mlsanityData to 7 Oct 2026

Tangent Space Backpropagation for 3D Transformation Groups

arXiv 2103.12032 ↗First posted 22 Mar 2021cs.CVcited by 40

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Abstract (arXiv)

We address the problem of performing backpropagation for computation graphs involving 3D transformation groups SO(3), SE(3), and Sim(3). 3D transformation groups are widely used in 3D vision and robotics, but they do not form vector spaces and instead lie on smooth manifolds. The standard backpropagation approach, which embeds 3D transformations in Euclidean spaces, suffers from numerical difficulties. We introduce a new library, which exploits the group structure of 3D transformations and performs backpropagation in the tangent spaces of manifolds. We show that our approach is numerically more stable, easier to implement, and beneficial to a diverse set of tasks. Our plug-and-play PyTorch library is available at https://github.com/princeton-vl/lietorch.

Key facts. Cited by 40 papers in the map (data through 7 Oct 2026). Builds on 25 of its 39 references that are in the map. First posted on arXiv 22 Mar 2021.

Builds on

25 of 39 references.

References · 25

  1. 2020RAFT: Recurrent All-Pairs Field Transforms for Optical Flowcited by 2,385
  2. 2019SuperGlue: Learning Feature Matching with Graph Neural Networkscited by 1,437
  3. 2015ORB-SLAM: a Versatile and Accurate Monocular SLAM Systemcited by 983
  4. 2015Automatic differentiation in machine learning: a surveycited by 846
  5. 2020Accelerating 3D Deep Learning with PyTorch3Dcited by 781
  6. 2020TartanAir: A Dataset to Push the Limits of Visual SLAMcited by 494
  7. 2019DenseFusion: 6D Object Pose Estimation by Iterative Dense Fusioncited by 352
  8. 2020Deep Global Registrationcited by 228
  9. 2020Consistent Video Depth Estimationcited by 220
  10. 2018DeepV2D: Video to Depth with Differentiable Structure from Motioncited by 185
  11. 2018BA-Net: Dense Bundle Adjustment Networkcited by 173
  12. 2018A micro Lie theory for state estimation in roboticscited by 117
13 more
  1. 2020DeepFactors: Real-Time Probabilistic Dense Monocular SLAMcited by 117
  2. 2013Manopt, a Matlab toolbox for optimization on manifoldscited by 112
  3. 2020Geoopt: Riemannian Optimization in PyTorchcited by 109
  4. 2018DeepTAM: Deep Tracking and Mappingcited by 87
  5. 2020Learning multiview 3D point cloud registrationcited by 78
  6. 2016Theano: A Python framework for fast computation of mathematical expressionscited by 64
  7. 2019Deep Rigid Instance Scene Flowcited by 54
  8. 2016SE3-Nets: Learning Rigid Body Motion using Deep Neural Networkscited by 48
  9. 2018Learning Rigidity in Dynamic Scenes with a Moving Camera for 3D Motion Field Estimationcited by 38
  10. 2019gradSLAM: Automagically differentiable SLAMcited by 27
  11. 2018Taking a Deeper Look at the Inverse Compositional Algorithmcited by 20
  12. 2018McTorch, a manifold optimization library for deep learningcited by 16
  13. 2018Manifold Geometry with Fast Automatic Derivatives and Coordinate Frame Semantics Checking in C++cited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 3; 2022: 10; 2023: 10; 2024: 11; 2025: 4; 2026: 2.

40 papers.

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  1. 2021DROID-SLAM: Deep Visual SLAM for Monocular, Stereo, and RGB-D Camerascited by 673
  2. 2021NICE-SLAM: Neural Implicit Scalable Encoding for SLAMcited by 586
  3. 2024MASt3R-SLAM: Real-Time Dense SLAM with 3D Reconstruction Priorscited by 198
  4. 2022Theseus: A Library for Differentiable Nonlinear Optimizationcited by 64
  5. 2024Vision-based Manipulation from Single Human Video with Open-World Object Graphscited by 46
  6. 2022Approximate Differentiable Rendering with Algebraic Surfacescited by 44
  7. 2023Flow supervision for Deformable NeRFcited by 42
  8. 2022RNNPose: Recurrent 6-DoF Object Pose Refinement with Robust Correspondence Field Estimation and Pose Optimizationcited by 38
  9. 2022The 8-Point Algorithm as an Inductive Bias for Relative Pose Prediction by ViTscited by 38
  10. 2023Neural Refinement for Absolute Pose Regression with Feature Synthesiscited by 37
  11. 2021Projective Manifold Gradient Layer for Deep Rotation Regressioncited by 31
  12. 2023HI-SLAM: Monocular Real-time Dense Mapping with Hybrid Implicit Fieldscited by 31
28 more
  1. 2024DarkGS: Learning Neural Illumination and 3D Gaussians Relighting for Robotic Exploration in the Darkcited by 25
  2. 2023Deep Learning for Camera Calibration and Beyond: A Surveycited by 20
  3. 2023Living Scenes: Multi-object Relocalization and Reconstruction in Changing 3D Environmentscited by 15
  4. 2022M-FUSE: Multi-frame Fusion for Scene Flow Estimationcited by 14
  5. 2022D3FlowSLAM: Self-Supervised Dynamic SLAM with Flow Motion Decomposition and DINO Guidancecited by 9
  6. 2023A Laplace-inspired Distribution on SO(3) for Probabilistic Rotation Estimationcited by 9
  7. 2022CPPF++: Uncertainty-Aware Sim2Real Object Pose Estimation by Vote Aggregationcited by 6
  8. 2023PlaneRecTR++: Unified Query Learning for Joint 3D Planar Reconstruction and Pose Estimationcited by 6
  9. 2024IG-SLAM: Instant Gaussian SLAMcited by 6
  10. 2023Towards Robust Probabilistic Modeling on SO(3) via Rotation Laplace Distributioncited by 5
  11. 2024Look Gauss, No Pose: Novel View Synthesis using Gaussian Splatting without Accurate Pose Initializationcited by 5
  12. 2024MambaVO: Deep Visual Odometry Based on Sequential Matching Refinement and Training Smoothingcited by 5
  13. 2023EMR-MSF: Self-Supervised Recurrent Monocular Scene Flow Exploiting Ego-Motion Rigiditycited by 4
  14. 2022SymForce: Symbolic Computation and Code Generation for Roboticscited by 3
  15. 2022TAToo: Vision-based Joint Tracking of Anatomy and Tool for Skull-base Surgerycited by 3
  16. 2025Forecasting Continuous Non-Conservative Dynamical Systems in SO(3)cited by 3
  17. 2024Fit-NGP: Fitting Object Models to Neural Graphics Primitivescited by 2
  18. 2024Alignist: CAD-Informed Orientation Distribution Estimation by Fusing Shape and Correspondencescited by 2
  19. 2025Continuous-Time SO(3) Forecasting with Savitzky--Golay Neural Controlled Differential Equationscited by 2
  20. 2022Deep Projective Rotation Estimation through Relative Supervisioncited by 1
  21. 2023UFD-PRiME: Unsupervised Joint Learning of Optical Flow and Stereo Depth through Pixel-Level Rigid Motion Estimationcited by 1
  22. 2024Stationary Velocity Fields on Matrix Groups for Deformable Image Registrationcited by 1
  23. 2025DNOI-4DRO: Deep 4D Radar Odometry with Differentiable Neural-Optimization Iterationscited by 1
  24. 2025ICP-3DGS: SfM-free 3D Gaussian Splatting for Large-scale Unbounded Scenescited by 1
  25. 2024Mitigating Heterogeneity among Factor Tensors via Lie Group Manifolds for Tensor Decomposition Based Temporal Knowledge Graph Embeddingcited by 0
  26. 2024Robust SG-NeRF: Robust Scene Graph Aided Neural Surface Reconstructioncited by 0
  27. 2026PlanaReLoc: Camera Relocalization in 3D Planar Primitives via Region-Based Structure Matchingcited by 0
  28. 2026Quasi-SVD: Learning a Lie-constrained matrix factorisation for real-time imagingcited by 0