Adaptive and deformable models based on simplex meshes

Simplex meshes are simply-connected meshes that are topologically the dual of triangulations. We have introduced a simplex mesh representation for recognizing partially-occluded smooth objects. In this paper, we present a physically-based approach for recovering 3D 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 vertex. Those functionals are viewpoint-invariant, intrinsic and scale-sensitive. Unlike deformable surfaces defined on regular grids, simplex meshes are highly adaptive structures, and we have developed a refinement process for increasing the mesh resolution at highly curved or inaccurate parts. End contours are created in a semi-automatic way. Finally, operations for connecting simplex meshes are performed to recover complex models from parts of simpler shapes