SALD: Sign Agnostic Learning with Derivatives

TL;DR

SALD introduces a novel sign-agnostic learning method that incorporates derivatives into the loss function, enabling high-quality implicit shape representations from raw 3D data with improved sample efficiency and minimal length solutions.

Contribution

The paper extends sign-agnostic learning to include derivatives, resulting in better shape fitting and theoretical guarantees of minimal length solutions.

Findings

Achieves state-of-the-art results on ShapeNet and D-Faust datasets.

Demonstrates improved shape fitting with fewer samples due to derivative incorporation.

Proves minimal length property holds for SALD, ensuring optimal solutions.

Abstract

Learning 3D geometry directly from raw data, such as point clouds, triangle soups, or unoriented meshes is still a challenging task that feeds many downstream computer vision and graphics applications. In this paper, we introduce SALD: a method for learning implicit neural representations of shapes directly from raw data. We generalize sign agnostic learning (SAL) to include derivatives: given an unsigned distance function to the input raw data, we advocate a novel sign agnostic regression loss, incorporating both pointwise values and gradients of the unsigned distance function. Optimizing this loss leads to a signed implicit function solution, the zero level set of which is a high quality and valid manifold approximation to the input 3D data. The motivation behind SALD is that incorporating derivatives in a regression loss leads to a lower sample complexity, and consequently better fitting. In addition, we prove that SAL enjoys a minimal length property in 2D, favoring minimal length solutions. More importantly, we are able to show that this property still holds for SALD, i.e., with derivatives included. We demonstrate the efficacy of SALD for shape space learning on two challenging datasets: ShapeNet that contains inconsistent orientation and non-manifold meshes, and D-Faust that contains raw 3D scans (triangle soups). On both these datasets, we present state-of-the-art results.