Quasi-Medial Distance Field (Q-MDF): A Robust Method for Approximating and Discretizing Neural Medial Axes

TL;DR

This paper introduces Quasi-Medial Distance Field (Q-MDF), an implicit method that robustly approximates and discretizes neural medial axes from noisy point clouds and meshes, improving accuracy over existing techniques.

Contribution

The paper presents a novel implicit approach using a modified double covering strategy to extract medial axes as zero level-sets of the unsigned distance field, enhancing robustness and accuracy.

Findings

Achieves higher accuracy than existing methods

Demonstrates robustness on challenging point clouds and meshes

Outperforms prior approaches in medial axis extraction

Abstract

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.