IoUCert: Robustness Verification for Anchor-based Object Detectors

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. As a fundamental step towards verifying complete detection pipelines, we introduce IoUCert, a novel formal verification framework designed specifically to overcome these core mathematical bottlenecks. By isolating the object localisation task in single-object settings, we propose a coordinate transformation that circumvents precision-degrading relaxations of non-linear box prediction functions. This approach allows us to optimise bounds directly with respect to anchor box offsets, enabling a novel Interval Bound Propagation method that derives optimal IoU bounds. We demonstrate that IoUCert enables, for the first time, the robustness verification of foundational, anchor-based architectures including tractable variants of SSD, YOLOv2, and YOLOv3 against various input perturbations, providing a rigorous theoretical basis for future end-to-end detector verification.