  We consider the attributes of a point cloud as samples of a vector-valued
volumetric function at discrete positions. To compress the attributes given the
positions, we compress the parameters of the volumetric function. We model the
volumetric function by tiling space into blocks, and representing the function
over each block by shifts of a coordinate-based, or implicit, neural network.
Inputs to the network include both spatial coordinates and a latent vector per
block. We represent the latent vectors using coefficients of the
region-adaptive hierarchical transform (RAHT) used in the MPEG geometry-based
point cloud codec G-PCC. The coefficients, which are highly compressible, are
rate-distortion optimized by back-propagation through a rate-distortion
Lagrangian loss in an auto-decoder configuration. The result outperforms RAHT
by 2--4 dB. This is the first work to compress volumetric functions represented
by local coordinate-based neural networks. As such, we expect it to be
applicable beyond point clouds, for example to compression of high-resolution
neural radiance fields.
