mlsanityData to 7 Oct 2026

Implicit-PDF: Non-Parametric Representation of Probability Distributions on the Rotation Manifold

arXiv 2106.05965 ↗First posted 10 Jun 2021cs.CVcited by 65

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Abstract (arXiv)

Single image pose estimation is a fundamental problem in many vision and robotics tasks, and existing deep learning approaches suffer by not completely modeling and handling: i) uncertainty about the predictions, and ii) symmetric objects with multiple (sometimes infinite) correct poses. To this end, we introduce a method to estimate arbitrary, non-parametric distributions on SO(3). Our key idea is to represent the distributions implicitly, with a neural network that estimates the probability given the input image and a candidate pose. Grid sampling or gradient ascent can be used to find the most likely pose, but it is also possible to evaluate the probability at any pose, enabling reasoning about symmetries and uncertainty. This is the most general way of representing distributions on manifolds, and to showcase the rich expressive power, we introduce a dataset of challenging symmetric and nearly-symmetric objects. We require no supervision on pose uncertainty -- the model trains only with a single pose per example. Nonetheless, our implicit model is highly expressive to handle complex distributions over 3D poses, while still obtaining accurate pose estimation on standard non-ambiguous environments, achieving state-of-the-art performance on Pascal3D+ and ModelNet10-SO(3) benchmarks.

Key facts. Cited by 65 papers in the map (data through 7 Oct 2026). Builds on 25 of its 53 references that are in the map. First posted on arXiv 10 Jun 2021.

Builds on

25 of 53 references.

References · 25

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2014ImageNet Large Scale Visual Recognition Challengecited by 8,441
  3. 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,416
  4. 2019DeepSDF: Learning Continuous Signed Distance Functions for Shape Representationcited by 2,682
  5. 2015Variational Inference with Normalizing Flowscited by 2,161
  6. 2018Occupancy Networks: Learning 3D Reconstruction in Function Spacecited by 2,037
  7. 2019Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representationscited by 864
  8. 2017T-LESS: An RGB-D Dataset for 6D Pose Estimation of Texture-less Objectscited by 210
  9. 2019Implicit 3D Orientation Learning for 6D Object Detection from RGB Imagescited by 170
  10. 2015Modelling Uncertainty in Deep Learning for Camera Relocalizationcited by 133
  11. 2020Normalizing Flows on Tori and Spherescited by 117
  12. 2015Render for CNN: Viewpoint Estimation in Images Using CNNs Trained with Rendered 3D Model Viewscited by 94
13 more
  1. 2020An Analysis of SVD for Deep Rotation Estimationcited by 85
  2. 2018Discovery of Latent 3D Keypoints via End-to-end Geometric Reasoningcited by 79
  3. 2018Explaining the Ambiguity of Object Detection and 6D Pose From Visual Datacited by 68
  4. 2014Viewpoints and Keypointscited by 59
  5. 2018Deep Directional Statistics: Pose Estimation with Uncertainty Quantificationcited by 45
  6. 2020Deep Bingham Networks: Dealing with Uncertainty and Ambiguity in Pose Estimationcited by 43
  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. 2018A Mixed Classification-Regression Framework for 3D Pose Estimation from 2D Imagescited by 19
  11. 2020Learning Orientation Distributions for Object Pose Estimationcited by 18
  12. 2018Pose Estimation for Objects with Rotational Symmetrycited by 15
  13. 2018Cross-Domain 3D Equivariant Image Embeddingscited by 12

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 4; 2022: 10; 2023: 24; 2024: 9; 2025: 13; 2026: 5.

65 papers.

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  1. 2021Neural Fields in Visual Computing and Beyondcited by 539
  2. 2023UniDexGrasp: Universal Robotic Dexterous Grasping via Learning Diverse Proposal Generation and Goal-Conditioned Policycited by 117
  3. 2022MagicPony: Learning Articulated 3D Animals in the Wildcited by 111
  4. 2022RelPose: Predicting Probabilistic Relative Rotation for Single Objects in the Wildcited by 102
  5. 2023RelPose++: Recovering 6D Poses from Sparse-view Observationscited by 87
  6. 2023GenPose: Generative Category-level Object Pose Estimation via Diffusion Modelscited by 47
  7. 2024Fourier Transporter: Bi-Equivariant Robotic Manipulation in 3Dcited by 32
  8. 2023Shelving, Stacking, Hanging: Relational Pose Diffusion for Multi-modal Rearrangementcited by 29
  9. 2024MatchU: Matching Unseen Objects for 6D Pose Estimation from RGB-D Imagescited by 28
  10. 2023Rigid Body Flows for Sampling Molecular Crystal Structurescited by 27
  11. 2022SC6D: Symmetry-agnostic and Correspondence-free 6D Object Pose Estimationcited by 17
  12. 2023Image to Sphere: Learning Equivariant Features for Efficient Pose Predictioncited by 17
38 more
  1. 2023Confronting Ambiguity in 6D Object Pose Estimation via Score-Based Diffusion on SE(3)cited by 17
  2. 2023Symphony: Symmetry-Equivariant Point-Centered Spherical Harmonics for 3D Molecule Generationcited by 17
  3. 2022FisherMatch: Semi-Supervised Rotation Regression via Entropy-based Filteringcited by 16
  4. 2023SpyroPose: SE(3) Pyramids for Object Pose Distribution Estimationcited by 14
  5. 2023Delving into Discrete Normalizing Flows on SO(3) Manifold for Probabilistic Rotation Modelingcited by 14
  6. 2025Rectified Point Flow: Generic Point Cloud Pose Estimationcited by 13
  7. 2023A Probabilistic Framework for Visual Localization in Ambiguous Scenescited by 12
  8. 2025AnyPlace: Learning Generalized Object Placement for Robot Manipulationcited by 10
  9. 2023A Laplace-inspired Distribution on SO(3) for Probabilistic Rotation Estimationcited by 9
  10. 2022Ki-Pode: Keypoint-based Implicit Pose Distribution Estimation of Rigid Objectscited by 7
  11. 2023Learning Distributions on Manifolds with Free-Form Flowscited by 7
  12. 2024Normalizing Flows on the Product Space of SO(3) Manifolds for Probabilistic Human Pose Modelingcited by 7
  13. 2025Temporal Score Rescaling for Temperature Sampling in Diffusion and Flow Modelscited by 7
  14. 2023Equivariant Single View Pose Prediction Via Induced and Restricted Representationscited by 6
  15. 2021Simulation-based Bayesian inference for multi-fingered robotic graspingcited by 5
  16. 2022Multi-view object pose estimation from correspondence distributions and epipolar geometrycited by 5
  17. 2023Towards Robust Probabilistic Modeling on SO(3) via Rotation Laplace Distributioncited by 5
  18. 2023Shape Completion with Prediction of Uncertain Regionscited by 5
  19. 2023Unified framework for diffusion generative models in SO(3): applications in computer vision and astrophysicscited by 5
  20. 2023MELON: NeRF with Unposed Images in SO(3)cited by 4
  21. 2023Stable Yaw Estimation of Boats from the Viewpoint of UAVs and USVscited by 4
  22. 2023Topological Obstructions and How to Avoid Themcited by 4
  23. 20243D Equivariant Pose Regression via Direct Wigner-D Harmonics Predictioncited by 4
  24. 2021Learning Proposals for Practical Energy-Based Regressioncited by 3
  25. 2024ADen: Adaptive Density Representations for Sparse-view Camera Pose Estimationcited by 3
  26. 2024BOP-Distrib: Revisiting 6D Pose Estimation Benchmarks for Better Evaluation under Visual Ambiguitiescited by 3
  27. 2025Corr2Distrib: Making Ambiguous Correspondences an Ally to Predict Reliable 6D Pose Distributionscited by 3
  28. 2022ObPose: Leveraging Pose for Object-Centric Scene Inference and Generation in 3Dcited by 2
  29. 2022Stable Object Reorientation using Contact Plane Registrationcited by 2
  30. 2022Learning Implicit Probability Distribution Functions for Symmetric Orientation Estimation from RGB Images Without Pose Labelscited by 2
  31. 2023A Probabilistic Rotation Representation for Symmetric Shapes With an Efficiently Computable Bingham Loss Functioncited by 2
  32. 2024Semi-Supervised Unconstrained Head Pose Estimation in the Wildcited by 2
  33. 2024Alignist: CAD-Informed Orientation Distribution Estimation by Fusing Shape and Correspondencescited by 2
  34. 2025MatrixNet: Learning over symmetry groups using learned group representationscited by 2
  35. 2025ArrowPose: Segmentation, Detection, and 5 DoF Pose Estimation Network for Colorless Point Cloudscited by 2
  36. 2021Incremental Non-Gaussian Inference for SLAM Using Normalizing Flowscited by 1
  37. 2022Accidental Turntables: Learning 3D Pose by Watching Objects Turncited by 1
  38. 2023AQuaMaM: An Autoregressive, Quaternion Manifold Model for Rapidly Estimating Complex SO(3) Distributionscited by 1

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