  This paper presents a novel point cloud compression method COT-PCC by
formulating the task as a constrained optimal transport (COT) problem. COT-PCC
takes the bitrate of compressed features as an extra constraint of optimal
transport (OT) which learns the distribution transformation between original
and reconstructed points. Specifically, the formulated COT is implemented with
a generative adversarial network (GAN) and a bitrate loss for training. The
discriminator measures the Wasserstein distance between input and reconstructed
points, and a generator calculates the optimal mapping between distributions of
input and reconstructed point cloud. Moreover, we introduce a learnable
sampling module for downsampling in the compression procedure. Extensive
results on both sparse and dense point cloud datasets demonstrate that COT-PCC
outperforms state-of-the-art methods in terms of both CD and PSNR metrics.
Source codes are available at \url{https://github.com/cognaclee/PCC-COT}.
