Transform Coding for Point Clouds Using a Gaussian Process Model

We propose using stationary Gaussian processes (GPs) to model the statistics of the signal on points in a point cloud, which can be considered samples of a GP at the positions of the points. Furthermore, we propose using Gaussian process transforms (GPTs), which are Karhunen-Loève transforms of the GP, as the basis of transform coding of the signal. Focusing on colored 3D point clouds, we propose a transform coder that breaks the point cloud into blocks, transforms the blocks using GPTs, and entropy codes the quantized coefficients. The GPT for each block is derived from both the covariance function of the GP and the locations of the points in the block, which are separately encoded. The covariance function of the GP is parameterized, and its parameters are sent as side information. The quantized coefficients are sorted by the eigenvalues of the GPTs, binned, and encoded using an arithmetic coder with bin-dependent Laplacian models, whose parameters are also sent as side information. Results indicate that transform coding of 3D point cloud colors using the proposed GPT and entropy coding achieves superior compression performance on most of our data sets.