General Neural Gauge Fields

TL;DR

This paper introduces a unified framework for learning gauge transformations jointly with neural fields, enhancing 3D scene representation by preserving information and improving efficiency through an information-invariant gauge approach.

Contribution

It proposes a general paradigm for end-to-end learning of gauge transformations with neural fields, including a regularization mechanism and an information-invariant gauge transformation.

Findings

Jointly learned gauge transformations improve scene representation quality.

Information-invariant gauge transformation preserves scene details effectively.

The method achieves superior performance with reduced computation cost.

Abstract

The recent advance of neural fields, such as neural radiance fields, has significantly pushed the boundary of scene representation learning. Aiming to boost the computation efficiency and rendering quality of 3D scenes, a popular line of research maps the 3D coordinate system to another measuring system, e.g., 2D manifolds and hash tables, for modeling neural fields. The conversion of coordinate systems can be typically dubbed as \emph{gauge transformation}, which is usually a pre-defined mapping function, e.g., orthogonal projection or spatial hash function. This begs a question: can we directly learn a desired gauge transformation along with the neural field in an end-to-end manner? In this work, we extend this problem to a general paradigm with a taxonomy of discrete \& continuous cases, and develop a learning framework to jointly optimize gauge transformations and neural fields. To counter the problem that the learning of gauge transformations can collapse easily, we derive a general regularization mechanism from the principle of information conservation during the gauge transformation. To circumvent the high computation cost in gauge learning with regularization, we directly derive an information-invariant gauge transformation which allows to preserve scene information inherently and yield superior performance. Project: https://fnzhan.com/Neural-Gauge-Fields