Higher Dimensional Image Analysis using Brunn-Minkowski Theorem, Convexity and Mathematical Morphology

Abstract

The theory of deterministic morphological operators is quite rich and has been used on set and lattice theory. Mathematical Morphology can benefit from the already developed theory in convex analysis. Mathematical Morphology introduced by Serra is a very important tool in image processing and Pattern recognition. The framework of Mathematical Morphology consists in Erosions and Dilations. Fractals are mathematical sets with a high degree of geometrical complexity that can model many natural phenomena. Examples include physical objects such as clouds, mountains, trees and coastlines as well as image intensity signals that emanate from certain type of fractal surfaces. So this article tries to link the relation between combinatorial convexity and Mathematical Morphology.

Keywords: Convex bodies, convex polyhedra, homothetics, morphological cover, fractal, dilation, erosion.