Asymptotic joint normality of the granulometric moments

If a random set (binary image) is composed of randomly sized, disjoint translates arising as homothetics of a ®nite 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 ®nite vector of granulometric moments possesses a multivariate distribution that is asymptotically normal. Since Gaussian maximum-likelihood classi®cation is often used when employing the granulometric moments for texture classi®cation, the asymptotic joint normality of the moments gives support to the good results thereby obtained .