Strictly Conservative Neural Distance Fields

Abstract

We propose a first method to generate neural unsigned or signed distance fields (SDFs) that are guaranteed to be conservative with respect to a given 3D shape. This means the true distance is never overestimated and the zero‐level set is a bounding volume for the shape. The method makes use of neural network architectures that ensure Lipschitz continuity by design in combination with a novel tailored training data selection scheme and constrained training strategy. We demonstrate that this yields both theoretical and empirical benefits over previous approaches to conservativeness (for non‐distance neural implicits), allowing for tighter approximation and additionally providing the valuable distance information.