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.

翻译：中轴是一种捕捉形状外部结构的低维描述符，在数字几何处理中扮演着重要角色。尽管其重要性不言而喻，从多样化的输入（尤其是有缺陷的点云）中鲁棒地计算中轴变换，仍然是一个具有挑战性的问题。本文提出了一种新的隐式方法，该方法有别于传统的显式中轴计算。我们的核心技术见解是：实体形状的有符号距离场（SDF）与其中轴场（MF）之间的差异，与该形状中轴的无符号距离场（UDF）相关。这一观察使我们能够将中轴提取表述为一个隐式重建问题。通过采用一种改进的双覆盖策略，我们将中轴恢复为UDF的零水平集。大量实验表明，我们的方法在从具有挑战性的网格和点云中学习紧凑的中轴变换时，实现了更高的精度和鲁棒性，优于现有方法。