# SIRE: SE(3) Intrinsic Rigidity Embeddings

arXiv: https://arxiv.org/abs/2503.07739 · HTML: https://mlsanity.com/paper/2503.07739/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 67 of its 79 references that are in the map.
- First posted on arXiv 10 Mar 2025.

## Builds on (most cited first, 30 of 67)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (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)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [SuperGlue: Learning Feature Matching with Graph Neural Networks](https://mlsanity.com/paper/1911.11763/) (2019)
- [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)
- [ORB-SLAM: a Versatile and Accurate Monocular SLAM System](https://mlsanity.com/paper/1502.00956/) (2015)
- [ORB-SLAM3: An Accurate Open-Source Library for Visual, Visual-Inertial and Multi-Map SLAM](https://mlsanity.com/paper/2007.11898/) (2020)
- [ORB-SLAM2: an Open-Source SLAM System for Monocular, Stereo and RGB-D Cameras](https://mlsanity.com/paper/1610.06475/) (2016)
- [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)
- [Common Objects in 3D: Large-Scale Learning and Evaluation of Real-life 3D Category Reconstruction](https://mlsanity.com/paper/2109.00512/) (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)
- [MonST3R: A Simple Approach for Estimating Geometry in the Presence of Motion](https://mlsanity.com/paper/2410.03825/) (2024)
- [Space-time Neural Irradiance Fields for Free-Viewpoint Video](https://mlsanity.com/paper/2011.12950/) (2020)
- [Depth Pro: Sharp Monocular Metric Depth in Less Than a Second](https://mlsanity.com/paper/2410.02073/) (2024)
- [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)
- [Neural Radiance Flow for 4D View Synthesis and Video Processing](https://mlsanity.com/paper/2012.09790/) (2020)
- [Shape of Motion: 4D Reconstruction from a Single Video](https://mlsanity.com/paper/2407.13764/) (2024)
- [Conditional Object-Centric Learning from Video](https://mlsanity.com/paper/2111.12594/) (2021)
- [Deep Global Registration](https://mlsanity.com/paper/2004.11540/) (2020)
- [MegaSaM: Accurate, Fast, and Robust Structure and Motion from Casual Dynamic Videos](https://mlsanity.com/paper/2412.04463/) (2024)
- [DynIBaR: Neural Dynamic Image-Based Rendering](https://mlsanity.com/paper/2211.11082/) (2022)

## Abstract (arXiv)

Motion serves as a powerful cue for scene perception and understanding by separating independently moving surfaces and organizing the physical world into distinct entities. We introduce SIRE, a self-supervised method for motion discovery of objects and dynamic scene reconstruction from casual scenes by learning intrinsic rigidity embeddings from videos. Our method trains an image encoder to estimate scene rigidity and geometry, supervised by a simple 4D reconstruction loss: a least-squares solver uses the estimated geometry and rigidity to lift 2D point track trajectories into SE(3) tracks, which are simply re-projected back to 2D and compared against the original 2D trajectories for supervision. Crucially, our framework is fully end-to-end differentiable and can be optimized either on video datasets to learn generalizable image priors, or even on a single video to capture scene-specific structure - highlighting strong data efficiency. We demonstrate the effectiveness of our rigidity embeddings and geometry across multiple settings, including downstream object segmentation, SE(3) rigid motion estimation, and self-supervised depth estimation. Our findings suggest that SIRE can learn strong geometry and motion rigidity priors from video data, with minimal supervision.