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Homeomorphic Tetrahedralization of Multi-material Images with Quality and Fidelity Guarantees

 

Jing Xu and Andrey Chernikov.

 

Published in 26th International Meshing Roundtable, pages 40 -- 52, Barcelona, Spain, September, 2017

 

Abstract

 

We present a novel algorithm for generating three-dimensional unstructured tetrahedral meshes of multi-material images. The algorithm produces meshes with high quality since it provides a guaranteed dihedral angle bound of up to 19.47 degrees for the output tetrahedra. In addition, it allows for user-specified guaranteed bounds on the two-sided Hausdorff distance between the boundaries of the mesh and the boundaries of the materials. Moreover, the mesh boundary is proved to be homeomorphic to the object surface. The algorithm is fast and robust, it produces a sufficiently small number of mesh elements that comply with these guarantees, as compared to other software. The theory and effectiveness of our method are illustrated with the experimental evaluation on synthetic and real medical data.