Geometric Neural Process Fields

TL;DR

This paper introduces Geometric Neural Process Fields, a probabilistic framework that enhances neural radiance fields' ability to generalize to new signals by explicitly modeling uncertainty and incorporating geometric structure.

Contribution

We propose G-NPF, a novel probabilistic approach that combines geometric bases with hierarchical latent variables to improve NeF generalization and uncertainty estimation.

Findings

G-NPF outperforms existing methods in novel-view synthesis.

It effectively captures uncertainty in 3D scene reconstructions.

The hierarchical model improves generalization to unseen signals.

Abstract

This paper addresses the challenge of Neural Field (NeF) generalization, where models must efficiently adapt to new signals given only a few observations. To tackle this, we propose Geometric Neural Process Fields (G-NPF), a probabilistic framework for neural radiance fields that explicitly captures uncertainty. We formulate NeF generalization as a probabilistic problem, enabling direct inference of NeF function distributions from limited context observations. To incorporate structural inductive biases, we introduce a set of geometric bases that encode spatial structure and facilitate the inference of NeF function distributions. Building on these bases, we design a hierarchical latent variable model, allowing G-NPF to integrate structural information across multiple spatial levels and effectively parameterize INR functions. This hierarchical approach improves generalization to novel scenes and unseen signals. Experiments on novel-view synthesis for 3D scenes, as well as 2D image and 1D signal regression, demonstrate the effectiveness of our method in capturing uncertainty and leveraging structural information for improved generalization.