Efficient tetrahedralization of multi-material images with quality, fidelity, and topological guarantees

Abstract

An algorithm is proposed for generating three-dimensional unstructured tetrahedral meshes of multi-material images. The algorithm produces a mesh whose boundary is proved to be homeomorphic to the object surface. In addition, it provides a guaranteed dihedral angle bound of up to 19 . 4 7 ∘ for the output tetrahedra. Moreover, it allows for user-specified guaranteed bounds on the distance between the boundaries of the mesh and the boundaries of the materials. It produces a small number of mesh elements that comply with these guarantees, and is compatible in performance with other software. The algorithm offers all of the following properties: bounded dihedral angles, customized two-sided Hausdorff distance, topological faithfulness, a small number of elements, and run-time performance. The experimental evaluation on synthetic and real medical data illustrates the efficiency and effectiveness of the method. • The mesh offers a faithful topology to the materials. • Elements with arbitrarily small angles do not appear in the mesh. • The mesh offers a close representation (fidelity) of the underlying materials. • The mesh contains a small number of elements that comply with the guarantees above. • The mesh can be constructed within tight time constraints.