# Uncertainty Quantification for Visual Object Pose Estimation: S-Lemma Ellipsoidal Bounds

arXiv: https://arxiv.org/abs/2511.21666 · HTML: https://mlsanity.com/paper/2511.21666/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 64 references that are in the map.
- First posted on arXiv 26 Nov 2025.

## Builds on (most cited first, 28 of 28)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [PoseCNN: A Convolutional Neural Network for 6D Object Pose Estimation in Cluttered Scenes](https://mlsanity.com/paper/1711.00199/) (2017)
- [FoundationPose: Unified 6D Pose Estimation and Tracking of Novel Objects](https://mlsanity.com/paper/2312.08344/) (2023)
- [BOP: Benchmark for 6D Object Pose Estimation](https://mlsanity.com/paper/1808.08319/) (2018)
- [BOP Challenge 2020 on 6D Object Localization](https://mlsanity.com/paper/2009.07378/) (2020)
- [EPOS: Estimating 6D Pose of Objects with Symmetries](https://mlsanity.com/paper/2004.00605/) (2020)
- [Theoretical Foundations of Conformal Prediction](https://mlsanity.com/paper/2411.11824/) (2024)
- [SurfEmb: Dense and Continuous Correspondence Distributions for Object Pose Estimation with Learnt Surface Embeddings](https://mlsanity.com/paper/2111.13489/) (2021)
- [PoseRBPF: A Rao-Blackwellized Particle Filter for 6D Object Pose Tracking](https://mlsanity.com/paper/1905.09304/) (2019)
- [se(3)-TrackNet: Data-driven 6D Pose Tracking by Calibrating Image Residuals in Synthetic Domains](https://mlsanity.com/paper/2007.13866/) (2020)
- [Deep Learning-Based Object Pose Estimation: A Comprehensive Survey](https://mlsanity.com/paper/2405.07801/) (2024)
- [Object Pose Estimation with Statistical Guarantees: Conformal Keypoint Detection and Geometric Uncertainty Propagation](https://mlsanity.com/paper/2303.12246/) (2023)
- [A Quaternion-based Certifiably Optimal Solution to the Wahba Problem with Outliers](https://mlsanity.com/paper/1905.12536/) (2019)
- [Robust 6D Object Pose Estimation by Learning RGB-D Features](https://mlsanity.com/paper/2003.00188/) (2020)
- [Keypoint-Based Category-Level Object Pose Tracking from an RGB Sequence with Uncertainty Estimation](https://mlsanity.com/paper/2205.11047/) (2022)
- [Learning Orientation Distributions for Object Pose Estimation](https://mlsanity.com/paper/2007.01418/) (2020)
- [Fast Uncertainty Quantification for Deep Object Pose Estimation](https://mlsanity.com/paper/2011.07748/) (2020)
- [DROP: Dexterous Reorientation via Online Planning](https://mlsanity.com/paper/2409.14562/) (2024)
- [Uncertainty Quantification with Deep Ensembles for 6D Object Pose Estimation](https://mlsanity.com/paper/2403.07741/) (2024)
- [Semantic keypoint-based pose estimation from single RGB frames](https://mlsanity.com/paper/2204.05864/) (2022)
- [CLOSURE: Fast Quantification of Pose Uncertainty Sets](https://mlsanity.com/paper/2403.09990/) (2024)
- [CS-TSSOS: Correlative and term sparsity for large-scale polynomial optimization](https://mlsanity.com/paper/2005.02828/) (2020)
- [Uncertainty Quantification of Set-Membership Estimation in Control and Perception: Revisiting the Minimum Enclosing Ellipsoid](https://mlsanity.com/paper/2311.15962/) (2023)
- [A Certifiable Algorithm for Simultaneous Shape Estimation and Object Tracking](https://mlsanity.com/paper/2406.16837/) (2024)
- [A generalization of L"owner-John's ellipsoid theorem](https://mlsanity.com/paper/1302.1056/) (2013)
- [Deep learning for 3D Object Detection and Tracking in Autonomous Driving: A Brief Survey](https://mlsanity.com/paper/2311.06043/) (2023)

## Built on by (most cited first, 1 of 1)

- [Detecting Pose Estimation Failures via Keypoint Self-Consistency](https://mlsanity.com/paper/2608.03516/) (2026)

## Abstract (arXiv)

Quantifying the uncertainty of an object's pose estimate is essential for robust control and planning. Although pose estimation is a well-studied robotics problem, attaching statistically rigorous uncertainty is not well understood without strict distributional assumptions. We develop distribution-free pose uncertainty bounds about a given pose estimate in the monocular setting. Our pose uncertainty only requires high probability noise bounds on pixel detections of 2D semantic keypoints on a known object. This noise model induces an implicit, non-convex set of pose uncertainty constraints. Our key contribution is SLUE (S-Lemma Uncertainty Estimation), a convex program to reduce this set to a single ellipsoidal uncertainty bound that is guaranteed to contain the true object pose with high probability. SLUE solves a relaxation of the minimum volume bounding ellipsoid problem inspired by the celebrated S-lemma. It requires no initial guess of the bound's shape or size and is guaranteed to contain the true object pose with high probability. For tighter uncertainty bounds at the same confidence, we extend SLUE to a sum-of-squares relaxation hierarchy which is guaranteed to converge to the minimum volume ellipsoidal uncertainty bound for a given set of keypoint constraints. We show this pose uncertainty bound can easily be projected to independent translation and axis-angle orientation bounds. We evaluate SLUE on two pose estimation datasets and a real-world drone tracking scenario. Compared to prior work, SLUE generates substantially smaller translation bounds and competitive orientation bounds. We release code at https://github.com/MIT-SPARK/PoseUncertaintySets.