用隐式方法从点云中更准确地提取形状中轴线。
Quasi-Medial Distance Field (Q-MDF): A Robust Method for Approximating and Discretizing Neural Medial Axes
- 通过SDF与MF的差异关系，将中轴提取转为隐式重建问题。
- 在带缺陷点云上比现有方法更准、更鲁棒，精度显著提升。
- 适合需要稳定中轴线的几何处理任务，如3D建模与分析。
中轴线作为描述形状外在结构的低维表示，在数字几何处理中具有重要作用。然而，从多样输入（尤其是有缺陷的点云）中稳健计算中轴变换仍是难题。本文提出一种新型隐式方法，突破传统显式中轴计算范式。核心洞察在于：实体形状的符号距离场（SDF）与中轴场（MF）之差，与中轴的无符号距离场（UDF）相关。基于此，我们将中轴提取建模为隐式重构问题。通过改进的双重覆盖策略，将中轴恢复为UDF的零等值面。大量实验表明，该方法在从挑战性网格和点云中学习紧凑中轴变换时，精度与鲁棒性均优于现有方法。
原文摘要 · Abstract (English)
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.
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