2024/10/23 by Jiayi Kong, Chen Zong, Kong, Jiayi +13 · 1 citation
Computer Science · #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #Graphics (cs.GR) #Neural Networks and Applications
paper · pdf · doi:10.48550/arxiv.2410.17774
openalex publication_date 2024/10/23 · openalex created_date 2024/11/13 · openalex updated_date 2026/07/28
The medial axis, a lower-dimensional descriptor that captures the extrinsic structure of a shape, plays an important role in digital geometry processing. Despite its importance, computing the medial axis transform robustly from diverse inputs, especially point clouds with defects, remains a challenging problem. In this paper, we propose a new implicit method that deviates from traditional explicit medial axis computation. Our key technical insight is that the difference between the signed distance field (SDF) and the medial field (MF) of a solid shape relates to the unsigned distance field (UDF) of the shape's medial axis. This observation allows us to formulate medial axis extraction as an implicit reconstruction problem. By employing a modified double covering strategy, we recover the medial axis as the zero level-set of the UDF. Extensive experiments demonstrate that our method achieves higher accuracy and robustness in learning compact medial axis transforms from challenging meshes and point clouds, outperforming existing approaches.