Reconstruction géométrique de formes - Application à la géologie

Stéphane Nullans 1
1 PRISME - Geometry, Algorithms and Robotics
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : Several methods based on the use of Voronoi diagrams, are proposed for the 3D and 2D reconstruction of natural objects. The main application domain is geology. A first algorithm enables volumes to be constructed starting from the combined use of geological maps, cross-sections and drill-lines. Input data have associated colors (object characteristics), but may be sparse and heterogeneous, and do not need to be organized in any special way. The method is based on Voronoi diagrams and produces volumes. Attributing colors to data allows to reconstruct simultaneously objects that are known to be distinct. Our reconstruction method is based on "proximity" and therefore uses Voronoi diagrams. For simplicity, the heterogeneous data set S (points, lines, surfaces) is discretized into a set of colored points Sd. The "colored" Voronoi diagram of Sd. gives a partition of the space into regions R, which approximates the scene. In Addition, we smooth the boundaries of the regions of R, in such a way that the topology of the Voronoi regions is preserved, i.e. each new deformed region contains the same set of points as initially. Specific methods are added to allow the insertion of faults in the reconstruction process. We propose an other way for representing reconstructed objects, using the combination of implicit functions, Voronoi diagrams and nearest neighbor interpolation. The goal of the method is to define a continuous and smooth function f, so that f=0 approximates the expected shape. We define local functions in the neighborhood of the initial data, and the final shape results in interpolating those functions.
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Stéphane Nullans. Reconstruction géométrique de formes - Application à la géologie. Géométrie algorithmique [cs.CG]. Université Nice Sophia Antipolis, 1998. Français. ⟨tel-00832483⟩

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