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 : ℝ³ ↦ 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 Φl (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.

1. INTRODUCTION

We study lossy compression of 3D point cloud attributes from a volumetric function approach. Specifically, assuming point cloud geometry is first encoded, we encode point cloud attributes, given that encoded geometry is known both at encoder and decoder—this is the dominant approach both in research [1] – [7] and in MPEG geometry-based point cloud compression (G-PCC) standard [8] – [11]. Mathematically, given known 3D locations x_i ∈ ℝ³ both at the encoder and decoder, we encode quantized parameters for a target volumentric attribute function f : ℝ³ ↦ ℝ from coarse to fine resolutions for scalability, so that it can be evaluated as at x_i at the decoder for signal reconstruction. [3], [12] proposed such a framework using volumetric B-spline basis functions Φ_l of order p = 1 that span a nested sequence of function spaces —called Region Adaptive Hierarchical Transform (RAHT(1))—and now forms the core in MPEG G-PCC [6]. Recently, [13] extended this framework to B-spline basis functions of order p ≥ 2(RAHT(p)) and demonstrated state-of-the-art (SOTA) coding performance. Moreover, the feedforward network obtained by unrolling a finite-term Taylor’s series of a matrix inverse to compute orthonormalized RAHT(p) coefficients is amenable to end-to-end data-driven parameter tuning. The goal of this paper is to further improve performance by designing a predictor for finer-grained unnormalized coefficients given coarser-grained coefficients , and training.