# Object Pose Estimation with Statistical Guarantees: Conformal Keypoint Detection and Geometric Uncertainty Propagation

arXiv: https://arxiv.org/abs/2303.12246 · HTML: https://mlsanity.com/paper/2303.12246/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- Builds on 52 of its 107 references that are in the map.
- First posted on arXiv 22 Mar 2023.

## Builds on (most cited first, 30 of 52)

- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [PoseCNN: A Convolutional Neural Network for 6D Object Pose Estimation in Cluttered Scenes](https://mlsanity.com/paper/1711.00199/) (2017)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [PVNet: Pixel-wise Voting Network for 6DoF Pose Estimation](https://mlsanity.com/paper/1812.11788/) (2018)
- [Uncertainty Sets for Image Classifiers using Conformal Prediction](https://mlsanity.com/paper/2009.14193/) (2020)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Distribution-Free, Risk-Controlling Prediction Sets](https://mlsanity.com/paper/2101.02703/) (2021)
- [CosyPose: Consistent multi-view multi-object 6D pose estimation](https://mlsanity.com/paper/2008.08465/) (2020)
- [TEASER: Fast and Certifiable Point Cloud Registration](https://mlsanity.com/paper/2001.07715/) (2020)
- [BOP: Benchmark for 6D Object Pose Estimation](https://mlsanity.com/paper/1808.08319/) (2018)
- [A General and Adaptive Robust Loss Function](https://mlsanity.com/paper/1701.03077/) (2017)
- [BB8: A Scalable, Accurate, Robust to Partial Occlusion Method for Predicting the 3D Poses of Challenging Objects without Using Depth](https://mlsanity.com/paper/1703.10896/) (2017)
- [Pix2Pose: Pixel-Wise Coordinate Regression of Objects for 6D Pose Estimation](https://mlsanity.com/paper/1908.07433/) (2019)
- [Real-Time Seamless Single Shot 6D Object Pose Prediction](https://mlsanity.com/paper/1711.08848/) (2017)
- [DPOD: 6D Pose Object Detector and Refiner](https://mlsanity.com/paper/1902.11020/) (2019)
- [Implicit 3D Orientation Learning for 6D Object Detection from RGB Images](https://mlsanity.com/paper/1902.01275/) (2019)
- [OnePose: One-Shot Object Pose Estimation without CAD Models](https://mlsanity.com/paper/2205.12257/) (2022)
- [kPAM: KeyPoint Affordances for Category-Level Robotic Manipulation](https://mlsanity.com/paper/1903.06684/) (2019)
- [EPOS: Estimating 6D Pose of Objects with Symmetries](https://mlsanity.com/paper/2004.00605/) (2020)
- [GDRNPP: A Geometry-guided and Fully Learning-based Object Pose Estimator](https://mlsanity.com/paper/2102.12145/) (2021)
- [Learning Less is More - 6D Camera Localization via 3D Surface Regression](https://mlsanity.com/paper/1711.10228/) (2017)
- [Learning Optimal Conformal Classifiers](https://mlsanity.com/paper/2110.09192/) (2021)
- [Render for CNN: Viewpoint Estimation in Images Using CNNs Trained with Rendered 3D Model Views](https://mlsanity.com/paper/1505.05641/) (2015)
- [Graduated Non-Convexity for Robust Spatial Perception: From Non-Minimal Solvers to Global Outlier Rejection](https://mlsanity.com/paper/1909.08605/) (2019)
- [6-DoF Object Pose from Semantic Keypoints](https://mlsanity.com/paper/1703.04670/) (2017)
- [SE-Sync: A Certifiably Correct Algorithm for Synchronization over the Special Euclidean Group](https://mlsanity.com/paper/1612.07386/) (2016)
- [Making Deep Heatmaps Robust to Partial Occlusions for 3D Object Pose Estimation](https://mlsanity.com/paper/1804.03959/) (2018)

## Built on by (most cited first, 30 of 33)

- [Conformal Decision Theory: Safe Autonomous Decisions from Imperfect Predictions](https://mlsanity.com/paper/2310.05921/) (2023)
- [Non-Exchangeable Conformal Risk Control](https://mlsanity.com/paper/2310.01262/) (2023)
- [6D-Diff: A Keypoint Diffusion Framework for 6D Object Pose Estimation](https://mlsanity.com/paper/2401.00029/) (2023)
- [Adaptive Bounding Box Uncertainties via Two-Step Conformal Prediction](https://mlsanity.com/paper/2403.07263/) (2024)
- [Challenges for Monocular 6D Object Pose Estimation in Robotics](https://mlsanity.com/paper/2307.12172/) (2023)
- [Probabilistically Correct Language-based Multi-Robot Planning using Conformal Prediction](https://mlsanity.com/paper/2402.15368/) (2024)
- [Uncertainty Quantification with Deep Ensembles for 6D Object Pose Estimation](https://mlsanity.com/paper/2403.07741/) (2024)
- [Cocoon: Robust Multi-Modal Perception with Uncertainty-Aware Sensor Fusion](https://mlsanity.com/paper/2410.12592/) (2024)
- [GeoReF: Geometric Alignment Across Shape Variation for Category-level Object Pose Refinement](https://mlsanity.com/paper/2404.11139/) (2024)
- [Robust Single Rotation Averaging Revisited](https://mlsanity.com/paper/2309.05388/) (2023)
- [Conformal Policy Learning for Sensorimotor Control Under Distribution Shifts](https://mlsanity.com/paper/2311.01457/) (2023)
- [PAC-Bayes Generalization Certificates for Learned Inductive Conformal Prediction](https://mlsanity.com/paper/2312.04658/) (2023)
- [Adapting Prediction Sets to Distribution Shifts Without Labels](https://mlsanity.com/paper/2406.01416/) (2024)
- [Calibrated Decomposition of Aleatoric and Epistemic Uncertainty in Deep Features for Inference-Time Adaptation](https://mlsanity.com/paper/2511.12389/) (2025)
- [CHAMP: Conformalized 3D Human Multi-Hypothesis Pose Estimators](https://mlsanity.com/paper/2407.06141/) (2024)
- [WQLCP: Weighted Adaptive Conformal Prediction for Robust Uncertainty Quantification Under Distribution Shifts](https://mlsanity.com/paper/2505.19587/) (2025)
- [Pseudo-keypoint RKHS Learning for Self-supervised 6DoF Pose Estimation](https://mlsanity.com/paper/2311.09500/) (2023)
- [Certifying Robustness of Learning-Based Keypoint Detection and Pose Estimation Methods](https://mlsanity.com/paper/2408.00117/) (2024)
- [Learning Better Keypoints for Multi-Object 6DoF Pose Estimation](https://mlsanity.com/paper/2308.07827/) (2023)
- [Active 6D Pose Estimation for Textureless Objects using Multi-View RGB Frames](https://mlsanity.com/paper/2503.03726/) (2025)
- [Alignist: CAD-Informed Orientation Distribution Estimation by Fusing Shape and Correspondences](https://mlsanity.com/paper/2409.06683/) (2024)
- [CUPS: Improving Human Pose-Shape Estimators with Conformalized Deep Uncertainty](https://mlsanity.com/paper/2412.10431/) (2024)
- [Uncertainty Quantification for Visual Object Pose Estimation: S-Lemma Ellipsoidal Bounds](https://mlsanity.com/paper/2511.21666/) (2025)
- [A Probabilistic Relaxation of the Two-Stage Object Pose Estimation Paradigm](https://mlsanity.com/paper/2306.00892/) (2023)
- [Towards Human-Level 3D Relative Pose Estimation: Generalizable, Training-Free, with Single Reference](https://mlsanity.com/paper/2406.18453/) (2024)
- [Deterministic Object Pose Confidence Region Estimation](https://mlsanity.com/paper/2506.22720/) (2025)
- [Doodle Your Keypoints: Sketch-Based Few-Shot Keypoint Detection](https://mlsanity.com/paper/2507.07994/) (2025)
- [Perception with Guarantees: Certified Pose Estimation via Reachability Analysis](https://mlsanity.com/paper/2602.10032/) (2026)
- [From Decoupled to Coupled: Robustness Verification for Learning-based Keypoint Detection with Joint Specifications](https://mlsanity.com/paper/2603.05604/) (2026)
- [Adaptive Geodesic Conformal Prediction for Egocentric Camera Pose Estimation](https://mlsanity.com/paper/2605.00233/) (2026)

## Abstract (arXiv)

The two-stage object pose estimation paradigm first detects semantic keypoints on the image and then estimates the 6D pose by minimizing reprojection errors. Despite performing well on standard benchmarks, existing techniques offer no provable guarantees on the quality and uncertainty of the estimation. In this paper, we inject two fundamental changes, namely conformal keypoint detection and geometric uncertainty propagation, into the two-stage paradigm and propose the first pose estimator that endows an estimation with provable and computable worst-case error bounds. On one hand, conformal keypoint detection applies the statistical machinery of inductive conformal prediction to convert heuristic keypoint detections into circular or elliptical prediction sets that cover the groundtruth keypoints with a user-specified marginal probability (e.g., 90%). Geometric uncertainty propagation, on the other, propagates the geometric constraints on the keypoints to the 6D object pose, leading to a Pose UnceRtainty SEt (PURSE) that guarantees coverage of the groundtruth pose with the same probability. The PURSE, however, is a nonconvex set that does not directly lead to estimated poses and uncertainties. Therefore, we develop RANdom SAmple averaGing (RANSAG) to compute an average pose and apply semidefinite relaxation to upper bound the worst-case errors between the average pose and the groundtruth. On the LineMOD Occlusion dataset we demonstrate: (i) the PURSE covers the groundtruth with valid probabilities; (ii) the worst-case error bounds provide correct uncertainty quantification; and (iii) the average pose achieves better or similar accuracy as representative methods based on sparse keypoints.