Improved Locally Adaptive Sampling Criterion for Topology Preserving Reconstruction of Multiple Regions

Abstract

Volume based digitization processes often deal with non-manifold shapes. Even though many reconstruction algorithms have been proposed for non-manifold surfaces, they usually don’t preserve topological properties. Only recently, methods were presented which—given a finite set of surface sample points—result in a mesh representation of the original boundary preserving all or certain neighbourhood relations, even if the sampling is sparse and highly noise corrupted. We show that the required sampling conditions of the algorithm called “refinement reduction” limit the guaranteed correctness of the outcome to a small class of shapes. We define new locally adaptive sampling conditions that depend on our new pruned medial axis and finally prove without any restriction on shapes that under these new conditions, the result of “refinement reduction” corresponds to a superset of a topologically equivalent mesh.