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

Jing Xu | Zendy; Andrey N. Chernikov | Zendy

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

Author(s) -

Jing Xu,

Andrey N. Chernikov

Publication year - 2017

Publication title -

procedia engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.32

H-Index - 74

ISSN - 1877-7058

DOI - 10.1016/j.proeng.2017.09.786

Subject(s) - polygon mesh , boundary (topology) , tetrahedron , dihedral angle , fidelity , hausdorff distance , computer science , geodesic , algorithm , mesh generation , surface (topology) , software , mathematics , artificial intelligence , geometry , computer graphics (images) , mathematical analysis , finite element method , engineering , structural engineering , telecommunications , hydrogen bond , chemistry , organic chemistry , molecule , programming language

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° 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.

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