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Delaunay Deformable Models: Topology-Adaptive Meshes Based on the Restricted Delaunay Triangulation

Abstract : In this paper, we propose a robust and efficient La- grangian approach, which we call Delaunay Deformable Models, for modeling moving surfaces undergoing large de- formations and topology changes. Our work uses the con- cept of restricted Delaunay triangulation, borrowed from computational geometry. In our approach, the interface is represented by a triangular mesh embedded in the Delau- nay tetrahedralization of interface points. The mesh is it- eratively updated by computing the restricted Delaunay tri- angulation of the deformed objects. Our method has many advantages over popular Eulerian techniques such as the level set method and over hybrid Eulerian-Lagrangian tech- niques such as the particle level set method: localization accuracy, adaptive resolution, ability to track properties as- sociated to the interface, seamless handling of triple junc- tions. Our work brings a rigorous and efficient alternative to existing topology-adaptive mesh techniques such as T- snakes.
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Contributor : Jean-Daniel Boissonnat <>
Submitted on : Tuesday, June 1, 2010 - 8:32:47 AM
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  • HAL Id : hal-00488042, version 1


Jean-Philippe Pons, Jean-Daniel Boissonnat. Delaunay Deformable Models: Topology-Adaptive Meshes Based on the Restricted Delaunay Triangulation. IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2007, Minneapolis, France. pp.200. ⟨hal-00488042⟩



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