Texture representation through multifractal analysis of optical mass distributions

The paper addresses the analysis of singular distributions defined on a fractal support, called fractal measures. In general, a fractal measure has an infinite number of singularities of infinitely many types. The term multifractals expresses the fact that points, corresponding to a given type of singularity, typically form a fractal subset whose dimensions depend on the type of singularity. The theory of the q-th order generalized fractal dimensions supplies a tool for the characterization of such multifractal measures. This theory results from an extension of the fractal dimension to different-order statistics. The paper exploits such concepts in order to face the problem of texture recognition. In particular the fractal measure taken into account is the 2D distribution of the optical mass of an image; some theoretical aspects related to this problem are addressed. Results on real images are presented and discussed