Lagrangian Hashing for Compressed Neural Field Representations

TL;DR

Lagrangian Hashing combines point-based and grid-based neural field representations to enable more compact signal reconstruction without quality loss, improving efficiency in neural rendering tasks.

Contribution

It introduces a novel point-based hierarchical hash table representation with a Gaussian influence field, enhancing neural field compression.

Findings

Allows more compact neural field representations

Maintains high-quality signal reconstruction

Integrates Gaussian influence into hash tables

Abstract

We present Lagrangian Hashing, a representation for neural fields combining the characteristics of fast training NeRF methods that rely on Eulerian grids (i.e.~InstantNGP), with those that employ points equipped with features as a way to represent information (e.g. 3D Gaussian Splatting or PointNeRF). We achieve this by incorporating a point-based representation into the high-resolution layers of the hierarchical hash tables of an InstantNGP representation. As our points are equipped with a field of influence, our representation can be interpreted as a mixture of Gaussians stored within the hash table. We propose a loss that encourages the movement of our Gaussians towards regions that require more representation budget to be sufficiently well represented. Our main finding is that our representation allows the reconstruction of signals using a more compact representation without compromising quality.