Quasi-Medial Distance Field (Q-MDF): A Robust Method for Approximating and Discretizing Neural Medial Axis
This addresses a significant problem in digital geometry processing for applications requiring shape analysis, though it appears incremental as it builds on implicit reconstruction techniques.
The paper tackled the challenge of robustly computing the medial axis transform from inputs like point clouds with defects by proposing an implicit method based on the difference between signed and medial distance fields, resulting in enhanced accuracy and robustness compared to existing methods.
The medial axis, a lower-dimensional shape descriptor, plays an important role in the field of digital geometry processing. Despite its importance, robust computation of the medial axis transform from diverse inputs, especially point clouds with defects, remains a significant challenge. In this paper, we tackle the challenge by proposing a new implicit method that diverges from mainstream explicit medial axis computation techniques. Our key technical insight is the difference between the signed distance field (SDF) and the medial field (MF) of a solid shape is the unsigned distance field (UDF) of the shape's medial axis. This allows for formulating medial axis computation as an implicit reconstruction problem. Utilizing a modified double covering method, we extract the medial axis as the zero level-set of the UDF. Extensive experiments show that our method has enhanced accuracy and robustness in learning compact medial axis transform from thorny meshes and point clouds compared to existing methods.