Learned Nonlinear Predictor for Critically Sampled 3D Point Cloud Attribute Compression

We study 3D point cloud attribute compression via a volumetric approach: assuming point cloud geometry is known at both encoder and decoder, parameters $\theta$ of a continuous attribute function $f: \mathbb{R}³ \mapsto \mathbb{R}$ are quantized to $\hat{\theta}$ and encoded, so that discrete samples $f{\hat{\theta}}(\mathbf{x}i)$ can be recovered at known 3D points $\mathbf{x}i \in \mathbb{R}^3$ at the decoder. Specifically, we consider a nested sequences of function subspaces $\mathcal{F}^{(p)}{l0} \subseteq \cdots \subseteq \mathcal{F}^{(p)}L$, where $\mathcal{F}l^{(p)}$ is a family of functions spanned by B-spline basis functions of order $p$, $fl^*$ is the projection of $f$ on $\mathcal{F}l^{(p)}$ and encoded as low-pass coefficients $Fl^*$, and $gl^*$ is the residual function in orthogonal subspace $\mathcal{G}l^{(p)}$ (where $\mathcal{G}l^{(p)} \oplus \mathcal{F}l^{(p)} = \mathcal{F}{l+1}^{(p)}$) and encoded as high-pass coefficients $Gl^*$. In this paper, to improve coding performance over [1], we study predicting $f{l+1}^*$ at level $l+1$ given $fl^*$ at level $l$ and encoding of $Gl^*$ for the $p=1$ case (RAHT($1$)). For the prediction, we formalize RAHT(1) linear prediction in MPEG-PCC in a theoretical framework, and propose a new nonlinear predictor using a polynomial of bilateral filter. We derive equations to efficiently compute the critically sampled high-pass coefficients $Gl^*$ amenable to encoding. We optimize parameters in our resulting feed-forward network on a large training set of point clouds by minimizing a rate-distortion Lagrangian. Experimental results show that our improved framework outperformed the MPEG G-PCC predictor by $11$ to $12\%$ in bit rate reduction.