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Définition et étude d'un modèle topologique minimal de représentation d'images 2d et 3d

Abstract : In this thesis, we define and study a topological model of 2 and 3 dimensional segmented image representation: the topological map. The definition of such a model is essential to define efficient segmentation algorithms. This problem was studied in many different works in dimension 2, but the proposed solutions are hardly extensible in upper dimensions.

To solve this problem, we first define the topological map in dimension 2, while keeping in mind our main concern, its extension in upper dimension. We introduce a notion of simplification level that allows a progressive definition, each level is obtained easily from the previous one by application of a particular type of merging. This notion allows to simplify the definition of the topological map that corresponds to the last level.

Moreover, these simplification levels can be easily extended to dimension 3, even to dimension n. They also make the study of the topological map and the proof of its properties easier. Indeed, this model is minimal, complete, stable for rotation, translation and homothety, and unique.

We present some extraction algorithms that allow to build this model from segmented images. A first <> algorithm performs several scans of the image and is not linear in dimension 3. We give then an optimal extraction algorithm based on theprecod notion, that performs a single scan of the image. The simplification levels allow to group the several cases to treat, by studying for each level the new cases in relation to the previous one.
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Contributor : Guillaume Damiand <>
Submitted on : Monday, January 21, 2008 - 2:17:48 PM
Last modification on : Wednesday, September 5, 2018 - 1:30:05 PM
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  • HAL Id : tel-00211340, version 1



Guillaume Damiand. Définition et étude d'un modèle topologique minimal de représentation d'images 2d et 3d. Interface homme-machine [cs.HC]. Université Montpellier II - Sciences et Techniques du Languedoc, 2001. Français. ⟨tel-00211340⟩



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