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Reconstruction, Détection et Régularisation de Données Discrètes

Abstract : This thesis deals with the problems of structuring and processing discrete data, organized or not. It is organized into two parts. The first part deals with the structuration of data represented by sets of points of the Euclidean plane or space. In this context, we consider the problems of the polygonal reconstruction of planar curves and the detection geometric 3D shapes. These two problems are handled by computational and combinatorial geometry techniques, based on the Voronoi diagram and the Delaunay triangulation. In the context of planar curve reconstruction, we propose a hierarchical family of subgraphs of the Gabriel graph, which we call the local beta-crusts. We study the properties of this family, which allow us to design a simple curves reconstruction algorithm. Then, we propose a method for detecting known shapes from a set of 3D points, embedded or not into a noisy background. This method is based on an extension of the alpha-shapes, generated from ellipsoidal balls. In a second part, we treat the problem of data regularization by discrete variational methods on weighted graphs of arbitrary topology. For this, we propose a broad family of discrete functionals, based on the L2 and Lp norms of the graph gradient. This leads to several linear and nonlinear diffusion processes on graphs. This formalism is applied to smooth, to restore, and to simplify discrete images, meshes and non-organized discrete data.
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Contributor : Hal System <>
Submitted on : Thursday, January 10, 2008 - 10:45:39 AM
Last modification on : Tuesday, February 5, 2019 - 12:12:10 PM
Long-term archiving on: : Tuesday, April 13, 2010 - 4:53:45 PM


  • HAL Id : tel-00203445, version 1


Sébastien Bougleux. Reconstruction, Détection et Régularisation de Données Discrètes. Interface homme-machine [cs.HC]. Université de Caen, 2007. Français. ⟨tel-00203445⟩



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