Euler Well-Composedness

Abstract

In this paper, we de ne a new avour of well-composedness, called Euler well-composedness, in the general setting of regular cell complexes: A regular cell complex is Euler well-composed if the Euler characteristic of the link of each boundary vertex is 1. A cell decomposi- tion of a picture I is a pair of regular cell complexes ����� K(I);K( I)

such that K(I) (resp. K( I)) is a topological and geometrical model represent- ing I (resp. its complementary, I). Then, a cell decomposition of a pic- ture I is self-dual Euler well-composed if both K(I) and K( I) are Euler well-composed. We prove in this paper that, rst, self-dual Euler well- composedness is equivalent to digital well-composedness in dimension 2 and 3, and second, in dimension 4, self-dual Euler well-composedness implies digital well-composedness, though the converse is not true.