Imperceptible adversarial attacks on 3D point clouds rely on effective constraints. While manifold constraints have notable advantages over Euclidean ones, the global parameterization used in current methods often fails to fully preserve manifold properties. In this paper, we propose to constrain lattice-based barycentric coordinates during attacks from a local parametric perspective to ensure imperceptibility. Specifically, we utilize a permutohedral lattice to partition point clouds into multiple cells, and then extract barycentric coordinates for each point within these cells, forming a local parametric representation of the point clouds. By enforcing local parametric constraints that minimize the displacement of barycentric coordinates, we largely preserve the manifold properties, ultimately leading to improved imperceptibility. Extensive experiments validate that integrating these local parametric constraints into conventional adversarial attacks yields superior imperceptibility, outperforming state-of-the-art methods.

Adversarial attacks on point clouds are crucial for assessing and improving the adversarial robustness of 3D deep learning models. Traditional solutions strictly limit point displacement during attacks, making it challenging to balance imperceptibility with adversarial effectiveness. In this paper, we attribute the inadequate imperceptibility of adversarial attacks on point clouds to deviations from the underlying surface. To address this, we introduce a novel point-to-surface (P2S) field that adjusts adversarial perturbation directions by dragging points back to their original underlying surface. Specifically, we use a denoising network to learn the gradient field of the logarithmic density function encoding the shape’s surface, and apply a distance-aware adjustment to perturbation directions during attacks, thereby enhancing imperceptibility. Extensive experiments show that adversarial attacks guided by our P2S field are more imperceptible, outperforming state-of-the-art methods.