Distortion quantification of point clouds plays a stealth, yet vital role in a wide range of human and machine perception tasks. For human perception tasks, a distortion quantification can substitute subjective experiments to guide 3D visualization; while for machine perception tasks, a distortion quantification can work as a loss function to guide the training of deep neural networks for unsupervised learning tasks. To handle a variety of demands in many applications, a distortion quantification needs to be distortion discriminable, differentiable, and have a low computational complexity. Currently, however, there is a lack of a general distortion quantification that can satisfy all three conditions. To fill this gap, this work proposes multiscale potential energy discrepancy (MPED), a distortion quantification to measure point cloud geometry and color difference. By evaluating at various neighborhood sizes, the proposed MPED achieves global-local tradeoffs, capturing distortion in a multiscale fashion. Extensive experimental studies validate MPEDs superiority for both human and machine perception tasks.
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