Volumetric 3D Point Cloud Attribute Compression: Learned polynomial bilateral filter for prediction

Abstract

We extend a previous study on 3D point cloud attribute compression scheme that uses a volumetric approach: given a target volumetric attribute function $f:{\mathbb{R}}^3\mapsto \mathbb{R}$, we quantize and encode parameters $\theta$ that characterize $f$ at the encoder, for reconstruction $f_{\hat{\theta }}((x))$ at known 3D points $(x)$ at the decoder. Specifically, parameters $\theta$ are quantized coefficients of B-spline basis vectors ${\mathbf{\Phi }}_l$ (for order $p\ge 2$) 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.