Asymptotic joint normality of the granulometric moments

If a random set (binary image) is composed of randomly sized, disjoint tran slates arising as homothetics of a finite number of compact primitives and a granulometry is generated by a convex, compact set, then the granulometri c moments of the random set can be expressed in terms of model parameters. This paper shows that, under mild conditions, any finite vector of granulom etric 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 asympt otic joint normality of the moments gives support to the good results there by obtained. (C) 2001 Elsevier Science B.V. All rights reserved.