# InfoNeRF: Ray Entropy Minimization for Few-Shot Neural Volume Rendering

arXiv: https://arxiv.org/abs/2112.15399 · HTML: https://mlsanity.com/paper/2112.15399/

## Key facts

- Cited by 182 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 42 references that are in the map.
- First posted on arXiv 31 Dec 2021.

## Builds on (most cited first, 23 of 23)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [pixelNeRF: Neural Radiance Fields from One or Few Images](https://mlsanity.com/paper/2012.02190/) (2020)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [PlenOctrees for Real-time Rendering of Neural Radiance Fields](https://mlsanity.com/paper/2103.14024/) (2021)
- [PIFu: Pixel-Aligned Implicit Function for High-Resolution Clothed Human Digitization](https://mlsanity.com/paper/1905.05172/) (2019)
- [Neural Scene Flow Fields for Space-Time View Synthesis of Dynamic Scenes](https://mlsanity.com/paper/2011.13084/) (2020)
- [Depth-supervised NeRF: Fewer Views and Faster Training for Free](https://mlsanity.com/paper/2107.02791/) (2021)
- [Neural Body: Implicit Neural Representations with Structured Latent Codes for Novel View Synthesis of Dynamic Humans](https://mlsanity.com/paper/2012.15838/) (2020)
- [NeRV: Neural Reflectance and Visibility Fields for Relighting and View Synthesis](https://mlsanity.com/paper/2012.03927/) (2020)
- [Putting NeRF on a Diet: Semantically Consistent Few-Shot View Synthesis](https://mlsanity.com/paper/2104.00677/) (2021)
- [Single-View View Synthesis with Multiplane Images](https://mlsanity.com/paper/2004.11364/) (2020)
- [DeepView: View Synthesis with Learned Gradient Descent](https://mlsanity.com/paper/1906.07316/) (2019)
- [NeX: Real-time View Synthesis with Neural Basis Expansion](https://mlsanity.com/paper/2103.05606/) (2021)
- [Stereo Magnification: Learning View Synthesis using Multiplane Images](https://mlsanity.com/paper/1805.09817/) (2018)
- [DeepStereo: Learning to Predict New Views from the World's Imagery](https://mlsanity.com/paper/1506.06825/) (2015)
- [View Synthesis by Appearance Flow](https://mlsanity.com/paper/1605.03557/) (2016)
- [Neural Human Performer: Learning Generalizable Radiance Fields for Human Performance Rendering](https://mlsanity.com/paper/2109.07448/) (2021)
- [NeRF--: Neural Radiance Fields Without Known Camera Parameters](https://mlsanity.com/paper/2102.07064/) (2021)
- [Learning to Synthesize a 4D RGBD Light Field from a Single Image](https://mlsanity.com/paper/1708.03292/) (2017)

## Built on by (most cited first, 30 of 182)

- [Magic123: One Image to High-Quality 3D Object Generation Using Both 2D and 3D Diffusion Priors](https://mlsanity.com/paper/2306.17843/) (2023)
- [DNGaussian: Optimizing Sparse-View 3D Gaussian Radiance Fields with Global-Local Depth Normalization](https://mlsanity.com/paper/2403.06912/) (2024)
- [SparseNeRF: Distilling Depth Ranking for Few-shot Novel View Synthesis](https://mlsanity.com/paper/2303.16196/) (2023)
- [NoPe-NeRF: Optimising Neural Radiance Field with No Pose Prior](https://mlsanity.com/paper/2212.07388/) (2022)
- [SPARF: Neural Radiance Fields from Sparse and Noisy Poses](https://mlsanity.com/paper/2211.11738/) (2022)
- [COLMAP-Free 3D Gaussian Splatting](https://mlsanity.com/paper/2312.07504/) (2023)
- [Depth-Regularized Optimization for 3D Gaussian Splatting in Few-Shot Images](https://mlsanity.com/paper/2311.13398/) (2023)
- [The Unreasonable Effectiveness of Entropy Minimization in LLM Reasoning](https://mlsanity.com/paper/2505.15134/) (2025)
- [SinNeRF: Training Neural Radiance Fields on Complex Scenes from a Single Image](https://mlsanity.com/paper/2204.00928/) (2022)
- [PF-LRM: Pose-Free Large Reconstruction Model for Joint Pose and Shape Prediction](https://mlsanity.com/paper/2311.12024/) (2023)
- [D2NeRF: Self-Supervised Decoupling of Dynamic and Static Objects from a Monocular Video](https://mlsanity.com/paper/2205.15838/) (2022)
- [CoR-GS: Sparse-View 3D Gaussian Splatting via Co-Regularization](https://mlsanity.com/paper/2405.12110/) (2024)
- [GES: Generalized Exponential Splatting for Efficient Radiance Field Rendering](https://mlsanity.com/paper/2402.10128/) (2024)
- [Fully Explicit Dynamic Gaussian Splatting](https://mlsanity.com/paper/2410.15629/) (2024)
- [Removing Objects From Neural Radiance Fields](https://mlsanity.com/paper/2212.11966/) (2022)
- [Behind the Scenes: Density Fields for Single View Reconstruction](https://mlsanity.com/paper/2301.07668/) (2023)
- [PF3plat: Pose-Free Feed-Forward 3D Gaussian Splatting](https://mlsanity.com/paper/2410.22128/) (2024)
- [BAD-Gaussians: Bundle Adjusted Deblur Gaussian Splatting](https://mlsanity.com/paper/2403.11831/) (2024)
- [Factor Fields: A Unified Framework for Neural Fields and Beyond](https://mlsanity.com/paper/2302.01226/) (2023)
- [GeCoNeRF: Few-shot Neural Radiance Fields via Geometric Consistency](https://mlsanity.com/paper/2301.10941/) (2023)
- [3D Convex Splatting: Radiance Field Rendering with 3D Smooth Convexes](https://mlsanity.com/paper/2411.14974/) (2024)
- [3D generation on ImageNet](https://mlsanity.com/paper/2303.01416/) (2023)
- [LiDAR-NeRF: Novel LiDAR View Synthesis via Neural Radiance Fields](https://mlsanity.com/paper/2304.10406/) (2023)
- [Generic 3D Diffusion Adapter Using Controlled Multi-View Editing](https://mlsanity.com/paper/2403.12032/) (2024)
- [Control3D: Towards Controllable Text-to-3D Generation](https://mlsanity.com/paper/2311.05461/) (2023)
- [PERF: Panoramic Neural Radiance Field from a Single Panorama](https://mlsanity.com/paper/2310.16831/) (2023)
- [PhyRecon: Physically Plausible Neural Scene Reconstruction](https://mlsanity.com/paper/2404.16666/) (2024)
- [SimpleNeRF: Regularizing Sparse Input Neural Radiance Fields with Simpler Solutions](https://mlsanity.com/paper/2309.03955/) (2023)
- [Robust e-NeRF: NeRF from Sparse & Noisy Events under Non-Uniform Motion](https://mlsanity.com/paper/2309.08596/) (2023)
- [ViP-NeRF: Visibility Prior for Sparse Input Neural Radiance Fields](https://mlsanity.com/paper/2305.00041/) (2023)

## Abstract (arXiv)

We present an information-theoretic regularization technique for few-shot novel view synthesis based on neural implicit representation. The proposed approach minimizes potential reconstruction inconsistency that happens due to insufficient viewpoints by imposing the entropy constraint of the density in each ray. In addition, to alleviate the potential degenerate issue when all training images are acquired from almost redundant viewpoints, we further incorporate the spatially smoothness constraint into the estimated images by restricting information gains from a pair of rays with slightly different viewpoints. The main idea of our algorithm is to make reconstructed scenes compact along individual rays and consistent across rays in the neighborhood. The proposed regularizers can be plugged into most of existing neural volume rendering techniques based on NeRF in a straightforward way. Despite its simplicity, we achieve consistently improved performance compared to existing neural view synthesis methods by large margins on multiple standard benchmarks.