# Rethinking Directional Integration in Neural Radiance Fields

arXiv: https://arxiv.org/abs/2311.16504 · HTML: https://mlsanity.com/paper/2311.16504/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 40 references that are in the map.
- First posted on arXiv 28 Nov 2023.

## Builds on (most cited first, 19 of 19)

- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [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)
- [Zip-NeRF: Anti-Aliased Grid-Based Neural Radiance Fields](https://mlsanity.com/paper/2304.06706/) (2023)
- [UNISURF: Unifying Neural Implicit Surfaces and Radiance Fields for Multi-View Reconstruction](https://mlsanity.com/paper/2104.10078/) (2021)
- [Ref-NeRF: Structured View-Dependent Appearance for Neural Radiance Fields](https://mlsanity.com/paper/2112.03907/) (2021)
- [Baking Neural Radiance Fields for Real-Time View Synthesis](https://mlsanity.com/paper/2103.14645/) (2021)
- [PhySG: Inverse Rendering with Spherical Gaussians for Physics-based Material Editing and Relighting](https://mlsanity.com/paper/2104.00674/) (2021)
- [Light Field Networks: Neural Scene Representations with Single-Evaluation Rendering](https://mlsanity.com/paper/2106.02634/) (2021)
- [MobileNeRF: Exploiting the Polygon Rasterization Pipeline for Efficient Neural Field Rendering on Mobile Architectures](https://mlsanity.com/paper/2208.00277/) (2022)
- [MERF: Memory-Efficient Radiance Fields for Real-time View Synthesis in Unbounded Scenes](https://mlsanity.com/paper/2302.12249/) (2023)
- [NeX: Real-time View Synthesis with Neural Basis Expansion](https://mlsanity.com/paper/2103.05606/) (2021)
- [AutoInt: Automatic Integration for Fast Neural Volume Rendering](https://mlsanity.com/paper/2012.01714/) (2020)
- [Learning-Based View Synthesis for Light Field Cameras](https://mlsanity.com/paper/1609.02974/) (2016)
- [Light Field Neural Rendering](https://mlsanity.com/paper/2112.09687/) (2021)
- [Extreme View Synthesis](https://mlsanity.com/paper/1812.04777/) (2018)
- [Learning to Synthesize a 4D RGBD Light Field from a Single Image](https://mlsanity.com/paper/1708.03292/) (2017)
- [Learning Neural Light Fields with Ray-Space Embedding Networks](https://mlsanity.com/paper/2112.01523/) (2021)
- [IGNOR: Image-guided Neural Object Rendering](https://mlsanity.com/paper/1811.10720/) (2018)

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

- [NERFIFY: A Multi-Agent Framework for Turning NeRF Papers into Code](https://mlsanity.com/paper/2603.00805/) (2026)

## Abstract (arXiv)

Recent works use the Neural radiance field (NeRF) to perform multi-view 3D reconstruction, providing a significant leap in rendering photorealistic scenes. However, despite its efficacy, NeRF exhibits limited capability of learning view-dependent effects compared to light field rendering or image-based view synthesis. To that end, we introduce a modification to the NeRF rendering equation which is as simple as a few lines of code change for any NeRF variations, while greatly improving the rendering quality of view-dependent effects. By swapping the integration operator and the direction decoder network, we only integrate the positional features along the ray and move the directional terms out of the integration, resulting in a disentanglement of the view-dependent and independent components. The modified equation is equivalent to the classical volumetric rendering in ideal cases on object surfaces with Dirac densities. Furthermore, we prove that with the errors caused by network approximation and numerical integration, our rendering equation exhibits better convergence properties with lower error accumulations compared to the classical NeRF. We also show that the modified equation can be interpreted as light field rendering with learned ray embeddings. Experiments on different NeRF variations show consistent improvements in the quality of view-dependent effects with our simple modification.