  Deep learning-based visual perception models lack robustness when faced with
camera motion perturbations in practice. 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. 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. The code is available at
https://github.com/HanjiangHu/pixel-wise-smoothing.
