  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.
