Robust morphological representation of binary images

A general theory for the morphological representation of discrete and binary images is presented. Particular cases of the general scheme are shown to yield a number of useful image representations. The effect of noise degradation is studied. It is proven that, under certain assumptions, the general reduced morphological skeleton is the best morphological representation among a collection of invertible morphological image representations. This representation results in a minimal upper-bound on the average probability of error of reconstructing a binary image from its noisy representation