A Combinatorial Method for Topology Adaptations in 3D Deformable Models

Authors:
Jochen Abhau;Otmar Scherzer
Affiliations:
Department of Mathematics, University of Innsbruck, Innsbruck, Austria 6020;Department of Mathematics, University of Innsbruck, Innsbruck, Austria 6020 and Radon Institute of Computational and Applied Mathematics, Linz, Austria 4040
Venue:
International Journal of Computer Vision
Year:
2010

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Abstract

In this paper we propose an efficient algorithm for topology adaptation of evolving surface meshes in 3D. This system has two novel features: First, a spatial hashing technique is used to detect self-colliding triangles of the evolving mesh. Secondly, for the topology adaptation itself, we use formulas which are derived from homology. In view of this the advantages of our algorithm are that it does not require global mesh re-parameterizations and the topology adaptation can be performed in a stable way via a rather coarse mesh.We apply our algorithm to segmentation of three-dimensional synthetic and ultrasound data.