RBF-MAT: Computing medial axis transform from point clouds by optimizing radial basis functions

Abstract

In this paper, we present a simple yet effective method RBF-MAT, for computing medial axis transform (MAT) from point cloud using radial basis functions (RBFs), where the surface is represented as the zero-level set of an interpolating function composed of a linear combination of RBFs. Firstly, we propose a new strategy for selecting the initial medial spheres based on the Voronoi vertices computed from the input points while preserving necessary geometric characteristics. Then the centers and radii of the generated medial spheres are iteratively optimized by minimizing the RBF-based surface reconstruction error. Additionally, the connectivity of the refined medial spheres is constructed as the dual of the restricted power diagram for these spheres. Experimental results across diverse 3D shapes demonstrate our method's efficacy in capturing global structural attributes and local geometric intricacies, with our connectivity approach surpassing existing methods. Besides, the experimental results show that the MATs computed with our method better approximate the point cloud surface than state-of-the-art methods.