Variational surface reconstruction based on Delaunay triangulation and graph cut

Abstract

Abstract 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 Delaunay‐based 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.