Grids Often Outperform Implicit Neural Representation at Compressing Dense Signals

TL;DR

This paper compares implicit neural representations and grid-based methods for compressing dense signals, finding grids often outperform INRs in speed and quality except for specific binary signal tasks.

Contribution

It provides a comprehensive analysis of INR and grid representations across various signals and tasks, highlighting the conditions where each method excels.

Findings

Grids train faster and achieve higher quality than INRs for most tasks.

INRs outperform grids mainly on binary signals like shape contours.

Performance varies significantly with signal type, bandwidth, and model size.

Abstract

Implicit Neural Representations (INRs) have recently shown impressive results, but their fundamental capacity, implicit biases, and scaling behavior remain poorly understood. We investigate the performance of diverse INRs across a suite of 2D and 3D real and synthetic signals with varying effective bandwidth, as well as both overfitting and generalization tasks including tomography, super-resolution, and denoising. By stratifying performance according to model size as well as signal type and bandwidth, our results shed light on how different INR and grid representations allocate their capacity. We find that, for most tasks and signals, a simple regularized grid with interpolation trains faster and to higher quality than any INR with the same number of parameters. We also find limited settings--namely fitting binary signals such as shape contours--where INRs outperform grids, to guide future development and use of INRs towards the most advantageous applications.