Asymptotic joint normality of the granulometric moments
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abstract
If a random set (binary image) is composed of randomly sized, disjoint translates arising as homothetics of a finite number of compact primitives and a granulometry is generated by a convex, compact set, then the granulometric moments of the random set can be expressed in terms of model parameters. This paper shows that, under mild conditions, any finite vector of granulometric moments possesses a multivariate distribution that is asymptotically normal. Since Gaussian maximum-likelihood classification is often used when employing the granulometric moments for texture classification, the asymptotic joint normality of the moments gives support to the good results thereby obtained. 2001 Elsevier Science B.V. All rights reserved.