Towards Better Gradient Consistency for Neural Signed Distance Functions
  via Level Set Alignment
Baorui Ma Junsheng Zhou Yu-Shen Liu Zhizhong Han
Neural signed distance functions (SDFs) have shown remarkable capability in
representing geometry with details. However, without signed distance
supervision, it is still a challenge to infer SDFs from point clouds or
multi-view images using neural networks. In this paper, we claim that gradient
consistency in the field, indicated by the parallelism of level sets, is the
key factor affecting the inference accuracy. Hence, we propose a level set
alignment loss to evaluate the parallelism of level sets, which can be
minimized to achieve better gradient consistency. Our novelty lies in that we
can align all level sets to the zero level set by constraining gradients at
queries and their projections on the zero level set in an adaptive way. Our
insight is to propagate the zero level set to everywhere in the field through
consistent gradients to eliminate uncertainty in the field that is caused by
the discreteness of 3D point clouds or the lack of observations from multi-view
images. Our proposed loss is a general term which can be used upon different
methods to infer SDFs from 3D point clouds and multi-view images. Our numerical
and visual comparisons demonstrate that our loss can significantly improve the
accuracy of SDFs inferred from point clouds or multi-view images under various
benchmarks. Code and data are available at
https://github.com/mabaorui/TowardsBetterGradient .