Geodesic Computations for Fast and Accurate Surface Remeshing and Parameterization

Gabriel Peyré (1) , Laurent D. Cohen (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

In this paper, we propose fast and accurate algorithms to remesh and flatten a genus-0 triangulated manifold. These methods naturally fits into a framework for 3D geometry modeling and processing that uses only fast geodesic computations. These techniques are gathered and extended from classical areas such as image processing or statistical perceptual learning. Using the Fast Marching algorithm, we are able to recast these powerful tools in the language of mesh processing. Thanks to some classical geodesic-based building blocks, we are able to derive a flattening method that exhibit a conservation of local structures of the surface. On large meshes (more than 500 000 vertices), our techniques speed up computation by over one order of magnitude in comparison to classical remeshing and parameterization methods. Our methods are easy to implement and do not need multilevel solvers to handle complex models that may contain poorly shaped triangles.

Mots clés: Remeshing; geodesic computation; fast marching algorithm; mesh segmentation; surface parameterization; texture mapping; deformable models

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Gabriel Peyré, Laurent D. Cohen. Geodesic Computations for Fast and Accurate Surface Remeshing and Parameterization. Progress in Nonlinear Differential Equations and Their Applications, Birkhäuser Basel, pp.157-171, 2005, Progress in Nonlinear Differential Equations and Their Applications, Vol. 63, ⟨10.1007/3-7643-7384-9⟩. ⟨hal-00365900⟩