Representation of Linear Granulometric Moments for Deterministic and Random Binary Euclidean Images
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A powerful method of morphological texture classification employs moments of the granulometric pattern spectrum. Classification depends on the statistical distributions of the granulometric moments and a fundamental problem is to find analytic expressions for the granulometric moments and, when possible, to characterize their probability distributions in terms of the underlying random image process. The present paper provides analytic expressions for the granulometric moments when the granulometric generator is linear. These expressions apply to all images likely to occur in practice. The expressions involve derivatives of length-functions for cross-cuts of the image. In addition, granulometric moments for random images composed of disjoint unions of randomly sized homothetics are shown to be asymptotically normal, independent of whether the image is generated by a convex primitive and of whether the image and granulometry share congruent generators. Asymptotic expressions are given for moments of these granulometric moments. For these, it is not assumed that the granulometric generator is linear. 1995 Academic Press. All rights reserved.
