# Shape of Motion: 4D Reconstruction from a Single Video

arXiv: https://arxiv.org/abs/2407.13764 · HTML: https://mlsanity.com/paper/2407.13764/

## Key facts

- Cited by 250 papers in the map (data through 14 Oct 2026).
- Builds on 80 of its 138 references that are in the map.
- First posted on arXiv 18 Jul 2024.

## Builds on (most cited first, 30 of 80)

- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [RAFT: Recurrent All-Pairs Field Transforms for Optical Flow](https://mlsanity.com/paper/2003.12039/) (2020)
- [DUSt3R: Geometric 3D Vision Made Easy](https://mlsanity.com/paper/2312.14132/) (2023)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [Depth Anything: Unleashing the Power of Large-Scale Unlabeled Data](https://mlsanity.com/paper/2401.10891/) (2024)
- [SuperPoint: Self-Supervised Interest Point Detection and Description](https://mlsanity.com/paper/1712.07629/) (2017)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [4D Gaussian Splatting for Real-Time Dynamic Scene Rendering](https://mlsanity.com/paper/2310.08528/) (2023)
- [2D Gaussian Splatting for Geometrically Accurate Radiance Fields](https://mlsanity.com/paper/2403.17888/) (2024)
- [FlowNet: Learning Optical Flow with Convolutional Networks](https://mlsanity.com/paper/1504.06852/) (2015)
- [PWC-Net: CNNs for Optical Flow Using Pyramid, Warping, and Cost Volume](https://mlsanity.com/paper/1709.02371/) (2017)
- [FlowNet 2.0: Evolution of Optical Flow Estimation with Deep Networks](https://mlsanity.com/paper/1612.01925/) (2016)
- [Deformable 3D Gaussians for High-Fidelity Monocular Dynamic Scene Reconstruction](https://mlsanity.com/paper/2309.13101/) (2023)
- [Neural Scene Flow Fields for Space-Time View Synthesis of Dynamic Scenes](https://mlsanity.com/paper/2011.13084/) (2020)
- [K-Planes: Explicit Radiance Fields in Space, Time, and Appearance](https://mlsanity.com/paper/2301.10241/) (2023)
- [Dynamic 3D Gaussians: Tracking by Persistent Dynamic View Synthesis](https://mlsanity.com/paper/2308.09713/) (2023)
- [DROID-SLAM: Deep Visual SLAM for Monocular, Stereo, and RGB-D Cameras](https://mlsanity.com/paper/2108.10869/) (2021)
- [HexPlane: A Fast Representation for Dynamic Scenes](https://mlsanity.com/paper/2301.09632/) (2023)
- [CoTracker: It is Better to Track Together](https://mlsanity.com/paper/2307.07635/) (2023)
- [HumanNeRF: Free-viewpoint Rendering of Moving People from Monocular Video](https://mlsanity.com/paper/2201.04127/) (2022)
- [Real-time Photorealistic Dynamic Scene Representation and Rendering with 4D Gaussian Splatting](https://mlsanity.com/paper/2310.10642/) (2023)
- [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)
- [UniDepth: Universal Monocular Metric Depth Estimation](https://mlsanity.com/paper/2403.18913/) (2024)
- [Kubric: A scalable dataset generator](https://mlsanity.com/paper/2203.03570/) (2022)
- [Spacetime Gaussian Feature Splatting for Real-Time Dynamic View Synthesis](https://mlsanity.com/paper/2312.16812/) (2023)
- [GMFlow: Learning Optical Flow via Global Matching](https://mlsanity.com/paper/2111.13680/) (2021)
- [TAPIR: Tracking Any Point with per-frame Initialization and temporal Refinement](https://mlsanity.com/paper/2306.08637/) (2023)
- [PointOdyssey: A Large-Scale Synthetic Dataset for Long-Term Point Tracking](https://mlsanity.com/paper/2307.15055/) (2023)

## Built on by (most cited first, 30 of 250)

- [MonST3R: A Simple Approach for Estimating Geometry in the Presence of Motion](https://mlsanity.com/paper/2410.03825/) (2024)
- [MegaSaM: Accurate, Fast, and Robust Structure and Motion from Casual Dynamic Videos](https://mlsanity.com/paper/2412.04463/) (2024)
- [Lotus: Diffusion-based Visual Foundation Model for High-quality Dense Prediction](https://mlsanity.com/paper/2409.18124/) (2024)
- [CAT4D: Create Anything in 4D with Multi-View Video Diffusion Models](https://mlsanity.com/paper/2411.18613/) (2024)
- [DimensionX: Create Any 3D and 4D Scenes from a Single Image with Controllable Video Diffusion](https://mlsanity.com/paper/2411.04928/) (2024)
- [TrajectoryCrafter: Redirecting Camera Trajectory for Monocular Videos via Diffusion Models](https://mlsanity.com/paper/2503.05638/) (2025)
- [TesserAct: Learning 4D Embodied World Models](https://mlsanity.com/paper/2504.20995/) (2025)
- [Stereo4D: Learning How Things Move in 3D from Internet Stereo Videos](https://mlsanity.com/paper/2412.09621/) (2024)
- [St4RTrack: Simultaneous 4D Reconstruction and Tracking in the World](https://mlsanity.com/paper/2504.13152/) (2025)
- [SpatialTrackerV2: 3D Point Tracking Made Easy](https://mlsanity.com/paper/2507.12462/) (2025)
- [STream3R: Scalable Sequential 3D Reconstruction with Causal Transformer](https://mlsanity.com/paper/2508.10893/) (2025)
- [Align3R: Aligned Monocular Depth Estimation for Dynamic Videos](https://mlsanity.com/paper/2412.03079/) (2024)
- [ReCapture: Generative Video Camera Controls for User-Provided Videos using Masked Video Fine-Tuning](https://mlsanity.com/paper/2411.05003/) (2024)
- [TAPIP3D: Tracking Any Point in Persistent 3D Geometry](https://mlsanity.com/paper/2504.14717/) (2025)
- [Geo4D: Leveraging Video Generators for Geometric 4D Scene Reconstruction](https://mlsanity.com/paper/2504.07961/) (2025)
- [STORM: Spatio-Temporal Reconstruction Model for Large-Scale Outdoor Scenes](https://mlsanity.com/paper/2501.00602/) (2024)
- [Feed-Forward Bullet-Time Reconstruction of Dynamic Scenes from Monocular Videos](https://mlsanity.com/paper/2412.03526/) (2024)
- [4DGT: Learning a 4D Gaussian Transformer Using Real-World Monocular Videos](https://mlsanity.com/paper/2506.08015/) (2025)
- [SplineGS: Robust Motion-Adaptive Spline for Real-Time Dynamic 3D Gaussians from Monocular Video](https://mlsanity.com/paper/2412.09982/) (2024)
- [Dynamic Point Maps: A Versatile Representation for Dynamic 3D Reconstruction](https://mlsanity.com/paper/2503.16318/) (2025)
- [GS-DiT: Advancing Video Generation with Pseudo 4D Gaussian Fields through Efficient Dense 3D Point Tracking](https://mlsanity.com/paper/2501.02690/) (2025)
- [GeometryCrafter: Consistent Geometry Estimation for Open-world Videos with Diffusion Priors](https://mlsanity.com/paper/2504.01016/) (2025)
- [Segment Any Motion in Videos](https://mlsanity.com/paper/2503.22268/) (2025)
- [MoVieS: Motion-Aware 4D Dynamic View Synthesis in One Second](https://mlsanity.com/paper/2507.10065/) (2025)
- [Any4D: Unified Feed-Forward Metric 4D Reconstruction](https://mlsanity.com/paper/2512.10935/) (2025)
- [EX-4D: EXtreme Viewpoint 4D Video Synthesis via Depth Watertight Mesh](https://mlsanity.com/paper/2506.05554/) (2025)
- [Uni4D: Unifying Visual Foundation Models for 4D Modeling from a Single Video](https://mlsanity.com/paper/2503.21761/) (2025)
- [Feat2GS: Probing Visual Foundation Models with Gaussian Splatting](https://mlsanity.com/paper/2412.09606/) (2024)
- [CityGS-X: A Scalable Architecture for Efficient and Geometrically Accurate Large-Scale Scene Reconstruction](https://mlsanity.com/paper/2503.23044/) (2025)
- [POMATO: Marrying Pointmap Matching with Temporal Motion for Dynamic 3D Reconstruction](https://mlsanity.com/paper/2504.05692/) (2025)

## Abstract (arXiv)

Monocular dynamic reconstruction is a challenging and long-standing vision problem due to the highly ill-posed nature of the task. Existing approaches depend on templates, are effective only in quasi-static scenes, or fail to model 3D motion explicitly. We introduce a method for reconstructing generic dynamic scenes, featuring explicit, persistent 3D motion trajectories in the world coordinate frame, from casually captured monocular videos. We tackle the problem with two key insights: First, we exploit the low-dimensional structure of 3D motion by representing scene motion with a compact set of SE(3) motion bases. Each point's motion is expressed as a linear combination of these bases, facilitating soft decomposition of the scene into multiple rigidly-moving groups. Second, we take advantage of off-the-shelf data-driven priors such as monocular depth maps and long-range 2D tracks, and devise a method to effectively consolidate these noisy supervisory signals, resulting in a globally consistent representation of the dynamic scene. Experiments show that our method achieves state-of-the-art performance for both long-range 3D/2D motion estimation and novel view synthesis on dynamic scenes. Project Page: https://shape-of-motion.github.io/