Weakly well-composed cell complexes over nD pictures
In previous work we proposed a combinatorial algorithm to “locally repair” the cubical
complex Q (I) that is canonically associated with a given 3D picture I. The algorithm …
complex Q (I) that is canonically associated with a given 3D picture I. The algorithm …
Introducing Poset-Based Connected n-Manifolds and -well-composedness in Partially Ordered Sets
N Boutry - Journal of Mathematical Imaging and Vision, 2024 - Springer
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 …
regularity properties. Their definition is recursive, and checking if a poset is a discrete …
How to Make n-D Plain Maps Defined on Discrete Surfaces Alexandrov-Well-Composed in a Self-Dual Way
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 …
representation of a gray-level image, we can compute what is called its tree of shapes, a …
A 4D Counter-Example Showing that DWCness Does Not Imply CWCness in nD
In this paper, we prove that the two flavours of well-composedness called Continuous Well-
Composedness (shortly CWCness), stating that the boundary of the continuous analog of a …
Composedness (shortly CWCness), stating that the boundary of the continuous analog of a …
Continuous Well-Composedness Implies Digital Well-Composedness in n-D
In this paper, we prove that when an-D cubical set is continuously well-composed (CWC),
that is, when the boundary of its continuous analog is a topological (n-1)(n-1)-manifold, then …
that is, when the boundary of its continuous analog is a topological (n-1)(n-1)-manifold, then …
Euler well-composedness
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 …
composedness, in the general setting of regular cell complexes: A regular cell complex is …
A 4D Counter-Example Showing that DWCness Does Not Imply CWCness in nD
T Géraud - … Image Analysis: 20th International Workshop, IWCIA …, 2020 - Springer
In this paper, we prove that the two flavours of well-composedness called Continuous Well-
Composedness (shortly CWCness), stating that the boundary of the continuous analog of a …
Composedness (shortly CWCness), stating that the boundary of the continuous analog of a …