Lipschitz Optimization for Formal Verification of Homographies
Existing methods struggle to formally verify the robustness of vision neural networks under 3D camera motion, particularly homographic transformations. This work presents the first closed-form mapping from camera pose to pixel values, enabling formal verification of projective geometry without relying on simulation, surrogate networks, or explicit imaging models. By integrating Lipschitz optimization with piecewise continuity analysis, we derive tight linear bounds on perturbed pixels. Our approach achieves up to an 89% speedup and a 7% improvement in bound tightness compared to prior methods. Evaluation on the VNN-COMP benchmark reveals systematic vulnerabilities of models to projective perturbations, and a case study on runway classifiers demonstrates tangible safety risks in real-world applications.