Topological Shortcut Independent Geodesic Distance and its Application

Topological shortcuts, as a special kind of model defects, have a significant impact on the computation of geodesic distance. Conventional algorithms cannot give desirable results. Therefore, a robust geodesic algorithm independent of topological shortcuts is proposed to meet requirements of intrinsic geometry analysis. During the first step, the shape diameter function of the input mesh is computed. Based on a given thickness tolerance, the initial feasible domain is determined for purpose of defining where geodesics can walk. By enforcing a dilation and erosion process, we can get a more meaningful feasible domain. In this way, it is natural to get a topological shortcut independent geodesic by restricting the paths inside the feasible domain. Experimental results show that the shortcut independent algorithm can induce a robust shape descriptor.