Topological invariants are extremely useful in many applications related to digital imaging and geometric modeling, and homology is a classical one, which has not yet been fully explored in image… (More)

The eccentricity transform associates to each point of a shape the geodesic distance to the points farthest away. This can be used to decompose shapes into parts based on the connectivity of the… (More)

During the previous decade, many works have shown that topological properties are of interest in an image context. Among all topological invariants (Euler characteristic, Betti numbers,… (More)

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and… (More)

Many combinatorial structures have been designed to represent the topology of space subdivisions and images. We focus here on two particular models, namely the n-G-maps used in geometric modeling and… (More)

In this paper, we define a border operator for generalized maps, a data structure for representing cellular quasi-manifolds. The interest of this work lies in the optimization of homology… (More)

This paper focuses on homology computation over ”cellular” structures whose cells are not necessarily homeomorphic to balls and which allow multiincidence between cells. We deal here with… (More)

The paper focuses on homology computation over cellular structures through the computation of incidence numbers. Roughly speaking, if two cells are incident, then their incidence number characterizes… (More)