Geometric invariant shape representation using morphological multiscale analyses and applications to shape classification

Abstract

This is a revised version of paper [2]. We have putted together papers [2] and [1], and we have included a lot of changes in order the paper be more understandable, readable and complete, we have also included a new application of the technique to the problem of shape classification. We present a new geometric invariant shape representation using morphological multiscale analyses. The geometric invariant is based on the area and perimeter evolution of the shape under the action of a morphological multiscale analysis. First, we present some theoretical results on the perimeter and area evolution across the scales of a shape. In the case of similarity transformations, the proposed geometric invariant is based on a scale-normalized evolution of the isoperimetric ratio of the shape. In the case of general affine geometric transformations the proposed geometric invariant is based on a scale-normalized evolution of the area. We present some numerical experiments to evaluate the performance of the proposed models. We present an application of this technique to the problem of shape classification on a real shape database and we study the well-posedness of the proposed models in the framework of viscosity solution theory