Gilles Bertrand

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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 basinsrdquo (through a steepest descent property) or by the "dividing linesrdquo separating(More)
In this paper, we investigate topological watersheds (Couprie and Bertrand, 1997). One of our main results is a necessary and sufficient condition for a map G to be a watershed of a map F, this condition is based on a notion of extension. A consequence of the theorem is that there exists a (greedy) polynomial time algorithm to decide whether a map G is a(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)
We consider a cross-section topology which is deened on grayscale images. The main interest of this topology is that it keeps track of the grayscale informations of an image. We deene some basic notions relative to that topology. Furthermore, we indicate how to get an homotopic kernel and a leveling kernel. Such kernels may be seen as \ultimate" topological(More)