# HyperNeRF: A Higher-Dimensional Representation for Topologically Varying Neural Radiance Fields

arXiv: https://arxiv.org/abs/2106.13228 · HTML: https://mlsanity.com/paper/2106.13228/

## Key facts

- Cited by 214 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 51 references that are in the map.
- First posted on arXiv 24 Jun 2021.

## Builds on (most cited first, 30 of 31)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [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)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [Neural Scene Flow Fields for Space-Time View Synthesis of Dynamic Scenes](https://mlsanity.com/paper/2011.13084/) (2020)
- [Face2Face: Real-time Face Capture and Reenactment of RGB Videos](https://mlsanity.com/paper/2007.14808/) (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)
- [Dynamic Neural Radiance Fields for Monocular 4D Facial Avatar Reconstruction](https://mlsanity.com/paper/2012.03065/) (2020)
- [Space-time Neural Irradiance Fields for Free-Viewpoint Video](https://mlsanity.com/paper/2011.12950/) (2020)
- [DeepVoxels: Learning Persistent 3D Feature Embeddings](https://mlsanity.com/paper/1812.01024/) (2018)
- [Neural Point-Based Graphics](https://mlsanity.com/paper/1906.08240/) (2019)
- [State of the Art on Neural Rendering](https://mlsanity.com/paper/2004.03805/) (2020)
- [Deep Video Portraits](https://mlsanity.com/paper/1805.11714/) (2018)
- [Deferred Neural Rendering: Image Synthesis using Neural Textures](https://mlsanity.com/paper/1904.12356/) (2019)
- [Neural Volumes: Learning Dynamic Renderable Volumes from Images](https://mlsanity.com/paper/1906.07751/) (2019)
- [Novel View Synthesis of Dynamic Scenes with Globally Coherent Depths from a Monocular Camera](https://mlsanity.com/paper/2004.01294/) (2020)
- [Optimizing the Latent Space of Generative Networks](https://mlsanity.com/paper/1707.05776/) (2017)
- [Single Image Portrait Relighting](https://mlsanity.com/paper/1905.00824/) (2019)
- [Neural Rerendering in the Wild](https://mlsanity.com/paper/1904.04290/) (2019)
- [Text-based Editing of Talking-head Video](https://mlsanity.com/paper/1906.01524/) (2019)
- [Neural Non-Rigid Tracking](https://mlsanity.com/paper/2006.13240/) (2020)
- [ShapeFlow: Learnable Deformations Among 3D Shapes](https://mlsanity.com/paper/2006.07982/) (2020)

## Built on by (most cited first, 30 of 214)

- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [K-Planes: Explicit Radiance Fields in Space, Time, and Appearance](https://mlsanity.com/paper/2301.10241/) (2023)
- [HexPlane: A Fast Representation for Dynamic Scenes](https://mlsanity.com/paper/2301.09632/) (2023)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Point-NeRF: Point-based Neural Radiance Fields](https://mlsanity.com/paper/2201.08845/) (2022)
- [Fast Dynamic Radiance Fields with Time-Aware Neural Voxels](https://mlsanity.com/paper/2205.15285/) (2022)
- [Spacetime Gaussian Feature Splatting for Real-Time Dynamic View Synthesis](https://mlsanity.com/paper/2312.16812/) (2023)
- [I M Avatar: Implicit Morphable Head Avatars from Videos](https://mlsanity.com/paper/2112.07471/) (2021)
- [BungeeNeRF: Progressive Neural Radiance Field for Extreme Multi-scale Scene Rendering](https://mlsanity.com/paper/2112.05504/) (2021)
- [HeadNeRF: A Real-time NeRF-based Parametric Head Model](https://mlsanity.com/paper/2112.05637/) (2021)
- [DynIBaR: Neural Dynamic Image-Based Rendering](https://mlsanity.com/paper/2211.11082/) (2022)
- [A Survey on 3D Gaussian Splatting](https://mlsanity.com/paper/2401.03890/) (2024)
- [NeRF-Editing: Geometry Editing of Neural Radiance Fields](https://mlsanity.com/paper/2205.04978/) (2022)
- [Tensor4D : Efficient Neural 4D Decomposition for High-fidelity Dynamic Reconstruction and Rendering](https://mlsanity.com/paper/2211.11610/) (2022)
- [Neural Head Avatars from Monocular RGB Videos](https://mlsanity.com/paper/2112.01554/) (2021)
- [Robust Dynamic Radiance Fields](https://mlsanity.com/paper/2301.02239/) (2023)
- [NeRSemble: Multi-view Radiance Field Reconstruction of Human Heads](https://mlsanity.com/paper/2305.03027/) (2023)
- [4D-Rotor Gaussian Splatting: Towards Efficient Novel View Synthesis for Dynamic Scenes](https://mlsanity.com/paper/2402.03307/) (2024)
- [Deblur-NeRF: Neural Radiance Fields from Blurry Images](https://mlsanity.com/paper/2111.14292/) (2021)
- [MoSca: Dynamic Gaussian Fusion from Casual Videos via 4D Motion Scaffolds](https://mlsanity.com/paper/2405.17421/) (2024)
- [HyperReel: High-Fidelity 6-DoF Video with Ray-Conditioned Sampling](https://mlsanity.com/paper/2301.02238/) (2023)
- [3DGStream: On-the-Fly Training of 3D Gaussians for Efficient Streaming of Photo-Realistic Free-Viewpoint Videos](https://mlsanity.com/paper/2403.01444/) (2024)
- [Instant Volumetric Head Avatars](https://mlsanity.com/paper/2211.12499/) (2022)
- [SUDS: Scalable Urban Dynamic Scenes](https://mlsanity.com/paper/2303.14536/) (2023)
- [Efficient Neural Radiance Fields for Interactive Free-viewpoint Video](https://mlsanity.com/paper/2112.01517/) (2021)
- [Periodic Vibration Gaussian: Dynamic Urban Scene Reconstruction and Real-time Rendering](https://mlsanity.com/paper/2311.18561/) (2023)
- [Reconstructing Personalized Semantic Facial NeRF Models From Monocular Video](https://mlsanity.com/paper/2210.06108/) (2022)
- [DriveDreamer4D: World Models Are Effective Data Machines for 4D Driving Scene Representation](https://mlsanity.com/paper/2410.13571/) (2024)
- [Drivable 3D Gaussian Avatars](https://mlsanity.com/paper/2311.08581/) (2023)
- [RadSplat: Radiance Field-Informed Gaussian Splatting for Robust Real-Time Rendering with 900+ FPS](https://mlsanity.com/paper/2403.13806/) (2024)

## Abstract (arXiv)

Neural Radiance Fields (NeRF) are able to reconstruct scenes with unprecedented fidelity, and various recent works have extended NeRF to handle dynamic scenes. A common approach to reconstruct such non-rigid scenes is through the use of a learned deformation field mapping from coordinates in each input image into a canonical template coordinate space. However, these deformation-based approaches struggle to model changes in topology, as topological changes require a discontinuity in the deformation field, but these deformation fields are necessarily continuous. We address this limitation by lifting NeRFs into a higher dimensional space, and by representing the 5D radiance field corresponding to each individual input image as a slice through this "hyper-space". Our method is inspired by level set methods, which model the evolution of surfaces as slices through a higher dimensional surface. We evaluate our method on two tasks: (i) interpolating smoothly between "moments", i.e., configurations of the scene, seen in the input images while maintaining visual plausibility, and (ii) novel-view synthesis at fixed moments. We show that our method, which we dub HyperNeRF, outperforms existing methods on both tasks. Compared to Nerfies, HyperNeRF reduces average error rates by 4.1% for interpolation and 8.6% for novel-view synthesis, as measured by LPIPS. Additional videos, results, and visualizations are available at https://hypernerf.github.io.