Medial Axis Aware Learning of Signed Distance Functions

TL;DR

This paper introduces a neural network-based variational approach for accurately computing signed distance functions from point clouds, explicitly incorporating medial axis information via a phase field approximation.

Contribution

It presents a novel higher-order variational formulation that explicitly models the medial axis within a neural network framework for SDF computation.

Findings

The method achieves high accuracy in both near and global regions.

Quantitative and qualitative results outperform existing approaches.

The phase field implicitly encodes the medial axis information.

Abstract

We propose a novel variational method to compute a highly accurate global signed distance function (SDF) to a given point cloud. To this end, the jump set of the gradient of the SDF, which coincides with the medial axis of the surface, is explicitly taken into account through a higher-order variational formulation that enforces linear growth along the gradient direction away from this discontinuity set. The eikonal equation and the zero-level set of the SDF are enforced as constraints. To make this variational problem computationally tractable, a phase field approximation of Ambrosio-Tortorelli type is employed. The associated phase field function implicitly describes the medial axis. The method is implemented for surfaces represented by unoriented point clouds using neural network approximations of both the SDF and the phase field. Experiments demonstrate the method's accuracy both in the near field and globally. Quantitative and qualitative comparisons with other approaches show the advantages of the proposed method.