Deep Manifold Attack on Point Clouds via Parameter Plane Stretching

Adversarial attack on point clouds plays a vital role in evaluating and improving the adversarial robustness of 3D deep learning models. Existing attack methods are mainly applied by point perturbation in a non-manifold manner. In this paper, we formulate a novel manifold attack, which deforms the underlying 2-manifold surfaces via parameter plane stretching to generate adversarial point clouds. First, we represent the mapping between the parameter plane and underlying surface using generative-based networks. Second, the stretching is learned in the 2D parameter domain such that the generated 3D point cloud fools a pretrained classifier with minimal geometric distortion. Extensive experiments show that adversarial point clouds generated by manifold attack are smooth, undefendable and transferable, and outperform those samples generated by the state-of-the-art non-manifold ones.