← 研踪 PaperTrailCVF · CVPR 2026:cvf:77fff41c6b5684ff7f6cb39684eb08db · 记录 #1
Lipschitz Optimization for Formal Verification of Homographies
来源日期（仅到年份） 2026
来源记录日期 2026
雷达观测 2026-11-02 00:07
摘要
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 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. Our implementation achieves up to 89% speedup and 7% tighter bounds over prior work. We 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, addressing a key challenge in the certification of learned models. Data and code are available at https://github.com/jeangud/homography-verification.
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记录 #1 · 2026 · 最新观测版本
Lipschitz Optimization for Formal Verification of Homographies
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 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. Our implementation achieves up to 89% speedup and 7% tighter bounds over prior work. We 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, addressing a key challenge in the certification of learned models. Data and code are available at https://github.com/jeangud/homography-verification.
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