  Due to the diverse sparsity, high dimensionality, and large temporal
variation of dynamic point clouds, it remains a challenge to design an
efficient point cloud compression method. We propose to code the geometry of a
given point cloud by learning a neural volumetric field. Instead of
representing the entire point cloud using a single overfit network, we divide
the entire space into small cubes and represent each non-empty cube by a neural
network and an input latent code. The network is shared among all the cubes in
a single frame or multiple frames, to exploit the spatial and temporal
redundancy. The neural field representation of the point cloud includes the
network parameters and all the latent codes, which are generated by using
back-propagation over the network parameters and its input. By considering the
entropy of the network parameters and the latent codes as well as the
distortion between the original and reconstructed cubes in the loss function,
we derive a rate-distortion (R-D) optimal representation. Experimental results
show that the proposed coding scheme achieves superior R-D performances
compared to the octree-based G-PCC, especially when applied to multiple frames
of a point cloud video. The code is available at
https://github.com/huzi96/NVFPCC/.
