Homeomorphic Tetrahedral Tessellation for Biomedical Images

We present a novel algorithm for generating three-dimensional unstructured tetrahedral meshes for biomedical images. The method uses an octree as the background grid from which to build the final graded conforming meshes. The algorithm is fast and robust. It produces meshes with high quality since it provides dihedral angle lower bound for the output tetrahedra. Moreover, the mesh boundary is a geometrically and topologically accurate approximation of the object surface in the sense that it allows for guaranteed bounds on the two-sided Hausdorff distance and the homeomorphism between the boundaries of the mesh and the boundaries of the materials. The theory and effectiveness of our method are illustrated with the experimental evaluation on synthetic and real medical data