While formal robustness verification has seen significant success in image classification, scaling these guarantees to object detection remains notoriously difficult due to complex non-linear coordinate transformations and Intersection-over-Union (IoU) metrics. We introduce {\sc \sf IoUCert}, a novel formal verification framework designed specifically to overcome these bottlenecks in foundational anchor-based object detection architectures. Focusing on the object localisation component in single-object settings, we propose a coordinate transformation that enables our algorithm to circumvent precision-degrading relaxations of non-linear box prediction functions. This allows us to optimise bounds directly with respect to the anchor box offsets which enables a novel Interval Bound Propagation method that derives optimal IoU bounds. We demonstrate that our method enables, for the first time, the robustness verification of realistic, anchor-based models including SSD, YOLOv2, and YOLOv3 variants against various input perturbations.

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