Simplex meshes: a general representation for 3D shape reconstruction

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 objects (ICCV´93, p.103-12). 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 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. Furthermore, operations for connecting Simplex meshes are performed to recover complex models from parts with simpler shapes