Mass-Driven Topology-Aware Curve Skeleton Extraction from Incomplete Point Clouds

Abstract

We introduce a mass-driven curve skeleton as a curve skeleton representation for 3D point cloud data. The mass-driven curve skeleton presents geometric properties and mass distribution of a curve skeleton simultaneously. The computation of the mass-driven curve skeleton is formulated as a minimization of Wasserstein distance, with an entropic regularization term, between mass distributions of point clouds and curve skeletons. Assuming that the mass of one sampling point should be transported to a line-like structure, a topology-aware rough curve skeleton is extracted via the optimal transport plan. A Dirichlet energy regularization term is then used to obtain a smooth curve skeleton via geometric optimization. Given that rough curve skeleton extraction does not depend on complete point clouds, our algorithm can be directly applied to curve skeleton extraction from incomplete point clouds. We demonstrate that a mass-driven curve skeleton can be directly applied to an unoriented raw point scan with significant noise, outliers and large areas of missing data. In comparison with state-of-the-art methods on curve skeleton extraction, the performance of the proposed mass-driven curve skeleton is more robust in terms of extracting a correct topology.