# L0-Sampler: An L0 Model Guided Volume Sampling for NeRF

arXiv: https://arxiv.org/abs/2311.07044 · HTML: https://mlsanity.com/paper/2311.07044/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 51 of its 69 references that are in the map.
- First posted on arXiv 13 Nov 2023.

## Builds on (most cited first, 30 of 51)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [pixelNeRF: Neural Radiance Fields from One or Few Images](https://mlsanity.com/paper/2012.02190/) (2020)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [Direct Voxel Grid Optimization: Super-fast Convergence for Radiance Fields Reconstruction](https://mlsanity.com/paper/2111.11215/) (2021)
- [PlenOctrees for Real-time Rendering of Neural Radiance Fields](https://mlsanity.com/paper/2103.14024/) (2021)
- [NeRF++: Analyzing and Improving Neural Radiance Fields](https://mlsanity.com/paper/2010.07492/) (2020)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervision](https://mlsanity.com/paper/1912.07372/) (2019)
- [Local Light Field Fusion: Practical View Synthesis with Prescriptive Sampling Guidelines](https://mlsanity.com/paper/1905.00889/) (2019)
- [UNISURF: Unifying Neural Implicit Surfaces and Radiance Fields for Multi-View Reconstruction](https://mlsanity.com/paper/2104.10078/) (2021)
- [Nerfstudio: A Modular Framework for Neural Radiance Field Development](https://mlsanity.com/paper/2302.04264/) (2023)
- [Point-NeRF: Point-based Neural Radiance Fields](https://mlsanity.com/paper/2201.08845/) (2022)
- [BlendedMVS: A Large-scale Dataset for Generalized Multi-view Stereo Networks](https://mlsanity.com/paper/1911.10127/) (2019)
- [Non-Rigid Neural Radiance Fields: Reconstruction and Novel View Synthesis of a Dynamic Scene From Monocular Video](https://mlsanity.com/paper/2012.12247/) (2020)
- [Making Convolutional Networks Shift-Invariant Again](https://mlsanity.com/paper/1904.11486/) (2019)
- [AD-NeRF: Audio Driven Neural Radiance Fields for Talking Head Synthesis](https://mlsanity.com/paper/2103.11078/) (2021)
- [Light Field Networks: Neural Scene Representations with Single-Evaluation Rendering](https://mlsanity.com/paper/2106.02634/) (2021)
- [Neural Radiance Flow for 4D View Synthesis and Video Processing](https://mlsanity.com/paper/2012.09790/) (2020)
- [DONeRF: Towards Real-Time Rendering of Compact Neural Radiance Fields using Depth Oracle Networks](https://mlsanity.com/paper/2103.03231/) (2021)
- [HeadNeRF: A Real-time NeRF-based Parametric Head Model](https://mlsanity.com/paper/2112.05637/) (2021)
- [AutoInt: Automatic Integration for Fast Neural Volume Rendering](https://mlsanity.com/paper/2012.01714/) (2020)

## Built on by (most cited first, 4 of 4)

- [VRP-UDF: Towards Unbiased Learning of Unsigned Distance Functions from Multi-view Images with Volume Rendering Priors](https://mlsanity.com/paper/2407.16396/) (2024)
- [GL-NeRF: Gauss-Laguerre Quadrature Enables Training-Free NeRF Acceleration](https://mlsanity.com/paper/2410.19831/) (2024)
- [NERFIFY: A Multi-Agent Framework for Turning NeRF Papers into Code](https://mlsanity.com/paper/2603.00805/) (2026)
- [Fine-detailed Neural Indoor Scene Reconstruction using multi-level importance sampling and multi-view consistency](https://mlsanity.com/paper/2410.07597/) (2024)

## Abstract (arXiv)

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 L0 distance between points and the surface have very high similarity, we propose L0-Sampler by incorporating the L0 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-L0 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 L0-Sampler to NeRF and its related tasks like 3D reconstruction. Code is available at https://ustc3dv.github.io/L0-Sampler/ .