# Certifiable 3D Object Pose Estimation: Foundations, Learning Models, and Self-Training

arXiv: https://arxiv.org/abs/2206.11215 · HTML: https://mlsanity.com/paper/2206.11215/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 72 of its 107 references that are in the map.
- First posted on arXiv 22 Jun 2022.

## Builds on (most cited first, 30 of 72)

- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [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)
- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [DROID-SLAM: Deep Visual SLAM for Monocular, Stereo, and RGB-D Cameras](https://mlsanity.com/paper/2108.10869/) (2021)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Normalized Object Coordinate Space for Category-Level 6D Object Pose and Size Estimation](https://mlsanity.com/paper/1901.02970/) (2019)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [DenseFusion: 6D Object Pose Estimation by Iterative Dense Fusion](https://mlsanity.com/paper/1901.04780/) (2019)
- [Deep Closest Point: Learning Representations for Point Cloud Registration](https://mlsanity.com/paper/1905.03304/) (2019)
- [PREDATOR: Registration of 3D Point Clouds with Low Overlap](https://mlsanity.com/paper/2011.13005/) (2020)
- [CosyPose: Consistent multi-view multi-object 6D pose estimation](https://mlsanity.com/paper/2008.08465/) (2020)
- [DeepIM: Deep Iterative Matching for 6D Pose Estimation](https://mlsanity.com/paper/1804.00175/) (2018)
- [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)
- [Deep Object Pose Estimation for Semantic Robotic Grasping of Household Objects](https://mlsanity.com/paper/1809.10790/) (2018)
- [PointNetLK: Robust & Efficient Point Cloud Registration using PointNet](https://mlsanity.com/paper/1903.05711/) (2019)
- [Deep Global Registration](https://mlsanity.com/paper/2004.11540/) (2020)
- [Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Robustness Verification](https://mlsanity.com/paper/2103.06624/) (2021)
- [Learning to Estimate 3D Human Pose and Shape from a Single Color Image](https://mlsanity.com/paper/1805.04092/) (2018)
- [Differentiation of Blackbox Combinatorial Solvers](https://mlsanity.com/paper/1912.02175/) (2019)
- [Pix2Pose: Pixel-Wise Coordinate Regression of Objects for 6D Pose Estimation](https://mlsanity.com/paper/1908.07433/) (2019)
- [T-LESS: An RGB-D Dataset for 6D Pose Estimation of Texture-less Objects](https://mlsanity.com/paper/1701.05498/) (2017)
- [BOP Challenge 2020 on 6D Object Localization](https://mlsanity.com/paper/2009.07378/) (2020)
- [Fast and Complete: Enabling Complete Neural Network Verification with Rapid and Massively Parallel Incomplete Verifiers](https://mlsanity.com/paper/2011.13824/) (2020)
- [RPM-Net: Robust Point Matching using Learned Features](https://mlsanity.com/paper/2003.13479/) (2020)

## Built on by (most cited first, 12 of 12)

- [Scalable Unseen Objects 6-DoF Absolute Pose Estimation with Robotic Integration](https://mlsanity.com/paper/2503.05578/) (2025)
- [CRISP: Object Pose and Shape Estimation with Test-Time Adaptation](https://mlsanity.com/paper/2412.01052/) (2024)
- [A Correct-and-Certify Approach to Self-Supervise Object Pose Estimators via Ensemble Self-Training](https://mlsanity.com/paper/2302.06019/) (2023)
- [Certifying Robustness of Learning-Based Keypoint Detection and Pose Estimation Methods](https://mlsanity.com/paper/2408.00117/) (2024)
- [Picasso: Holistic Scene Reconstruction with Physics-Constrained Sampling](https://mlsanity.com/paper/2602.08058/) (2026)
- [Test-Time Certifiable Self-Supervision to Bridge the Sim2Real Gap in Event-Based Satellite Pose Estimation](https://mlsanity.com/paper/2409.06240/) (2024)
- [Box Pose and Shape Estimation and Domain Adaptation for Large-Scale Warehouse Automation](https://mlsanity.com/paper/2507.00984/) (2025)
- [Correspondence-Free Fast and Robust Spherical Point Pattern Registration](https://mlsanity.com/paper/2508.02339/) (2025)
- [Enhancing Certifiable Semantic Robustness via Robust Pruning of Deep Neural Networks](https://mlsanity.com/paper/2510.00083/) (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 World Memory 3D Foundation Model for Scalable 3D Mapping, Localization, and Rendering](https://mlsanity.com/paper/2609.21502/) (2026)

## Abstract (arXiv)

We consider a certifiable object pose estimation problem, where -- given a partial point cloud of an object -- the goal is to not only estimate the object pose, but also to provide a certificate of correctness for the resulting estimate. Our first contribution is a general theory of certification for end-to-end perception models. In particular, we introduce the notion of zeta-correctness, which bounds the distance between an estimate and the ground truth. We show that zeta-correctness can be assessed by implementing two certificates: (i) a certificate of observable correctness, that asserts if the model output is consistent with the input data and prior information, (ii) a certificate of non-degeneracy, that asserts whether the input data is sufficient to compute a unique estimate. Our second contribution is to apply this theory and design a new learning-based certifiable pose estimator. We propose C-3PO, a semantic-keypoint-based pose estimation model, augmented with the two certificates, to solve the certifiable pose estimation problem. C-3PO also includes a keypoint corrector, implemented as a differentiable optimization layer, that can correct large detection errors (e.g. due to the sim-to-real gap). Our third contribution is a novel self-supervised training approach that uses our certificate of observable correctness to provide the supervisory signal to C-3PO during training. In it, the model trains only on the observably correct input-output pairs, in each training iteration. As training progresses, we see that the observably correct input-output pairs grow, eventually reaching near 100% in many cases. Our experiments show that (i) standard semantic-keypoint-based methods outperform more recent alternatives, (ii) C-3PO further improves performance and significantly outperforms all the baselines, and (iii) C-3PO's certificates are able to discern correct pose estimates.