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Invariant High Level Reeb Graphs of 3D Polygonal Meshes

Julien Tierny 1 Jean-Philippe Vandeborre 1, 2, * Mohamed Daoudi 1, 2
* Corresponding author
1 LIFL - FOX MIIRE
LIFL - Laboratoire d'Informatique Fondamentale de Lille
Abstract : Many applications in computer graphics need high level shape descriptions, in order to benefit from a global understanding of shapes. Topological approaches enable pertinent surface decompositions, providing structural descriptions of 3D polygonal meshes; but in practice, their use raises several difficulties. In this paper, we present a novel method for the construction of invariant high level Reeb graphs, topological entities that give a good overview of the shape structure. With this aim, we propose an accurate and straightforward feature point extraction algorithm for the computation of an invariant and meaningful quotient function. Moreover, we propose a new graph construction algorithm, based on an analysis of the connectivity evolutions of discrete level lines. This algorithm brings a practical solution for the suppression of non-significant critical points over piecewise continuous functions, providing meaningful Reeb graphs. Presented method gives accurate results, with satisfactory execution times and without input parameter. The geo- metrical invariance of resulting graphs and their robustness to variation in model pose and mesh sampling make them good candidates for several applications, like shape deformation (experimented in this paper), recognition, compression, indexing, etc.
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Julien Tierny, Jean-Philippe Vandeborre, Mohamed Daoudi. Invariant High Level Reeb Graphs of 3D Polygonal Meshes. 3rd IEEE International Symposium on 3D Data Processing, Visualization and Transmission (3DPVT'06), Jun 2006, Chapel Hill, North Carolina, United States. ⟨hal-00725581⟩

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