Distance functions and geodesics on points clouds

摘要: Abstract : An algorithm for computing intrinsic distance functions and geodesics on sub-manifolds vector r(sup d) given by point clouds is introduced in this paper. The basic idea that, as shown paper general co-dimension can be accurately approximated the extrinsic Euclidean ones computed a thin offset band surrounding manifold. This permits use of computationally optimal algorithms Cartesian grids. We then these algorithms, modified to deal with spaces boundaries, obtain also case d), approach. For clouds. constructed without need explicitly find underlying manifold, thereby while skipping manifold reconstruction step. representing noisy samples sub-manifold space studied well. All theoretical results are presented. together experimental examples, comparisons graph-based algorithms.