$L_0$-Sampler: An $L_{0}$ Model Guided Volume Sampling for NeRF

TL;DR

This paper introduces the $L_0$-Sampler, a novel volume sampling method guided by an $L_0$ model that improves NeRF rendering accuracy by using exponential functions for better distribution approximation.

Contribution

It proposes integrating an $L_0$ model into NeRF's sampling process with piecewise exponential functions, enhancing performance without extra computational cost.

Findings

Achieves stable performance improvements in NeRF tasks.

Effectively approximates $L_0$ weight distributions along rays.

Simple implementation with minimal code changes.

Abstract

Since being proposed, Neural Radiance Fields (NeRF) have achieved great success in related tasks, mainly adopting the hierarchical volume sampling (HVS) strategy for volume rendering. However, the HVS of NeRF approximates distributions using piecewise constant functions, which provides a relatively rough estimation. Based on the observation that a well-trained weight function $w(t)$ and the $L_0$ distance between points and the surface have very high similarity, we propose $L_0$-Sampler by incorporating the $L_0$ model into $w(t)$ to guide the sampling process. Specifically, we propose to use piecewise exponential functions rather than piecewise constant functions for interpolation, which can not only approximate quasi-$L_0$ weight distributions along rays quite well but also can be easily implemented with few lines of code without additional computational burden. Stable performance improvements can be achieved by applying $L_0$-Sampler to NeRF and its related tasks like 3D reconstruction. Code is available at https://ustc3dv.github.io/L0-Sampler/ .