In recent years, computer vision has made remarkable advancements in autonomous driving and robotics. However, it has been observed that deep learning-based visual perception models lack robustness when faced with camera motion perturbations. The current certification process for assessing robustness is costly and time-consuming due to the extensive number of image projections required for Monte Carlo sampling in the 3D camera motion space. To address these challenges, we present a novel, efficient, and practical framework for certifying the robustness of 3D-2D projective transformations against camera motion perturbations. Our approach leverages a smoothing distribution over the 2D pixel space instead of in the 3D physical space, eliminating the need for costly camera motion sampling and significantly enhancing the efficiency of robustness certifications. With the pixel-wise smoothed classifier, we are able to fully upper bound the projection errors using a technique of uniform partitioning in camera motion space. Additionally, we extend our certification framework to a more general scenario where only a single-frame point cloud is required in the projection oracle. This is achieved by deriving Lipschitz-based approximated partition intervals. Through extensive experimentation, we validate the trade-off between effectiveness and efficiency enabled by our proposed method. Remarkably, our approach achieves approximately 80% certified accuracy while utilizing only 30% of the projected image frames.

A vast literature shows that the learning-based visual perception model is sensitive to adversarial noises, but few works consider the robustness of robotic perception models under widely-existing camera motion perturbations. To this end, we study the robustness of the visual perception model under camera motion perturbations to investigate the influence of camera motion on robotic perception. Specifically, we propose a motion smoothing technique for arbitrary image classification models, whose robustness under camera motion perturbations could be certified. The proposed robustness certification framework based on camera motion smoothing provides tight and scalable robustness guarantees for visual perception modules so that they are applicable to wide robotic applications. As far as we are aware, this is the first work to provide robustness certification for the deep perception module against camera motions, which improves the trustworthiness of robotic perception. A realistic indoor robotic dataset with a dense point cloud map for the entire room, MetaRoom, is introduced for the challenging certifiable robust perception task. We conduct extensive experiments to validate the certification approach via motion smoothing against camera motion perturbations. Our framework guarantees the certified accuracy of 81.7% against camera translation perturbation along depth direction within -0.1m ~ 0.1m. We also validate the effectiveness of our method on the real-world robot by conducting hardware experiments on the robotic arm with an eye-in-hand camera. The code is available at https://github.com/HanjiangHu/camera-motion-smoothing.