Pixel-wise Smoothing for Certified Robustness against Camera Motion Perturbations

TL;DR

This paper introduces a novel pixel-wise smoothing framework for efficiently certifying robustness of visual models against camera motion perturbations, significantly reducing computational costs while maintaining high certification accuracy.

Contribution

It proposes a new pixel-wise smoothing approach that eliminates the need for extensive camera motion sampling in robustness certification.

Findings

Achieves approximately 80% certified accuracy.

Uses only 30% of the projected image frames.

Significantly improves certification efficiency.

Abstract

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.