Lipschitz Optimization for Formal Verification of Homographies
Quick Take
This paper presents a novel formal verification method for robustness against 3D motion perturbations in vision neural networks, achieving up to 89% speedup and 7% tighter bounds compared to previous methods. It addresses a critical gap in safety-critical applications like autonomous driving and healthcare by validating projective geometry transforms without complex simulations.
Key Points
- Introduces formal verification for robustness against 3D camera motion perturbations.
- Achieves up to 89% speedup and 7% tighter bounds over prior work.
- Validates projective geometry transforms without complex simulations.
- Evaluated on VNN-COMP benchmark, revealing weaknesses to projective perturbations.
- Demonstrates real-world application on a safety-critical runway classifier.
Article Content
From source RSS / original summaryarXiv:2605. 23203v1 Announce Type: new Abstract: The adoption of vision neural networks in regulated industries requires formal robustness guarantees, especially in safety-critical domains such as healthcare, autonomous vehicles, and aerospace. However, current approaches are confined to incomplete statistical verification or robustness to $\ell_p$-norm and affine transforms, which cover only a narrow subset of perturbations to the image formation process.
In particular, robustness to camera motion remains an open problem despite being key to deploy many vision applications. We present a formal verification approach that targets robustness against 3D motion perturbations of the capturing camera. We first establish a closed-form mapping from camera pose to pixel values.
By analyzing the continuity properties of the resulting homographies, we show that recent work on Lipschitz optimization and piecewise continuity can be extended to derive tight linear bounds on perturbed pixel values. Our approach applies to scenes with predominantly planar structure, such as ground planes in augmented reality, road markings and traffic signs in autonomous driving, or planar workspaces in robotic manipulation.
This enables the first formal verification of projective geometry transforms, without complex simulation, surrogate networks, or explicit image-formation models. We validate our implementation and show up to 89% speedup and 7% tighter bounds over prior work. We then evaluate our method on the VNN-COMP benchmark and reveal systematic weaknesses to projective perturbations.
Finally, we demonstrate a real-world case study on a safety-critical runway classifier, highlighting practical vulnerabilities to camera motion, and addressing a key challenge in the certification of learned models. Data and code are publicly available at https://github. com/jeangud/homography-verification .
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