DiffCD: A Symmetric Differentiable Chamfer Distance for Neural Implicit Surface Fitting

TL;DR

This paper introduces DiffCD, a symmetric differentiable Chamfer distance, to improve neural implicit surface fitting by accurately capturing shape details and eliminating spurious surfaces without extra regularization.

Contribution

The paper proposes DiffCD, a novel symmetric loss function for neural implicit surface fitting, addressing limitations of one-sided Chamfer distances in existing methods.

Findings

DiffCD outperforms existing methods across various surface complexities.

It reliably recovers detailed shapes even with noisy point clouds.

Eliminates spurious surfaces without additional regularization.

Abstract

Neural implicit surfaces can be used to recover accurate 3D geometry from imperfect point clouds. In this work, we show that state-of-the-art techniques work by minimizing an approximation of a one-sided Chamfer distance. This shape metric is not symmetric, as it only ensures that the point cloud is near the surface but not vice versa. As a consequence, existing methods can produce inaccurate reconstructions with spurious surfaces. Although one approach against spurious surfaces has been widely used in the literature, we theoretically and experimentally show that it is equivalent to regularizing the surface area, resulting in over-smoothing. As a more appealing alternative, we propose DiffCD, a novel loss function corresponding to the symmetric Chamfer distance. In contrast to previous work, DiffCD also assures that the surface is near the point cloud, which eliminates spurious surfaces without the need for additional regularization. We experimentally show that DiffCD reliably recovers a high degree of shape detail, substantially outperforming existing work across varying surface complexity and noise levels. Project code is available at https://github.com/linusnie/diffcd.