Explicitly Perceiving and Preserving the Local Geometric Structures for 3D Point Cloud Attack

Deep learning models for point clouds have shown to be vulnerable to adversarial attacks, which have received increasing attention in various safety-critical applications such as autonomous driving, robotics, and surveillance. Existing 3D attack methods generally employ global distance losses to implicitly constrain the point-wise perturbations for optimization. However, these simple losses are quite difficult to accurately measure and restrict the proper 3D geometry as point clouds are highly structured. Although few recent works try to exploit additional shape-aware surface knowledge to globally constrain the point position, they still fail to preserve the detailed point-to-point geometric dependency in different local regions. To this end, in this paper, we propose a novel Multi-grained Geometry-aware Attack (MGA), which explicitly captures the local topology characteristics in different 3D regions for adversarial constraint. Specifically, we first develop multi-scale local spectral filter banks adapting to different 3D object shapes to explore potential geometric structures in different local regions. Considering that objects may contain complex geometries, we then extend each filter bank into multi-layer ones to gradually capture different-granularity topology contexts of the same region in a coarse-to-fine manner. Hence, the focused local geometries will be highlighted in the coefficients calculated by the filtering process. At last, by restricting these coefficients between benign and adversarial samples, our MGA is able to properly measure and preserve the detailed geometry contexts in the whole 3D object with trivial perturbations. Experiments demonstrate that our attack can achieve superior performance on various 3D classification models, with satisfying adversarial imperceptibility and strong resistance to different defense methods.