Beyond Positional Encoding: A 5D Spatio-Directional Hash Encoding

TL;DR

This paper introduces a novel 5D spatio-directional hash encoding that improves the representation of high-frequency signals in space and direction, enhancing neural path guiding performance.

Contribution

It presents a new hierarchical geodesic grid-based directional encoding and a 5D spatio-directional encoding that outperform existing hash-based methods.

Findings

Outperforms other hash-based encodings in experiments.

Achieves up to 2x variance reduction in neural path guiding.

Supports all-frequency signals in space and direction.

Abstract

In this work, we propose a new spatio-directional neural encoding that is compact and efficient, and supports all-frequency signals in both space and direction. Current learnable encodings focus on Cartesian orthonormal spaces, which have been shown to be useful for representing high-frequency signals in the spatial domain. However, directly applying these encodings in the directional domain results in distortions, singularities, and discontinuities. As a result, most related works have used more traditional encodings for the directional domain, which lack the expressivity of learnable neural encodings. We address this by proposing a new angular encoding that generalizes the hash-grid approach from proach from M\"uller et al. [2022] to the directional domain by encoding directions using a hierarchical geodesic grid. Each vertex in the geodesic grid stores a learnable latent parameter, which is used to feed a neural network. Armed with this directional encoding, we propose a five-dimensional encoding for spatio-directional signals. We demonstrate that both encodings significantly outperform other hash-based alternatives. We apply our five-dimensional encoding in the context of neural path guiding, outperforming the state of the art by up to a factor of 2 in terms of variance reduction for the same number of samples.