Learn More
This article proposes a new approach to segment a discrete 3-D object into a structure of characteristic topological primitives with attached qualitative features. This structure can be seen itself as a qualitative description of the object, because-it is intrinsic to the 3-D object, which means it is stable to rigid transformations (rotations and(More)
We study the watersheds in edge-weighted graphs. We define the watershed cuts following the intuitive idea of drops of water flowing on a topographic surface. We first establish the consistency of these watersheds: They can be equivalently defined by their "catchment basins" (through a steepest descent property) or by the "dividing lines" separating these(More)
A point of a discrete object is called simple if it can be deleted from this object without altering topology. In this article, we present new characterizations of simple points which hold in dimensions 2, 3 and 4, and which lead to efficient algorithms for detecting such points. In order to prove these characterizations, we establish two confluence(More)
In a recent work, we introduced some topological notions for grayscale images based on a cross-section topology. In particular, the notion of destructible point, which corresponds to the classical notion of simple point, allows us to build operators that simplify a grayscale image while preserving its topology. In this paper, we introduce new notions and(More)
In this paper, we propose a new methodology to conceive a thinning scheme based on the parallel deletion of P-simple points. This scheme needs neither a preliminary labelling nor an extended neighborhood, in the opposite of the already proposed thinning algorithms based on P-simple points. Moreover, from an existent thinning algorithm A, we construct(More)
We propose a method for collapsing simplicial complexes in a symmetric manner. For that purpose, we introduce the notions of a simple cell, of an essential face, and the one of a core of a cell. Then, we define the critical kernel of a complex. Our main result is that the critical kernel of a given complex X is a collapse of X. We extend this result by(More)