PEPS: Positional Encoding Projected Sampling -- Extended

TL;DR

This paper introduces PEPS, a novel approach to positional encoding in neural representations that decomposes coordinate projections into meaningful points, improving efficiency and performance across various applications.

Contribution

It proposes a new method for learned positional encoding using point-based decompositions, outperforming existing techniques with fewer parameters.

Findings

Outperforms current state-of-the-art methods in image representation, texture compression, and signed distance functions.

Often requires 25% fewer parameters for similar reconstruction or rendering quality.

Demonstrates the effectiveness of decomposing positional encoding into meaningful points.

Abstract

Implicit neural representations (INRs) are increasingly being used as tools to map coordinates to signals, encompassing applications from neural fields to texture compression, shape representations, and beyond. Most INR methods are based on using high-dimensional projections of the initial coordinates through encoders such as grid or positional encoding. Nevertheless, positional encoding is often insufficient and grids, as we show in this paper, require high resolution for being able to learn. In this paper, we demonstrate that positional encoding can be used not only as a high-dimensional embedding but also decomposed as a series of meaningful points. We propose the Positional Encoding Projected Sampling, where we treat the projection of the original coordinate at each frequency as a point of interest. We describe the motion of each point with respect to the frequencies and show that it follows a unique pattern. Finally, we use the unique motion of each point as a basis decomposition for doing learned positional encoding using grids. We prove, using three competitive applications; image representation, texture compression, and signed distance function; that the proposed approach outperforms the current state of the art methods, and often requires 25\% less parameters for equivalent reconstruction error or rendering.