Gradient Distance Function

TL;DR

Gradient Distance Functions (GDFs) improve the representation of non-watertight surfaces in deep learning by being differentiable at the surface, enabling better 3D shape modeling and reconstruction.

Contribution

This work introduces GDFs, a novel differentiable function that accurately represents open surfaces and enhances learning stability over traditional UDFs.

Findings

GDFs outperform UDFs in representing open surfaces.

GDFs enable more stable and accurate 3D reconstructions.

Effective across multiple datasets and network architectures.

Abstract

Unsigned Distance Functions (UDFs) can be used to represent non-watertight surfaces in a deep learning framework. However, UDFs tend to be brittle and difficult to learn, in part because the surface is located exactly where the UDF is non-differentiable. In this work, we show that Gradient Distance Functions (GDFs) can remedy this by being differentiable at the surface while still being able to represent open surfaces. This is done by associating to each 3D point a 3D vector whose norm is taken to be the unsigned distance to the surface and whose orientation is taken to be the direction towards the closest surface point. We demonstrate the effectiveness of GDFs on ShapeNet Car, Multi-Garment, and 3D-Scene datasets with both single-shape reconstruction networks or categorical auto-decoders.