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 fθ(x) at known 3D points x at the decoder. Specifically, parameters θ are quantized coefficients of B-spline basis vectors Φ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</inf> (for order p ≥ 2) that span the function space Fₗ⁽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.