Affine Invariant Distance Using Multiscale Analysis

Abstract

In this paper we introduce an affine invariant distance definition from a $$2D$$2D point to the boundary of a bounded shape using morphological multiscale analysis. We study the mathematical behavior of this distance by examining separately the cases of convex and non-convex shapes. We prove that the proposed distance is bounded in the convex hull of the shape and infinite otherwise. A numerical scheme is given as well as experiments illustrating the behavior of the affine invariant distance.