Volumetric 3d Point Cloud Attribute Compression: Learned Polynomial Bilateral Filter for Prediction

We extend a previous study on 3D point cloud attribute compression scheme that uses a volumetric approach: given a target volumetric attribute function f : ℝ
³
↦ ℝ, we quantize and encode parameters θ that characterize f at the encoder, for reconstruction ${f_{\hat \theta }}({\mathbf{x}})$ at known 3D points x at the decoder. Specifically, parameters $\hat \theta $ are quantized coefficients of B-spline basis vectors Φ
l
(for order p ≥ 2) that span the function space $\mathcal{F}_l^{(p)}$ at a particular resolution l, which are coded from coarse to fine resolutions for scalability. In this work, we focus on the prediction of finer-grained coefficients given coarser-grained ones by learning parameters of a polynomial bilateral filter (PBF) from data. PBF is a pseudo-linear filter that is signal-dependent with a graph spectral interpretation common in the graph signal processing (GSP) field. We demonstrate PBF’s predictive performance over a linear predictor inspired by MPEG standardization over a wide range of point cloud datasets.