Learning a More Continuous Zero Level Set in Unsigned Distance Fields through Level Set Projection

TL;DR

This paper introduces a novel level set projection method to learn more continuous zero level sets in unsigned distance functions, improving surface reconstruction and other 3D shape tasks.

Contribution

It proposes a level set projection technique that guides the learning of zero level sets using smoother non-zero level sets, enhancing the continuity of UDFs.

Findings

Improved surface reconstruction quality on point clouds and scans.

Enhanced performance in unsupervised point cloud upsampling.

Better normal estimation accuracy using the learned UDF.

Abstract

Latest methods represent shapes with open surfaces using unsigned distance functions (UDFs). They train neural networks to learn UDFs and reconstruct surfaces with the gradients around the zero level set of the UDF. However, the differential networks struggle from learning the zero level set where the UDF is not differentiable, which leads to large errors on unsigned distances and gradients around the zero level set, resulting in highly fragmented and discontinuous surfaces. To resolve this problem, we propose to learn a more continuous zero level set in UDFs with level set projections. Our insight is to guide the learning of zero level set using the rest non-zero level sets via a projection procedure. Our idea is inspired from the observations that the non-zero level sets are much smoother and more continuous than the zero level set. We pull the non-zero level sets onto the zero level set with gradient constraints which align gradients over different level sets and correct unsigned distance errors on the zero level set, leading to a smoother and more continuous unsigned distance field. We conduct comprehensive experiments in surface reconstruction for point clouds, real scans or depth maps, and further explore the performance in unsupervised point cloud upsampling and unsupervised point normal estimation with the learned UDF, which demonstrate our non-trivial improvements over the state-of-the-art methods. Code is available at https://github.com/junshengzhou/LevelSetUDF .