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- Gilles Bertrand
- Pattern Recognition Letters
- 1994

We introduce the notion of geodesic neighborhood in order to define some topological numbers associated with a point in a three-dimensional cubic grid. For {6, 26} and {6, 18} connectivities, these numbers lead to a characterization of simple points which consists in only two local conditions.

- Grégoire Malandain, Gilles Bertrand, Nicholas Ayache
- International Journal of Computer Vision
- 1991

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)

- Jean Cousty, Gilles Bertrand, Laurent Najman, Michel Couprie
- IEEE Transactions on Pattern Analysis and Machine…
- 2009

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)

We propose an original approach to the watershed problem, based on topology. We introduce a “one-dimensional” topology for grayscale images, and more generally for weighted graphs. This topology allows us to precisely define a topological grayscale transformation that generalizes the action of a watershed transformation. Furthermore, we propose an efficient… (More)

- Gilles Bertrand
- Journal of Mathematical Imaging and Vision
- 2005

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)

- Gilles Bertrand
- Pattern Recognition Letters
- 1995

A new 3D parallel thinning algorithm for medial surfaces is proposed. It works in cubic grids with the 6-connectivity. This algorithm is based on a precise definition of end points which are points belonging to surfaces or curves. We give a necessary and sufficient Boolean condition for characterizing points which are simple, non-ends and which are border… (More)

- Gilles Bertrand, Grégoire Malandain
- Pattern Recognition Letters
- 1994

- Michel Couprie, Francisco Nivando Bezerra, Gilles Bertrand
- J. Electronic Imaging
- 2001

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)

- Gilles Bertrand, Jean-Christophe Everat, Michel Couprie
- J. Electronic Imaging
- 1997

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)

- Gilles Bertrand
- Pattern Recognition Letters
- 1996