# SM4RT: Learning Structured Motion Geometry for 4D Reconstruction

arXiv: https://arxiv.org/abs/2607.22534 · HTML: https://mlsanity.com/paper/2607.22534/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 54 references that are in the map.
- First posted on arXiv 24 Jul 2026.

## Builds on (most cited first, 30 of 42)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Scalability in Perception for Autonomous Driving: Waymo Open Dataset](https://mlsanity.com/paper/1912.04838/) (2019)
- [Vision Transformers for Dense Prediction](https://mlsanity.com/paper/2103.13413/) (2021)
- [VGGT: Visual Geometry Grounded Transformer](https://mlsanity.com/paper/2503.11651/) (2025)
- [ScanNet++: A High-Fidelity Dataset of 3D Indoor Scenes](https://mlsanity.com/paper/2308.11417/) (2023)
- [Depth Anything 3: Recovering the Visual Space from Any Views](https://mlsanity.com/paper/2511.10647/) (2025)
- [Hypersim: A Photorealistic Synthetic Dataset for Holistic Indoor Scene Understanding](https://mlsanity.com/paper/2011.02523/) (2020)
- [Continuous 3D Perception Model with Persistent State](https://mlsanity.com/paper/2501.12387/) (2025)
- [CoTracker: It is Better to Track Together](https://mlsanity.com/paper/2307.07635/) (2023)
- [MonST3R: A Simple Approach for Estimating Geometry in the Presence of Motion](https://mlsanity.com/paper/2410.03825/) (2024)
- [Kubric: A scalable dataset generator](https://mlsanity.com/paper/2203.03570/) (2022)
- [Relation-Shape Convolutional Neural Network for Point Cloud Analysis](https://mlsanity.com/paper/1904.07601/) (2019)
- [From Softmax to Sparsemax: A Sparse Model of Attention and Multi-Label Classification](https://mlsanity.com/paper/1602.02068/) (2016)
- [MapAnything: Universal Feed-Forward Metric 3D Reconstruction](https://mlsanity.com/paper/2509.13414/) (2025)
- [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)
- [Shape of Motion: 4D Reconstruction from a Single Video](https://mlsanity.com/paper/2407.13764/) (2024)
- [SpatialTracker: Tracking Any 2D Pixels in 3D Space](https://mlsanity.com/paper/2404.04319/) (2024)
- [Streaming 4D Visual Geometry Transformer](https://mlsanity.com/paper/2507.11539/) (2025)
- [DynamicStereo: Consistent Dynamic Depth from Stereo Videos](https://mlsanity.com/paper/2305.02296/) (2023)
- [RAFT-3D: Scene Flow using Rigid-Motion Embeddings](https://mlsanity.com/paper/2012.00726/) (2020)
- [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)
- [Point3R: Streaming 3D Reconstruction with Explicit Spatial Pointer Memory](https://mlsanity.com/paper/2507.02863/) (2025)
- [TAPVid-3D: A Benchmark for Tracking Any Point in 3D](https://mlsanity.com/paper/2407.05921/) (2024)
- [DELTA: Dense Efficient Long-range 3D Tracking for any video](https://mlsanity.com/paper/2410.24211/) (2024)
- [Efficiently Reconstructing Dynamic Scenes One D4RT at a Time](https://mlsanity.com/paper/2512.08924/) (2025)
- [EmbodiedOcc: Embodied 3D Occupancy Prediction for Vision-based Online Scene Understanding](https://mlsanity.com/paper/2412.04380/) (2024)
- [Segment Any Motion in Videos](https://mlsanity.com/paper/2503.22268/) (2025)

## Built on by (most cited first, 5 of 5)

- [GAUGE: Group-Wise View-Inconsistency Rectification for Feed-Forward 4D Tracking](https://mlsanity.com/paper/2609.32596/) (2026)
- [ARROW: Arbitrary Reconstruction and Tracking of 4D Observations in the Wild](https://mlsanity.com/paper/2610.01314/) (2026)
- [SCOPE-4D: Endoscopic 4D Geometry Foundation Models](https://mlsanity.com/paper/2610.02343/) (2026)
- [Slot3R: Set-Associative Spatial Memory for Streaming 3D Reconstruction](https://mlsanity.com/paper/2610.12282/) (2026)
- [Cepheid: Decoupling Scale from Structure for Cross-Family Motion Completion](https://mlsanity.com/paper/2610.18871/) (2026)

## Abstract (arXiv)

Geometry Foundation Models (GFMs) have substantially advanced monocular 3D reconstruction, yet extending this capability to 4D dynamic understanding remains a fundamental challenge. Most existing motion perception methods (e.g., sparse tracking, dense point-wise flow) treat motion as independent point-wise displacements, ignoring the structured nature of physical motion. However, real-world objects usually obey rigid-body kinematics, and points thus usually move collectively, not in isolation. Motion itself possesses geometric structure: physical objects undergo a set of rigid-body transformations governed by SE(3), rather than unstructured point-wise displacements. Building on this insight, we propose SM4RT, a Structured Motion 4D Reconstruction Transformer for end-to-end 3D reconstruction and structured motion perception. SM4RT introduces Structure-of-Motion to represent scene dynamics, where scene motion is decomposed into a compact set of motion bases, each represented as a temporal sequence of 6D twists in SE(3). Dense scene motion is then recovered by sparse, time-shared per-pixel assignment weights over these bases, ensuring points on the same object share a common rigid-body motion trajectory. SM4RT introduces a parallel motion geometry encoder and decoder that jointly infer 3D geometry, world-coordinate motion, and scene kinematic structure in a single forward pass from monocular RGB video. SM4RT achieves strong motion reconstruction performance while preserving the geometric structure of scene motion.