# Volume Rendering Digest (for NeRF)

arXiv: https://arxiv.org/abs/2209.02417 · HTML: https://mlsanity.com/paper/2209.02417/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 3 references that are in the map.
- First posted on arXiv 29 Aug 2022.

## Built on by (most cited first, 30 of 32)

- [pixelSplat: 3D Gaussian Splats from Image Pairs for Scalable Generalizable 3D Reconstruction](https://mlsanity.com/paper/2312.12337/) (2023)
- [Magic123: One Image to High-Quality 3D Object Generation Using Both 2D and 3D Diffusion Priors](https://mlsanity.com/paper/2306.17843/) (2023)
- [Human Gaussian Splatting: Real-time Rendering of Animatable Avatars](https://mlsanity.com/paper/2311.17113/) (2023)
- [Learning to Render Novel Views from Wide-Baseline Stereo Pairs](https://mlsanity.com/paper/2304.08463/) (2023)
- [RobustNeRF: Ignoring Distractors with Robust Losses](https://mlsanity.com/paper/2302.00833/) (2023)
- [GES: Generalized Exponential Splatting for Efficient Radiance Field Rendering](https://mlsanity.com/paper/2402.10128/) (2024)
- [Bayes' Rays: Uncertainty Quantification for Neural Radiance Fields](https://mlsanity.com/paper/2309.03185/) (2023)
- [Neural LiDAR Fields for Novel View Synthesis](https://mlsanity.com/paper/2305.01643/) (2023)
- [Triangle Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2505.19175/) (2025)
- [Robust e-NeRF: NeRF from Sparse & Noisy Events under Non-Uniform Motion](https://mlsanity.com/paper/2309.08596/) (2023)
- [nerf2nerf: Pairwise Registration of Neural Radiance Fields](https://mlsanity.com/paper/2211.01600/) (2022)
- [ParticleNeRF: A Particle-Based Encoding for Online Neural Radiance Fields](https://mlsanity.com/paper/2211.04041/) (2022)
- [Dynamic LiDAR Re-simulation using Compositional Neural Fields](https://mlsanity.com/paper/2312.05247/) (2023)
- [DDGS-CT: Direction-Disentangled Gaussian Splatting for Realistic Volume Rendering](https://mlsanity.com/paper/2406.02518/) (2024)
- [DReg-NeRF: Deep Registration for Neural Radiance Fields](https://mlsanity.com/paper/2308.09386/) (2023)
- [StochasticSplats: Stochastic Rasterization for Sorting-Free 3D Gaussian Splatting](https://mlsanity.com/paper/2503.24366/) (2025)
- [TrackNeRF: Bundle Adjusting NeRF from Sparse and Noisy Views via Feature Tracks](https://mlsanity.com/paper/2408.10739/) (2024)
- [DehazeNeRF: Multiple Image Haze Removal and 3D Shape Reconstruction using Neural Radiance Fields](https://mlsanity.com/paper/2303.11364/) (2023)
- [CATSplat: Context-Aware Transformer with Spatial Guidance for Generalizable 3D Gaussian Splatting from A Single-View Image](https://mlsanity.com/paper/2412.12906/) (2024)
- [BlendFields: Few-Shot Example-Driven Facial Modeling](https://mlsanity.com/paper/2305.07514/) (2023)
- [These Magic Moments: Differentiable Uncertainty Quantification of Radiance Field Models](https://mlsanity.com/paper/2503.14665/) (2025)
- [Feed-Forward 3D Scene Modeling: A Problem-Driven Perspective](https://mlsanity.com/paper/2604.14025/) (2026)
- [Reconstructive Latent-Space Neural Radiance Fields for Efficient 3D Scene Representations](https://mlsanity.com/paper/2310.17880/) (2023)
- [Mesh2NeRF: Direct Mesh Supervision for Neural Radiance Field Representation and Generation](https://mlsanity.com/paper/2403.19319/) (2024)
- [6Img-to-3D: Few-Image Large-Scale Outdoor Driving Scene Reconstruction](https://mlsanity.com/paper/2404.12378/) (2024)
- [Volumetric Surfaces: Representing Fuzzy Geometries with Layered Meshes](https://mlsanity.com/paper/2409.02482/) (2024)
- [Lagrangian Hashing for Compressed Neural Field Representations](https://mlsanity.com/paper/2409.05334/) (2024)
- [Power Foam: Unifying Real-Time Differentiable Ray Tracing and Rasterization](https://mlsanity.com/paper/2604.24994/) (2026)
- [FusedRF: Fusing Multiple Radiance Fields](https://mlsanity.com/paper/2306.04180/) (2023)
- [Neural Inverse Rendering from Propagating Light](https://mlsanity.com/paper/2506.05347/) (2025)

## Abstract (arXiv)

Neural Radiance Fields employ simple volume rendering as a way to overcome the challenges of differentiating through ray-triangle intersections by leveraging a probabilistic notion of visibility. This is achieved by assuming the scene is composed by a cloud of light-emitting particles whose density changes in space. This technical report summarizes the derivations for differentiable volume rendering. It is a condensed version of previous reports, but rewritten in the context of NeRF, and adopting its commonly used notation.