# Tensor4D : Efficient Neural 4D Decomposition for High-fidelity Dynamic Reconstruction and Rendering

arXiv: https://arxiv.org/abs/2211.11610 · HTML: https://mlsanity.com/paper/2211.11610/

## Key facts

- Cited by 217 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 79 references that are in the map.
- First posted on arXiv 21 Nov 2022.

## Builds on (most cited first, 30 of 47)

- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (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)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [Direct Voxel Grid Optimization: Super-fast Convergence for Radiance Fields Reconstruction](https://mlsanity.com/paper/2111.11215/) (2021)
- [Neural Sparse Voxel Fields](https://mlsanity.com/paper/2007.11571/) (2020)
- [PlenOctrees for Real-time Rendering of Neural Radiance Fields](https://mlsanity.com/paper/2103.14024/) (2021)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [pi-GAN: Periodic Implicit Generative Adversarial Networks for 3D-Aware Image Synthesis](https://mlsanity.com/paper/2012.00926/) (2020)
- [Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervision](https://mlsanity.com/paper/1912.07372/) (2019)
- [GRAF: Generative Radiance Fields for 3D-Aware Image Synthesis](https://mlsanity.com/paper/2007.02442/) (2020)
- [UNISURF: Unifying Neural Implicit Surfaces and Radiance Fields for Multi-View Reconstruction](https://mlsanity.com/paper/2104.10078/) (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)
- [HumanNeRF: Free-viewpoint Rendering of Moving People from Monocular Video](https://mlsanity.com/paper/2201.04127/) (2022)
- [StyleNeRF: A Style-based 3D-Aware Generator for High-resolution Image Synthesis](https://mlsanity.com/paper/2110.08985/) (2021)
- [Non-Rigid Neural Radiance Fields: Reconstruction and Novel View Synthesis of a Dynamic Scene From Monocular Video](https://mlsanity.com/paper/2012.12247/) (2020)
- [NeRD: Neural Reflectance Decomposition from Image Collections](https://mlsanity.com/paper/2012.03918/) (2020)
- [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)
- [Function4D: Real-time Human Volumetric Capture from Very Sparse Consumer RGBD Sensors](https://mlsanity.com/paper/2105.01859/) (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)
- [CodeNeRF: Disentangled Neural Radiance Fields for Object Categories](https://mlsanity.com/paper/2109.01750/) (2021)

## Built on by (most cited first, 30 of 217)

- [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)
- [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)
- [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)
- [A Survey on 3D Gaussian Splatting](https://mlsanity.com/paper/2401.03890/) (2024)
- [Gaussian-Flow: 4D Reconstruction with Dynamic 3D Gaussian Particle](https://mlsanity.com/paper/2312.03431/) (2023)
- [DreamGaussian4D: Generative 4D Gaussian Splatting](https://mlsanity.com/paper/2312.17142/) (2023)
- [GPS-Gaussian: Generalizable Pixel-wise 3D Gaussian Splatting for Real-time Human Novel View Synthesis](https://mlsanity.com/paper/2312.02155/) (2023)
- [HumanRF: High-Fidelity Neural Radiance Fields for Humans in Motion](https://mlsanity.com/paper/2305.06356/) (2023)
- [Recent Advances in 3D Gaussian Splatting](https://mlsanity.com/paper/2403.11134/) (2024)
- [State of the Art on Diffusion Models for Visual Computing](https://mlsanity.com/paper/2310.07204/) (2023)
- [Consistent4D: Consistent 360deg Dynamic Object Generation from Monocular Video](https://mlsanity.com/paper/2311.02848/) (2023)
- [DynMF: Neural Motion Factorization for Real-time Dynamic View Synthesis with 3D Gaussian Splatting](https://mlsanity.com/paper/2312.00112/) (2023)
- [Gaussian in the Wild: 3D Gaussian Splatting for Unconstrained Image Collections](https://mlsanity.com/paper/2403.15704/) (2024)
- [Animate124: Animating One Image to 4D Dynamic Scene](https://mlsanity.com/paper/2311.14603/) (2023)
- [textitS3Gaussian: Self-Supervised Street Gaussians for Autonomous Driving](https://mlsanity.com/paper/2405.20323/) (2024)
- [3D Gaussian as a New Era: A Survey](https://mlsanity.com/paper/2402.07181/) (2024)
- [Motion-aware 3D Gaussian Splatting for Efficient Dynamic Scene Reconstruction](https://mlsanity.com/paper/2403.11447/) (2024)
- [GaussianFlow: Splatting Gaussian Dynamics for 4D Content Creation](https://mlsanity.com/paper/2403.12365/) (2024)
- [GauFRe: Gaussian Deformation Fields for Real-time Dynamic Novel View Synthesis](https://mlsanity.com/paper/2312.11458/) (2023)
- [4K4D: Real-Time 4D View Synthesis at 4K Resolution](https://mlsanity.com/paper/2310.11448/) (2023)
- [AvatarMAV: Fast 3D Head Avatar Reconstruction Using Motion-Aware Neural Voxels](https://mlsanity.com/paper/2211.13206/) (2022)
- [HiFi4G: High-Fidelity Human Performance Rendering via Compact Gaussian Splatting](https://mlsanity.com/paper/2312.03461/) (2023)
- [MotionGS: Exploring Explicit Motion Guidance for Deformable 3D Gaussian Splatting](https://mlsanity.com/paper/2410.07707/) (2024)
- [Neural Parametric Gaussians for Monocular Non-Rigid Object Reconstruction](https://mlsanity.com/paper/2312.01196/) (2023)
- [CG-SLAM: Efficient Dense RGB-D SLAM in a Consistent Uncertainty-aware 3D Gaussian Field](https://mlsanity.com/paper/2403.16095/) (2024)
- [Factor Fields: A Unified Framework for Neural Fields and Beyond](https://mlsanity.com/paper/2302.01226/) (2023)
- [MIME: Human-Aware 3D Scene Generation](https://mlsanity.com/paper/2212.04360/) (2022)

## Abstract (arXiv)

We present Tensor4D, an efficient yet effective approach to dynamic scene modeling. The key of our solution is an efficient 4D tensor decomposition method so that the dynamic scene can be directly represented as a 4D spatio-temporal tensor. To tackle the accompanying memory issue, we decompose the 4D tensor hierarchically by projecting it first into three time-aware volumes and then nine compact feature planes. In this way, spatial information over time can be simultaneously captured in a compact and memory-efficient manner. When applying Tensor4D for dynamic scene reconstruction and rendering, we further factorize the 4D fields to different scales in the sense that structural motions and dynamic detailed changes can be learned from coarse to fine. The effectiveness of our method is validated on both synthetic and real-world scenes. Extensive experiments show that our method is able to achieve high-quality dynamic reconstruction and rendering from sparse-view camera rigs or even a monocular camera. The code and dataset will be released at https://liuyebin.com/tensor4d/tensor4d.html.