mlsanityData to 7 Oct 2026

Deep Regression on Manifolds: A 3D Rotation Case Study

arXiv 2103.16317 ↗First posted 30 Mar 2021cs.CVcited by 67

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Abstract (arXiv)

Many machine learning problems involve regressing variables on a non-Euclidean manifold -- e.g. a discrete probability distribution, or the 6D pose of an object. One way to tackle these problems through gradient-based learning is to use a differentiable function that maps arbitrary inputs of a Euclidean space onto the manifold. In this paper, we establish a set of desirable properties for such mapping, and in particular highlight the importance of pre-images connectivity/convexity. We illustrate these properties with a case study regarding 3D rotations. Through theoretical considerations and methodological experiments on a variety of tasks, we review various differentiable mappings on the 3D rotation space, and conjecture about the importance of their local linearity. We show that a mapping based on Procrustes orthonormalization generally performs best among the mappings considered, but that a rotation vector representation might also be suitable when restricted to small angles.

Key facts. Cited by 67 papers in the map (data through 7 Oct 2026). Builds on 24 of its 39 references that are in the map. First posted on arXiv 30 Mar 2021.

Builds on

24 of 39 references.

References · 24

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  3. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  4. 2015ShapeNet: An Information-Rich 3D Model Repositorycited by 2,880
  5. 2018On the Continuity of Rotation Representations in Neural Networkscited by 1,186
  6. 2016Geometric deep learning: going beyond Euclidean datacited by 1,042
  7. 2017Unsupervised Learning of Depth and Ego-Motion from Videocited by 778
  8. 2019VIBE: Video Inference for Human Body Pose and Shape Estimationcited by 615
  9. 2017SSD-6D: Making RGB-based 3D detection and 6D pose estimation great againcited by 243
  10. 2017BB8: A Scalable, Accurate, Robust to Partial Occlusion Method for Predicting the 3D Poses of Challenging Objects without Using Depthcited by 225
  11. 2019PVN3D: A Deep Point-wise 3D Keypoints Voting Network for 6DoF Pose Estimationcited by 204
  12. 2020BOP Challenge 2020 on 6D Object Localizationcited by 192
12 more
  1. 2018Neural Body Fitting: Unifying Deep Learning and Model-Based Human Pose and Shape Estimationcited by 185
  2. 2016Image-based localization using LSTMs for structured feature correlationcited by 136
  3. 2020An Analysis of SVD for Deep Rotation Estimationcited by 85
  4. 2019TexturePose: Supervising Human Mesh Estimation with Texture Consistencycited by 53
  5. 2017On Pre-Trained Image Features and Synthetic Images for Deep Learningcited by 51
  6. 2019Delving Deep Into Hybrid Annotations for 3D Human Recovery in the Wildcited by 38
  7. 2019Spherical Regression: Learning Viewpoints, Surface Normals and 3D Rotations on n-Spherescited by 37
  8. 2020Probabilistic orientation estimation with matrix Fisher distributionscited by 36
  9. 2019On Object Symmetries and 6D Pose Estimation from Imagescited by 33
  10. 2020A Smooth Representation of Belief over SO(3) for Deep Rotation Learning with Uncertaintycited by 29
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  12. 2013A compact formula for the derivative of a 3-D rotation in exponential coordinatescited by 14

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 9; 2023: 15; 2024: 15; 2025: 21; 2026: 6.

67 papers.

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  1. 2022CroCo: Self-Supervised Pre-training for 3D Vision Tasks by Cross-View Completioncited by 158
  2. 2022DeXtreme: Transfer of Agile In-hand Manipulation from Simulation to Realitycited by 136
  3. 2024Multi-HMR: Multi-Person Whole-Body Human Mesh Recovery in a Single Shotcited by 98
  4. 2022PoseGPT: Quantization-based 3D Human Motion Generation and Forecastingcited by 78
  5. 2025RayZer: A Self-supervised Large View Synthesis Modelcited by 74
  6. 2024Scene Coordinate Reconstruction: Posing of Image Collections via Incremental Learning of a Relocalizercited by 73
  7. 2025Pow3R: Empowering Unconstrained 3D Reconstruction with Camera and Scene Priorscited by 69
  8. 2023CARTO: Category and Joint Agnostic Reconstruction of ARTiculated Objectscited by 64
  9. 2024Learning Robotic Manipulation Policies from Point Clouds with Conditional Flow Matchingcited by 63
  10. 2024LoopSplat: Loop Closure by Registering 3D Gaussian Splatscited by 59
  11. 2022Local-to-Global Registration for Bundle-Adjusting Neural Radiance Fieldscited by 58
  12. 2023gSDF: Geometry-Driven Signed Distance Functions for 3D Hand-Object Reconstructioncited by 49
38 more
  1. 2024Learning with 3D rotations, a hitchhiker's guide to SO(3)cited by 39
  2. 2021Projective Manifold Gradient Layer for Deep Rotation Regressioncited by 31
  3. 2024Scaling 4D Representationscited by 30
  4. 2025RenderFormer: Transformer-based Neural Rendering of Triangle Meshes with Global Illuminationcited by 23
  5. 2023SoftZoo: A Soft Robot Co-design Benchmark For Locomotion In Diverse Environmentscited by 18
  6. 2023Image to Sphere: Learning Equivariant Features for Efficient Pose Predictioncited by 17
  7. 2023SHOWMe: Benchmarking Object-agnostic Hand-Object 3D Reconstructioncited by 16
  8. 2023End-to-End (Instance)-Image Goal Navigation through Correspondence as an Emergent Phenomenoncited by 16
  9. 2022PoseBERT: A Generic Transformer Module for Temporal 3D Human Modelingcited by 15
  10. 2024SurFhead: Affine Rig Blending for Geometrically Accurate 2D Gaussian Surfel Head Avatarscited by 15
  11. 2025From Image to Video: An Empirical Study of Diffusion Representationscited by 14
  12. 2023Bridging the Gap between Human Motion and Action Semantics via Kinematic Phrasescited by 13
  13. 2023CenterGrasp: Object-Aware Implicit Representation Learning for Simultaneous Shape Reconstruction and 6-DoF Grasp Estimationcited by 13
  14. 2025Detection Based Part-level Articulated Object Reconstruction from Single RGBD Imagecited by 13
  15. 2022Spacecraft Pose Estimation Based on Unsupervised Domain Adaptation and on a 3D-Guided Loss Combinationcited by 12
  16. 2023MFOS: Model-Free & One-Shot Object Pose Estimationcited by 10
  17. 2025Flexible MOF Generation with Torsion-Aware Flow Matchingcited by 9
  18. 2023Learning to Predict 3D Rotational Dynamics from Images of a Rigid Body with Unknown Mass Distributioncited by 7
  19. 2025Cloth-Splatting: 3D Cloth State Estimation from RGB Supervisioncited by 7
  20. 2023Equivariant Single View Pose Prediction Via Induced and Restricted Representationscited by 6
  21. 2025StereoDiff: Stereo-Diffusion Synergy for Video Depth Estimationcited by 6
  22. 2024AutoURDF: Unsupervised Robot Modeling from Point Cloud Frames Using Cluster Registrationcited by 5
  23. 2024CondiMen: Conditional Multi-Person Mesh Recoverycited by 5
  24. 2025Differentiable Simulation of Hard Contacts with Soft Gradients for Learning and Controlcited by 5
  25. 2022Learning Interpretable Dynamics from Images of a Freely Rotating 3D Rigid Bodycited by 4
  26. 20243D Equivariant Pose Regression via Direct Wigner-D Harmonics Predictioncited by 4
  27. 2026Rays as Pixels: Learning A Joint Distribution of Videos and Camera Trajectoriescited by 4
  28. 2022Image to Icosahedral Projection for SO(3) Object Reasoning from Single-View Imagescited by 3
  29. 2023SyNDock: N Rigid Protein Docking via Learnable Group Synchronizationcited by 3
  30. 2025ViTa-Zero: Zero-shot Visuotactile Object 6D Pose Estimationcited by 3
  31. 2025Scalable Non-Equivariant 3D Molecule Generation via Rotational Alignmentcited by 3
  32. 2025Forecasting Continuous Non-Conservative Dynamical Systems in SO(3)cited by 3
  33. 2024Towards Unstructured Unlabeled Optical Mocap: A Video Helps!cited by 2
  34. 20243D Foundation Models Enable Simultaneous Geometry and Pose Estimation of Grasped Objectscited by 2
  35. 2024Alignist: CAD-Informed Orientation Distribution Estimation by Fusing Shape and Correspondencescited by 2
  36. 2025MatrixNet: Learning over symmetry groups using learned group representationscited by 2
  37. 2025Bi-Manual Joint Camera Calibration and Scene Representationcited by 2
  38. 2025Continuous-Time SO(3) Forecasting with Savitzky--Golay Neural Controlled Differential Equationscited by 2

50 most cited of 67 All 67 (JSON)