HHA: Hierarchical Hyperbolic Constraints for Imperceptible Point Cloud Attacks

Adversarial attacks on point clouds require effective constraints to ensure imperceptibility. However, existing methods often overlook the intrinsic hierarchical organization of 3D shapes, thereby limiting their ability to preserve structural coherence. In this paper, we propose HHA, a novel framework that generates hierarchy-aware adversarial perturbations by leveraging hyperbolic geometry. HHA first decomposes the input point cloud into semantic and geometric substructures to capture its multi-scale organization. Then, each substructure is embedded into hyperbolic space, where localized constraints limit distortion and maintain hierarchical consistency. This hyperbolic regularization keeps perturbations aligned with the underlying structure and thereby enhances imperceptibility. Extensive experiments validate that HHA produces adversarial point clouds with improved structural coherence and imperceptibility, outperforming state-of-the-art methods.