  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 MPED's superiority
for both human and machine perception tasks.
