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.

通过在 2D 像素空间上使用平滑分布，而不是在 3D 物理空间中进行采样，增强了鲁棒性认证的效率，并在融合车辆运动空间的均匀分区技术的基础上，实现了对 3D-2D 投影转换的鲁棒性认证。