# AutoInt: Automatic Integration for Fast Neural Volume Rendering

arXiv: https://arxiv.org/abs/2012.01714 · HTML: https://mlsanity.com/paper/2012.01714/

## Key facts

- Cited by 204 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Dec 2020.

## Built on by (most cited first, 30 of 204)

- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [Efficient Geometry-aware 3D Generative Adversarial Networks](https://mlsanity.com/paper/2112.07945/) (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)
- [KiloNeRF: Speeding up Neural Radiance Fields with Thousands of Tiny MLPs](https://mlsanity.com/paper/2103.13744/) (2021)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [FastNeRF: High-Fidelity Neural Rendering at 200FPS](https://mlsanity.com/paper/2103.10380/) (2021)
- [Advances in Neural Rendering](https://mlsanity.com/paper/2111.05849/) (2021)
- [Fast Dynamic Radiance Fields with Time-Aware Neural Voxels](https://mlsanity.com/paper/2205.15285/) (2022)
- [Light Field Networks: Neural Scene Representations with Single-Evaluation Rendering](https://mlsanity.com/paper/2106.02634/) (2021)
- [3D Neural Field Generation using Triplane Diffusion](https://mlsanity.com/paper/2211.16677/) (2022)
- [SparseNeRF: Distilling Depth Ranking for Few-shot Novel View Synthesis](https://mlsanity.com/paper/2303.16196/) (2023)
- [DONeRF: Towards Real-Time Rendering of Compact Neural Radiance Fields using Depth Oracle Networks](https://mlsanity.com/paper/2103.03231/) (2021)
- [Gaussian-Flow: 4D Reconstruction with Dynamic 3D Gaussian Particle](https://mlsanity.com/paper/2312.03431/) (2023)
- [VR-GS: A Physical Dynamics-Aware Interactive Gaussian Splatting System in Virtual Reality](https://mlsanity.com/paper/2401.16663/) (2024)
- [HyperReel: High-Fidelity 6-DoF Video with Ray-Conditioned Sampling](https://mlsanity.com/paper/2301.02238/) (2023)
- [Fourier PlenOctrees for Dynamic Radiance Field Rendering in Real-time](https://mlsanity.com/paper/2202.08614/) (2022)
- [Segment Any 3D Gaussians](https://mlsanity.com/paper/2312.00860/) (2023)
- [NeRF: Neural Radiance Field in 3D Vision: A Comprehensive Review (Updated Post-Gaussian Splatting)](https://mlsanity.com/paper/2210.00379/) (2022)
- [NeRFPlayer: A Streamable Dynamic Scene Representation with Decomposed Neural Radiance Fields](https://mlsanity.com/paper/2210.15947/) (2022)
- [BACON: Band-limited Coordinate Networks for Multiscale Scene Representation](https://mlsanity.com/paper/2112.04645/) (2021)
- [Tri-MipRF: Tri-Mip Representation for Efficient Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2307.11335/) (2023)
- [D2NeRF: Self-Supervised Decoupling of Dynamic and Static Objects from a Monocular Video](https://mlsanity.com/paper/2205.15838/) (2022)
- [Mixed Neural Voxels for Fast Multi-view Video Synthesis](https://mlsanity.com/paper/2212.00190/) (2022)
- [NeRF-Art: Text-Driven Neural Radiance Fields Stylization](https://mlsanity.com/paper/2212.08070/) (2022)
- [NeSF: Neural Semantic Fields for Generalizable Semantic Segmentation of 3D Scenes](https://mlsanity.com/paper/2111.13260/) (2021)
- [EfficientNeRF: Efficient Neural Radiance Fields](https://mlsanity.com/paper/2206.00878/) (2022)
- [Light Field Neural Rendering](https://mlsanity.com/paper/2112.09687/) (2021)
- [Neural Lumigraph Rendering](https://mlsanity.com/paper/2103.11571/) (2021)
- [Generative Neural Articulated Radiance Fields](https://mlsanity.com/paper/2206.14314/) (2022)

## Abstract (arXiv)

Numerical integration is a foundational technique in scientific computing and is at the core of many computer vision applications. Among these applications, neural volume rendering has recently been proposed as a new paradigm for view synthesis, achieving photorealistic image quality. However, a fundamental obstacle to making these methods practical is the extreme computational and memory requirements caused by the required volume integrations along the rendered rays during training and inference. Millions of rays, each requiring hundreds of forward passes through a neural network are needed to approximate those integrations with Monte Carlo sampling. Here, we propose automatic integration, a new framework for learning efficient, closed-form solutions to integrals using coordinate-based neural networks. For training, we instantiate the computational graph corresponding to the derivative of the network. The graph is fitted to the signal to integrate. After optimization, we reassemble the graph to obtain a network that represents the antiderivative. By the fundamental theorem of calculus, this enables the calculation of any definite integral in two evaluations of the network. Applying this approach to neural rendering, we improve a tradeoff between rendering speed and image quality: improving render times by greater than 10 times with a tradeoff of slightly reduced image quality.