Abstract A 3D image I is well-composed if it does not contain critical edges or vertices
(where the boundary of I is non-manifold). The process of transforming an image into a well …

In discrete topology, discrete surfaces are well-known for their strong topological and
regularity properties. Their definition is recursive, and checking if a poset is a discrete …

For well-composed (manifold) objects in the 3D cubical grid, the Euler characteristic is equal
to half of the Euler characteristic of the object boundary, which in turn is equal to the number …

In 2013, Najman and Géraud proved that by working on a well-composed discrete
representation of a gray-level image, we can compute what is called its tree of shapes, a …

A 2D binary image is well-composed if it does not contain a 2 * 2 configuration of two
diagonal black and two diagonal white squares. We propose a simple repairing algorithm to …

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 …

An nD pure regular cell complex K is weakly well-composed (wWC) if, for each vertex v of K,
the set of n-cells incident to v is face-connected. In previous work we proved that if an nD …

The notion of Abstract Cellular Complex, which was initiated by Kovalevsky, is a consistent
topology for representing images through lower-dimensional cells in the combinatorial grid …

In this paper, we define a new flavour of well-composedness, called Euler well-
composedness, in the general setting of regular cell complexes: A regular cell complex is …

In discrete topology, we like digitally well-composed (shortly DWC) interpolations because
they remove pinches in cubical images. Usual well-composed interpolations are local and …