The Euler-Poincaré Formula Through Contact Surfaces of Voxelized Objects

Abstract

Two new versions of the Euler-Poincaré formula are proposed considering two new defined cuboids: the tetra-voxeland the octo-voxel, without losing information on the number of vertices and edges. The well-known relationshipbetween contact and enclosing surface concepts, as well as the relationships between vertices, edges and enclosingsurfaces, allowed us to compute an innovative algorithm for obtaining alternative versions of the Euler-Poincaréformula. This is a very important topological descriptor of 3D binary images. We considered not only topological butgeometric aspects. Our method was compared to other proposals, obtaining that our proposed contact surface-basedmethod offers more advantages.