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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)

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)

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)

In this paper, we investigate topological watersheds [1]. 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 watershed of a map F or… (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)

Region merging methods consist of improving an initial segmentation by merging some pairs of neighboring regions. In this paper, we consider a segmentation as a set of connected regions, separated by a frontier. If the frontier set cannot be reduced without merging some regions then we call it a cleft, or binary watershed. In a general graph framework,… (More)