Exploring the Devil in Graph Spectral Domain for 3D Point Cloud Attacks

3D dynamic point clouds provide a discrete representation of real-world objects or scenes in motion, which have been widely applied in immersive telepresence, autonomous driving, surveillance, \textit{etc}. However, point clouds acquired from sensors are usually perturbed by noise, which affects downstream tasks such as surface reconstruction and analysis. Although many efforts have been made for static point cloud denoising, few works address dynamic point cloud denoising. In this paper, we propose a novel gradient-based dynamic point cloud denoising method, exploiting the temporal correspondence for the estimation of gradient fields -- also a fundamental problem in dynamic point cloud processing and analysis. The gradient field is the gradient of the log-probability function of the noisy point cloud, based on which we perform gradient ascent so as to converge each point to the underlying clean surface. We estimate the gradient of each surface patch by exploiting the temporal correspondence, where the temporally corresponding patches are searched leveraging on rigid motion in classical mechanics. In particular, we treat each patch as a rigid object, which moves in the gradient field of an adjacent frame via force until reaching a balanced state, i.e., when the sum of gradients over the patch reaches 0. Since the gradient would be smaller when the point is closer to the underlying surface, the balanced patch would fit the underlying surface well, thus leading to the temporal correspondence. Finally, the position of each point in the patch is updated along the direction of the gradient averaged from corresponding patches in adjacent frames. Experimental results demonstrate that the proposed model outperforms state-of-the-art methods.