrum is found. It is seen that the pattern-spectrum mean remains close to its theoretical distribution.