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 basinsrdquo (through a steepest descent property) or by the "dividing linesrdquo separating(More)
To prepare images for better segmentation, we need preprocessing applications, such as smoothing, to reduce noise. In this paper, we present an enhanced computation method for smoothing 2D object in binary case. Unlike existing approaches, proposed method provides a parallel computation and better memory management, while preserving the topology (number of(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 recently introduced watershed cuts, a notion of watershed in edge-weighted graphs. In this paper, our main contribution is a thinning paradigm from which we derive three algorithmic watershed cut strategies: The first one is well suited to parallel implementations, the second one leads to a flexible linear-time sequential implementation, whereas the(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)