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

• URL: http://arxiv.org/abs/2311.13539v1
• Date: Wed, 22 Nov 2023 17:26:54 GMT
• Title: Learned Nonlinear Predictor for Critically Sampled 3D Point Cloud Attribute Compression
• Authors: Tam Thuc Do, Philip A. Chou, and Gene Cheung
• Abstract summary: We study 3D point cloud compression via a decoder approach. In this paper, we study predicting $f_l*$ at level $l+1$ given $f_l*$ $l$ and encoding of $G_l*$ for the $p=1$ case.
• Score: 24.001318485207207
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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 $\mathcal{F}^{(p)}_{l_0} \subseteq \cdots \subseteq \mathcal{F}^{(p)}_L$, where $\mathcal{F}_l^{(p)}$ is a family of functions spanned by B-spline basis functions of order $p$, $f_l^*$ is the projection of $f$ on $\mathcal{F}_l^{(p)}$ and encoded as low-pass coefficients $F_l^*$, and $g_l^*$ 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 $G_l^*$. In this paper, to improve coding performance over [1], we study predicting $f_{l+1}^*$ at level $l+1$ given $f_l^*$ at level $l$ and encoding of $G_l^*$ 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 $G_l^*$ 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.

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