Strong Euler well-composedness

Abstract

In this paper, we define a new flavour of well-composedness, called strong Euler well composedness. In the general setting of regular cell complexes, a regular cell complex of dimension n is strongly Euler well-composed if the Euler characteristic of the link of each boundary cell is 1, which is the Euler characteristic of an (n−1)-dimensional ball. Working in the particular setting of cubical complexes canonically associated with nD pictures, we formally prove in this paper that strong Euler well-composedness implies digital well-composedness in any dimension n ≥ 2 and that the converse is not true when n ≥ 4