Variational surface reconstruction based on Delaunay triangulation and graph cut

A novel method for surface reconstruction from an unorganized point set is presented. An energy functional based on a weighted minimal surface model is proposed for surface reconstruction, which is efficiently minimized by graph cut methods. By solving the minimization problem on the graph dual to a Delaunaybased tetrahedral mesh, the advantages of explicit and implicit methods for surface reconstruction are well integrated. A triangular surface mesh homeomorphic to the original surface can be extracted directly from the tetrahedral mesh provided a sufficient sampling density exists. Difficult cases involving undersampling, non-uniformity, noises and topological complexities can be handled effectively as well. Furthermore, for the first time, multi-phase surface reconstruction is realized based on the graph cut methods. Various examples are included for demonstrating the efficiency and effectiveness of the proposed method. Copyright 2010 John Wiley & Sons, Ltd.