# Regularization of NeRFs using differential geometry

arXiv: https://arxiv.org/abs/2206.14938 · HTML: https://mlsanity.com/paper/2206.14938/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 43 references that are in the map.
- First posted on arXiv 29 Jun 2022.

## Builds on (most cited first, 27 of 27)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [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)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [Revisiting Unreasonable Effectiveness of Data in Deep Learning Era](https://mlsanity.com/paper/1707.02968/) (2017)
- [Neural Scene Flow Fields for Space-Time View Synthesis of Dynamic Scenes](https://mlsanity.com/paper/2011.13084/) (2020)
- [MVSNeRF: Fast Generalizable Radiance Field Reconstruction from Multi-View Stereo](https://mlsanity.com/paper/2103.15595/) (2021)
- [Depth-supervised NeRF: Fewer Views and Faster Training for Free](https://mlsanity.com/paper/2107.02791/) (2021)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [pi-GAN: Periodic Implicit Generative Adversarial Networks for 3D-Aware Image Synthesis](https://mlsanity.com/paper/2012.00926/) (2020)
- [GRAF: Generative Radiance Fields for 3D-Aware Image Synthesis](https://mlsanity.com/paper/2007.02442/) (2020)
- [Local Light Field Fusion: Practical View Synthesis with Prescriptive Sampling Guidelines](https://mlsanity.com/paper/1905.00889/) (2019)
- [RegNeRF: Regularizing Neural Radiance Fields for View Synthesis from Sparse Inputs](https://mlsanity.com/paper/2112.00724/) (2021)
- [NeRV: Neural Reflectance and Visibility Fields for Relighting and View Synthesis](https://mlsanity.com/paper/2012.03927/) (2020)
- [Non-Rigid Neural Radiance Fields: Reconstruction and Novel View Synthesis of a Dynamic Scene From Monocular Video](https://mlsanity.com/paper/2012.12247/) (2020)
- [Putting NeRF on a Diet: Semantically Consistent Few-Shot View Synthesis](https://mlsanity.com/paper/2104.00677/) (2021)
- [NeRD: Neural Reflectance Decomposition from Image Collections](https://mlsanity.com/paper/2012.03918/) (2020)
- [Dense Depth Priors for Neural Radiance Fields from Sparse Input Views](https://mlsanity.com/paper/2112.03288/) (2021)
- [State of the Art on Neural Rendering](https://mlsanity.com/paper/2004.03805/) (2020)
- [Stereo Radiance Fields (SRF): Learning View Synthesis for Sparse Views of Novel Scenes](https://mlsanity.com/paper/2104.06935/) (2021)
- [InfoNeRF: Ray Entropy Minimization for Few-Shot Neural Volume Rendering](https://mlsanity.com/paper/2112.15399/) (2021)
- [LOLNeRF: Learn from One Look](https://mlsanity.com/paper/2111.09996/) (2021)
- [Pix2NeRF: Unsupervised Conditional π-GAN for Single Image to Neural Radiance Fields Translation](https://mlsanity.com/paper/2202.13162/) (2022)
- [Sat-NeRF: Learning Multi-View Satellite Photogrammetry With Transient Objects and Shadow Modeling Using RPC Cameras](https://mlsanity.com/paper/2203.08896/) (2022)

## Built on by (most cited first, 3 of 3)

- [PlaNeRF: SVD Unsupervised 3D Plane Regularization for NeRF Large-Scale Scene Reconstruction](https://mlsanity.com/paper/2305.16914/) (2023)
- [Multiplane Prior Guided Few-Shot Aerial Scene Rendering](https://mlsanity.com/paper/2406.04961/) (2024)
- [Sharpening Neural Implicit Functions with Frequency Consolidation Priors](https://mlsanity.com/paper/2412.19720/) (2024)

## Abstract (arXiv)

Neural radiance fields, or NeRF, represent a breakthrough in the field of novel view synthesis and 3D modeling of complex scenes from multi-view image collections. Numerous recent works have shown the importance of making NeRF models more robust, by means of regularization, in order to train with possibly inconsistent and/or very sparse data. In this work, we explore how differential geometry can provide elegant regularization tools for robustly training NeRF-like models, which are modified so as to represent continuous and infinitely differentiable functions. In particular, we present a generic framework for regularizing different types of NeRFs observations to improve the performance in challenging conditions. We also show how the same formalism can also be used to natively encourage the regularity of surfaces by means of Gaussian or mean curvatures.