3D dynamic point clouds provide a natural discrete representation of real-world objects or scenes in motion, with a wide range of applications in immersive telepresence, autonomous driving, surveillance, \etc. Nevertheless, dynamic point clouds are often perturbed by noise due to hardware, software or other causes. While a plethora of methods have been proposed for static point cloud denoising, few efforts are made for the denoising of dynamic point clouds, which is quite challenging due to the irregular sampling patterns both spatially and temporally. In this paper, we represent dynamic point clouds naturally on spatial-temporal graphs, and exploit the temporal consistency with respect to the underlying surface (manifold). In particular, we define a manifold-to-manifold distance and its discrete counterpart on graphs to measure the variation-based intrinsic distance between surface patches in the temporal domain, provided that graph operators are discrete counterparts of functionals on Riemannian manifolds. Then, we construct the spatial-temporal graph connectivity between corresponding surface patches based on the temporal distance and between points in adjacent patches in the spatial domain. Leveraging the initial graph representation, we formulate dynamic point cloud denoising as the joint optimization of the desired point cloud and underlying graph representation, regularized by both spatial smoothness and temporal consistency. We reformulate the optimization and present an efficient algorithm. Experimental results show that the proposed method significantly outperforms independent denoising of each frame from state-of-the-art static point cloud denoising approaches, on both Gaussian noise and simulated LiDAR noise.

中文翻译：

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通过流形到流形距离的动态点云降噪

3D 动态点云提供了真实世界物体或运动场景的自然离散表示，在沉浸式远程呈现、自动驾驶、监控等方面具有广泛的应用。然而，由于硬件、软件或其他原因，动态点云经常受到噪声的干扰。虽然已经提出了大量的静态点云去噪方法，但对动态点云去噪的努力很少，由于空间和时间上的不规则采样模式，这非常具有挑战性。在本文中，我们在时空图上自然地表示动态点云，并利用相对于下层表面（流形）的时间一致性。特别是，我们在图上定义了流形到流形的距离及其离散对应物，以测量时域中表面块之间基于变化的内在距离，前提是图算子是黎曼流形上函数的离散对应物。然后，我们基于时间距离构建相应表面补丁之间以及空间域中相邻补丁中点之间的时空图连通性。利用初始图形表示，我们将动态点云去噪制定为所需点云和底层图形表示的联合优化，并通过空间平滑度和时间一致性进行正则化。我们重新制定优化并提出一种有效的算法。