# Alpha Invariance: On Inverse Scaling Between Distance and Volume Density in Neural Radiance Fields

arXiv: https://arxiv.org/abs/2404.02155 · HTML: https://mlsanity.com/paper/2404.02155/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 38 references that are in the map.
- First posted on arXiv 2 Apr 2024.

## Builds on (most cited first, 25 of 25)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [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)
- [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)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [4D Gaussian Splatting for Real-Time Dynamic Scene Rendering](https://mlsanity.com/paper/2310.08528/) (2023)
- [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)
- [Dynamic 3D Gaussians: Tracking by Persistent Dynamic View Synthesis](https://mlsanity.com/paper/2308.09713/) (2023)
- [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)
- [Zip-NeRF: Anti-Aliased Grid-Based Neural Radiance Fields](https://mlsanity.com/paper/2304.06706/) (2023)
- [Nerfstudio: A Modular Framework for Neural Radiance Field Development](https://mlsanity.com/paper/2302.04264/) (2023)
- [HexPlane: A Fast Representation for Dynamic Scenes](https://mlsanity.com/paper/2301.09632/) (2023)
- [MERF: Memory-Efficient Radiance Fields for Real-time View Synthesis in Unbounded Scenes](https://mlsanity.com/paper/2302.12249/) (2023)
- [Pushing the Boundaries of View Extrapolation with Multiplane Images](https://mlsanity.com/paper/1905.00413/) (2019)
- [Progressively Optimized Local Radiance Fields for Robust View Synthesis](https://mlsanity.com/paper/2303.13791/) (2023)
- [Normalization Techniques in Training DNNs: Methodology, Analysis and Application](https://mlsanity.com/paper/2009.12836/) (2020)
- [Approximate Differentiable Rendering with Algebraic Surfaces](https://mlsanity.com/paper/2207.10606/) (2022)
- [Flexible Techniques for Differentiable Rendering with 3D Gaussians](https://mlsanity.com/paper/2308.14737/) (2023)

## Built on by (most cited first, 1 of 1)

- [Rebenchmarking Unsupervised Monocular 3D Occupancy Prediction](https://mlsanity.com/paper/2602.06488/) (2026)

## Abstract (arXiv)

Scale-ambiguity in 3D scene dimensions leads to magnitude-ambiguity of volumetric densities in neural radiance fields, i.e., the densities double when scene size is halved, and vice versa. We call this property alpha invariance. For NeRFs to better maintain alpha invariance, we recommend 1) parameterizing both distance and volume densities in log space, and 2) a discretization-agnostic initialization strategy to guarantee high ray transmittance. We revisit a few popular radiance field models and find that these systems use various heuristics to deal with issues arising from scene scaling. We test their behaviors and show our recipe to be more robust.