CertOD: Class-Conditional Pair Certificates for Matched Object Detections in Autonomous Driving

Object detection combines a discrete class and a continuous box. Certifying both under class-specific error budgets requires a joint guarantee conditional on the true class, which is unknown at inference, so selecting a geometric margin by the detector's possibly incorrect top-1 label does not establish that guarantee. CertOD instead emits per-class pair certificates: one calibrated box for each surviving class hypothesis. Under within-class exchangeability it provides finite-sample coverage of the event that the true class is retained and its associated box contains the object, at each class's prescribed level for matched detections of certifiable classes. Against a matched single-box control, pairs reduce retained true-class pedestrian area by $6.8\%$ (median) and $22.2\%$ (p90) on BDD100K at a $0.47\%$ exclusion rate; CODA2022 reproduces the tail benefit ($6.6\%$–$35.6\%$ across four common classes). The gain requires a consumer that retains class–box associations: the smallest axis-aligned envelope of all pairs is exactly the conservative single box. Supremum scoring lowers the finite-quantile sample threshold roughly fourfold against coordinate Bonferroni without shrinking pedestrian boxes, and unified joint scoring is larger in median area wherever the class set is held fixed. We also report three boundaries: $33.3\%$ of BDD100K pedestrians match no proposal, zero-shot transfer of BDD thresholds to CODA2022 misses all eight tested score–class targets, and the repair weakens as the detector sharpens—on the misclassified slices its joint coverage falls from $67.9\%$ to $12.7\%$ across four backbones, because a better classifier yields smaller class sets.