# K-Planes: Explicit Radiance Fields in Space, Time, and Appearance

arXiv: https://arxiv.org/abs/2301.10241 · HTML: https://mlsanity.com/paper/2301.10241/

## Key facts

- Cited by 746 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 50 references that are in the map.
- First posted on arXiv 24 Jan 2023.

## Builds on (most cited first, 30 of 38)

- [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)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [Efficient Geometry-aware 3D Generative Adversarial Networks](https://mlsanity.com/paper/2112.07945/) (2021)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [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)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Neural Scene Flow Fields for Space-Time View Synthesis of Dynamic Scenes](https://mlsanity.com/paper/2011.13084/) (2020)
- [Block-NeRF: Scalable Large Scene Neural View Synthesis](https://mlsanity.com/paper/2202.05263/) (2022)
- [Local Light Field Fusion: Practical View Synthesis with Prescriptive Sampling Guidelines](https://mlsanity.com/paper/1905.00889/) (2019)
- [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 View Synthesis from Dynamic Monocular Video](https://mlsanity.com/paper/2105.06468/) (2021)
- [Space-time Neural Irradiance Fields for Free-Viewpoint Video](https://mlsanity.com/paper/2011.12950/) (2020)
- [Fast Dynamic Radiance Fields with Time-Aware Neural Voxels](https://mlsanity.com/paper/2205.15285/) (2022)
- [Neural Radiance Flow for 4D View Synthesis and Video Processing](https://mlsanity.com/paper/2012.09790/) (2020)
- [Learned Initializations for Optimizing Coordinate-Based Neural Representations](https://mlsanity.com/paper/2012.02189/) (2020)
- [Image Matching across Wide Baselines: From Paper to Practice](https://mlsanity.com/paper/2003.01587/) (2020)
- [Tensor4D : Efficient Neural 4D Decomposition for High-fidelity Dynamic Reconstruction and Rendering](https://mlsanity.com/paper/2211.11610/) (2022)
- [NeX: Real-time View Synthesis with Neural Basis Expansion](https://mlsanity.com/paper/2103.05606/) (2021)
- [HyperNeRF: A Higher-Dimensional Representation for Topologically Varying Neural Radiance Fields](https://mlsanity.com/paper/2106.13228/) (2021)
- [Monocular Dynamic View Synthesis: A Reality Check](https://mlsanity.com/paper/2210.13445/) (2022)
- [Neural Volumes: Learning Dynamic Renderable Volumes from Images](https://mlsanity.com/paper/1906.07751/) (2019)
- [Optimizing the Latent Space of Generative Networks](https://mlsanity.com/paper/1707.05776/) (2017)
- [NeRFPlayer: A Streamable Dynamic Scene Representation with Decomposed Neural Radiance Fields](https://mlsanity.com/paper/2210.15947/) (2022)
- [D2NeRF: Self-Supervised Decoupling of Dynamic and Static Objects from a Monocular Video](https://mlsanity.com/paper/2205.15838/) (2022)

## Built on by (most cited first, 30 of 746)

- [4D Gaussian Splatting for Real-Time Dynamic Scene Rendering](https://mlsanity.com/paper/2310.08528/) (2023)
- [Deformable 3D Gaussians for High-Fidelity Monocular Dynamic Scene Reconstruction](https://mlsanity.com/paper/2309.13101/) (2023)
- [Dynamic 3D Gaussians: Tracking by Persistent Dynamic View Synthesis](https://mlsanity.com/paper/2308.09713/) (2023)
- [Scaffold-GS: Structured 3D Gaussians for View-Adaptive Rendering](https://mlsanity.com/paper/2312.00109/) (2023)
- [Real-time Photorealistic Dynamic Scene Representation and Rendering with 4D Gaussian Splatting](https://mlsanity.com/paper/2310.10642/) (2023)
- [Compact 3D Gaussian Representation for Radiance Field](https://mlsanity.com/paper/2311.13681/) (2023)
- [Feature 3DGS: Supercharging 3D Gaussian Splatting to Enable Distilled Feature Fields](https://mlsanity.com/paper/2312.03203/) (2023)
- [SC-GS: Sparse-Controlled Gaussian Splatting for Editable Dynamic Scenes](https://mlsanity.com/paper/2312.14937/) (2023)
- [Spacetime Gaussian Feature Splatting for Real-Time Dynamic View Synthesis](https://mlsanity.com/paper/2312.16812/) (2023)
- [Text-to-3D using Gaussian Splatting](https://mlsanity.com/paper/2309.16585/) (2023)
- [GaussianAvatars: Photorealistic Head Avatars with Rigged 3D Gaussians](https://mlsanity.com/paper/2312.02069/) (2023)
- [DNGaussian: Optimizing Sparse-View 3D Gaussian Radiance Fields with Global-Local Depth Normalization](https://mlsanity.com/paper/2403.06912/) (2024)
- [Shape of Motion: 4D Reconstruction from a Single Video](https://mlsanity.com/paper/2407.13764/) (2024)
- [No Pose, No Problem: Surprisingly Simple 3D Gaussian Splats from Sparse Unposed Images](https://mlsanity.com/paper/2410.24207/) (2024)
- [Octree-GS: Towards Consistent Real-time Rendering with LOD-Structured 3D Gaussians](https://mlsanity.com/paper/2403.17898/) (2024)
- [GS-IR: 3D Gaussian Splatting for Inverse Rendering](https://mlsanity.com/paper/2311.16473/) (2023)
- [A Survey on 3D Gaussian Splatting](https://mlsanity.com/paper/2401.03890/) (2024)
- [Street Gaussians: Modeling Dynamic Urban Scenes with Gaussian Splatting](https://mlsanity.com/paper/2401.01339/) (2024)
- [Gaussian-Flow: 4D Reconstruction with Dynamic 3D Gaussian Particle](https://mlsanity.com/paper/2312.03431/) (2023)
- [VastGaussian: Vast 3D Gaussians for Large Scene Reconstruction](https://mlsanity.com/paper/2402.17427/) (2024)
- [HAC: Hash-grid Assisted Context for 3D Gaussian Splatting Compression](https://mlsanity.com/paper/2403.14530/) (2024)
- [Text-To-4D Dynamic Scene Generation](https://mlsanity.com/paper/2301.11280/) (2023)
- [NeRSemble: Multi-view Radiance Field Reconstruction of Human Heads](https://mlsanity.com/paper/2305.03027/) (2023)
- [DreamGaussian4D: Generative 4D Gaussian Splatting](https://mlsanity.com/paper/2312.17142/) (2023)
- [PhysDreamer: Physics-Based Interaction with 3D Objects via Video Generation](https://mlsanity.com/paper/2404.13026/) (2024)
- [4D-Rotor Gaussian Splatting: Towards Efficient Novel View Synthesis for Dynamic Scenes](https://mlsanity.com/paper/2402.03307/) (2024)
- [4D-fy: Text-to-4D Generation Using Hybrid Score Distillation Sampling](https://mlsanity.com/paper/2311.17984/) (2023)
- [MoSca: Dynamic Gaussian Fusion from Casual Videos via 4D Motion Scaffolds](https://mlsanity.com/paper/2405.17421/) (2024)
- [MARS: An Instance-aware, Modular and Realistic Simulator for Autonomous Driving](https://mlsanity.com/paper/2307.15058/) (2023)
- [HumanRF: High-Fidelity Neural Radiance Fields for Humans in Motion](https://mlsanity.com/paper/2305.06356/) (2023)

## Abstract (arXiv)

We introduce k-planes, a white-box model for radiance fields in arbitrary dimensions. Our model uses d choose 2 planes to represent a d-dimensional scene, providing a seamless way to go from static (d=3) to dynamic (d=4) scenes. This planar factorization makes adding dimension-specific priors easy, e.g. temporal smoothness and multi-resolution spatial structure, and induces a natural decomposition of static and dynamic components of a scene. We use a linear feature decoder with a learned color basis that yields similar performance as a nonlinear black-box MLP decoder. Across a range of synthetic and real, static and dynamic, fixed and varying appearance scenes, k-planes yields competitive and often state-of-the-art reconstruction fidelity with low memory usage, achieving 1000x compression over a full 4D grid, and fast optimization with a pure PyTorch implementation. For video results and code, please see https://sarafridov.github.io/K-Planes.