Generating quality tetrahedral meshes from binary volumes

This paper presents two new quality measures for tetrahedra which are smooth and well-suited for gradient based optimization. Both measures are formulated as a distance from the regular tetrahedron and utilize the fact that the covariance of the vertices of a regular tetrahedron is isotropic. We use these measures to generate high quality meshes from signed distance maps. This paper also describes an approach for computing (smooth) signed distance maps from binary volumes as volumetric data in many cases originate from segmentation of objects from imaging techniques such as CT, MRI, etc. The mesh generation is split into two stages; a candidate mesh generation stage and a compression stage, where the surface of the candidate mesh is moved to the zero iso-surface of the signed distance maps, while one of the quality measures ensures that the quality remains high. We apply the mesh generation algorithm on four examples (torus, Stanford dragon, brain mask, and pig back) and report the dihedral angle, aspect ratio and radius-edge ratio. Even though, the algorithm incorporates none of the mentioned quality measures in the compression stage it receives a good score for all these measures. The minimum dihedral angle is in none of the examples smaller than $15^o$.