Manifold Constraints for Imperceptible Adversarial Attacks on Point Clouds

Adversarial attacks on 3D point clouds often exhibit unsatisfactory imperceptibility, which primarily stems from the disregard for manifold-aware distortion, i.e., distortion of the underlying 2-manifold surfaces. In this paper, we develop novel manifold constraints to reduce such distortion, aiming to enhance the imperceptibility of adversarial attacks on 3D point clouds. Specifically, we construct a bijective manifold mapping between point clouds and a simple parameter shape using an invertible auto-encoder. Consequently, manifold-aware distortion during attacks can be captured within the parameter space. By enforcing manifold constraints that preserve local properties of the parameter shape, manifold-aware distortion is effectively mitigated, ultimately leading to enhanced imperceptibility. Extensive experiments demonstrate that integrating manifold constraints into conventional adversarial attack solutions yields superior imperceptibility, outperforming the state-of-the-art methods.