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With the increasing attention in various 3D safety-critical applications,point cloud learning models have been shown to be vulnerable to adversarialattacks. Although existing 3D attack methods achieve high success rates, theydelve into the data space with point-wise perturbation, which may neglect thegeometric characteristics. Instead, we propose point cloud attacks from a newperspective -- the graph spectral domain attack, aiming to perturb graphtransform coefficients in the spectral domain that corresponds to varyingcertain geometric structure. Specifically, leveraging on graph signalprocessing, we first adaptively transform the coordinates of points onto thespectral domain via graph Fourier transform (GFT) for compact representation.Then, we analyze the influence of different spectral bands on the geometricstructure, based on which we propose to perturb the GFT coefficients via alearnable graph spectral filter. Considering the low-frequency componentsmainly contribute to the rough shape of the 3D object, we further introduce alow-frequency constraint to limit perturbations within imperceptiblehigh-frequency components. Finally, the adversarial point cloud is generated bytransforming the perturbed spectral representation back to the data domain viathe inverse GFT. Experimental results demonstrate the effectiveness of theproposed attack in terms of both the imperceptibility and attack success rates.

Point Cloud Attacks in Graph Spectral Domain: When 3D Geometry Meets Graph Signal Processing