[Paper] Uncertainty Quantification for Visual Object Pose Estimation

Source: arXiv - 2511.21666v1

Overview

This paper tackles a surprisingly overlooked problem in visual robotics: how to rigorously quantify the uncertainty of a 3‑D object pose estimated from a single camera. By moving beyond ad‑hoc heuristics and restrictive Gaussian assumptions, the authors present a mathematically sound way to bound pose errors using only pixel‑level noise guarantees on detected keypoints. The result is a practical tool—called SLUE—that delivers tight, provably correct ellipsoidal uncertainty regions for both translation and orientation.

Key Contributions

• Distribution‑free pose uncertainty bounds that require only high‑probability pixel noise limits on 2‑D semantic keypoints.
• SLUE (S‑Lemma Uncertainty Estimation): a convex optimization formulation that computes a single ellipsoidal bound guaranteed to contain the true pose with the prescribed confidence.
• Sum‑of‑Squares (SOS) hierarchy extending SLUE to obtain progressively tighter bounds, provably converging to the minimum‑volume ellipsoid for the given constraints.
• Closed‑form projection of the ellipsoidal bound into separate translation and axis‑angle orientation bounds, making the output directly usable for downstream planners and controllers.
• Extensive empirical validation on two benchmark pose‑estimation datasets and a real‑world drone‑tracking experiment, showing markedly smaller translation bounds than prior methods while maintaining competitive orientation bounds.
• Open‑source release of the implementation (MIT‑SPARK/PoseUncertaintySets), facilitating immediate adoption.

Methodology

1. Keypoint Noise Model – The authors assume that each detected 2‑D semantic keypoint lies within a known pixel‑radius with high probability (e.g., 99 %). No distributional shape (Gaussian, Laplace, etc.) is required.
2. Implicit Pose Constraints – These pixel bounds translate into a set of non‑convex quadratic constraints on the 6‑DoF pose (3 translation + 3 rotation parameters).
3. S‑Lemma Relaxation – By invoking the classic S‑lemma from control theory, the non‑convex constraint set is relaxed to a convex semidefinite program (SDP) that searches for the smallest ellipsoid enclosing all feasible poses.
4. Minimum‑Volume Ellipsoid Approximation – The SDP solves a surrogate of the minimum‑volume ellipsoid problem, yielding an ellipsoidal uncertainty region that is guaranteed to contain the true pose with the chosen confidence level.
5. SOS Hierarchy (Optional) – For applications demanding tighter bounds, the authors formulate a hierarchy of sum‑of‑squares programs that iteratively tighten the ellipsoid, converging to the true minimum‑volume solution.
6. Projection to Translation & Orientation – The final ellipsoid is analytically split into independent bounds on the 3‑D translation vector and the axis‑angle representation of rotation, which are the formats most robotics stacks expect.

Results & Findings

• Translation Bounds: Across the LINEMOD and YCB‑Video datasets, SLUE reduced the average translation bound volume by 30‑45 % compared to the state‑of‑the‑art Monte‑Carlo and covariance‑based methods.
• Orientation Bounds: The angular uncertainty (measured in degrees) remained on par with existing techniques, confirming that the tighter translation bounds do not come at the expense of rotation accuracy.
• Real‑World Drone Tracking: In a live indoor flight test, the SLUE‑derived bounds allowed a downstream trajectory planner to maintain a safe clearance margin with ≤ 5 % over‑conservatism, whereas a naïve Gaussian bound required a ≈ 20 % safety margin.
• Computation: Solving the base SLUE SDP takes ≈ 15 ms on a modern laptop CPU for a typical 8‑keypoint object, well within real‑time budgets. The SOS refinement adds a modest overhead (≈ 30 ms for the first refinement level).

Practical Implications

• Robust Motion Planning – Planners can now ingest statistically guaranteed pose uncertainty ellipsoids, enabling risk‑aware path generation without resorting to overly conservative padding.
• Safe Human‑Robot Interaction – In collaborative settings, tighter translation bounds translate directly into smaller safety zones, increasing workspace efficiency while preserving safety certifications.
• Autonomous Drone & UAV Operations – Accurate pose uncertainty is critical for visual‑servoing and obstacle avoidance; SLUE’s real‑time performance makes it a drop‑in upgrade for existing vision‑based state estimators.
• Sim‑to‑Real Transfer – Simulation pipelines that generate synthetic keypoint detections can embed realistic pixel‑noise budgets, producing uncertainty bounds that faithfully reflect real‑world sensor noise.
• Modular Integration – Because SLUE only needs keypoint detections and pixel‑noise radii, it can be paired with any upstream pose estimator (PnP, deep‑learning keypoint regressors, etc.) without modifying the estimator’s internals.

Limitations & Future Work

• Dependence on Accurate Noise Bounds – The guarantee holds only if the supplied pixel‑noise radii truly bound the detection errors with the claimed confidence; overly optimistic bounds will break the guarantee.
• Scalability to Very High‑DoF Objects – While the base SDP scales well, the SOS hierarchy can become computationally heavy for objects with many keypoints or when higher‑order relaxations are needed.
• Monocular Assumption – The current formulation is limited to single‑camera setups; extending the theory to stereo or multi‑view configurations is an open direction.
• Dynamic Objects – The method treats pose as static during the estimation window; incorporating temporal dynamics (e.g., motion models) could tighten bounds further.

The authors plan to explore adaptive noise‑bound estimation, real‑time SOS updates, and integration with probabilistic motion planners in upcoming work.

Authors

• Lorenzo Shaikewitz
• Charis Georgiou
• Luca Carlone

Paper Information

• arXiv ID: 2511.21666v1
• Categories: cs.RO, cs.CV
• Published: November 26, 2025
• PDF: Download PDF