Sobolev Training for Implicit Neural Representations with Approximated Image Derivatives

TL;DR

This paper introduces Sobolev training for implicit neural representations, incorporating approximated image derivatives to enhance data efficiency and generalization in image regression and inverse rendering tasks.

Contribution

It proposes a novel training paradigm that encodes image derivatives in INRs using finite differences, improving their performance over traditional methods.

Findings

Enhanced data-efficiency in INRs

Improved generalization capabilities

Effective in image regression and inverse rendering

Abstract

Recently, Implicit Neural Representations (INRs) parameterized by neural networks have emerged as a powerful and promising tool to represent different kinds of signals due to its continuous, differentiable properties, showing superiorities to classical discretized representations. However, the training of neural networks for INRs only utilizes input-output pairs, and the derivatives of the target output with respect to the input, which can be accessed in some cases, are usually ignored. In this paper, we propose a training paradigm for INRs whose target output is image pixels, to encode image derivatives in addition to image values in the neural network. Specifically, we use finite differences to approximate image derivatives. We show how the training paradigm can be leveraged to solve typical INRs problems, i.e., image regression and inverse rendering, and demonstrate this training paradigm can improve the data-efficiency and generalization capabilities of INRs. The code of our method is available at \url{https://github.com/megvii-research/Sobolev_INRs}.