Simplex Meshes : a General Representation for 3 D

Simplex meshes are simply connected meshes that are topologically dual of triangulations. In a previous work, we have introduced the simplex mesh representation for performing recognition of partially occluded smooth objectss3]. In this paper, we present a physically-based approach for recovering three-dimensional objects, based on the geometry of simplex meshes. Elastic behavior is modelled by local stabilizing functionals, controlling the mean curvature through the simplex angle extracted at each ver-tex. Those functionals are viewpoint-invariant, intrinsic and scale-sensitive. Unlike deformable surfaces de-ned on regular grids, simplex meshes are highly adap-tive structures, and we have developed a reenement process for increasing the mesh resolution at highly curved or inaccurate parts. Furthermore, operations for connecting simplex meshes are performed to recover complex models from parts with simpler shapes.