Curvature-Invariant Adversarial Attacks for 3D Point Clouds

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Abstract
Imperceptibility is one of the crucial requirements for adversarial examples. Previous adversarial attacks on 3D point cloud recognition suffer from noticeable outliers, resulting in low imperceptibility. We think that the drawbacks can be alleviated via taking the local curvature of the point cloud into consideration. Existing approaches introduce the local geometry distance into the attack objective function. However, their definition of the local geometry distance neglects different perceptibility of distortions along different directions. In this paper, we aim to enhance the imperceptibility of adversarial attacks on 3D point cloud recognition by better preserving the local curvature of the original 3D point clouds. To this end, we propose the Curvature-Invariant Method (CIM), which directly regularizes the back-propagated gradient during the generation of adversarial point clouds based on two assumptions. Specifically, we first decompose the back-propagated gradients into the tangent plane and the normal direction. Then we directly reduce the gradient along the large curvature direction on the tangent plane and only keep the gradient along the negative normal direction. Comprehensive experimental comparisons confirm the superiority of our approach. Notably, our strategy can achieve 7.2% and 14.5% improvements in Hausdorff distance and Gaussian curvature measurements of the imperceptibility.

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