Simplex meshes: a general representation for 3D shape reconstruction

In this report, we develop the concept of simplex mesh as a representation of deformable models. 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. In this paper, we present a physically-based approach for recovering three-dimensional objects, based on the geometry of simplex meshes. Elastic behavior is modeled 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. They control either the normal orientation or the curvature continuity of the mesh or its closeness to a given reference shape. Unlike deformable surfaces de ned on regular grids, simplex meshes can have their topology locally altered. We have developed an adaptation and re nement process that respectively concentrates vertices and increases the mesh resolution at highly curved or inaccurate parts. The adaptivity of a mesh is governed by the minimization of a local energy. Furthermore, we have de ned some general mesh transformations that enables the recovery of complex models from parts of simpler shapes. We present several modeling results extracted from structured range data or three dimensional images, including objects of complex topology and a complete model of a human body.