Deep Unrolling of Sparsity-Induced RDO for 3D Point Cloud Attribute Coding

Abstract

Given encoded 3D point cloud geometry available at the decoder, we study the problem of lossy attribute compression in a multi-resolution B-spline projection framework. A target continuous 3D attribute function is first projected onto a sequence of nested subspaces ${\mathcal{F}}_{l_0}^{(p)}\subseteq \cdots \subseteq {\mathcal{F}}_L^{(p)}$, where ${\mathcal{F}}_l^{(p)}$ is a family of functions spanned by a B-spline basis function of order $p$ at a chosen scale and its integer shifts. The projected low-pass coefficients $F_l^{\ast }$ are computed by variable-complexity unrolling of a rate-distortion (RD) optimization algorithm into a feed-forward network, where the rate term is the sparsity-promoting ${\ell }_1$-norm. Thus, the projection operation is end-to-end differentiable. For a chosen coarse-to-fine predictor, the coefficients are then adjusted to account for the prediction from a lower-resolution to a higher-resolution, which is also optimized in a data-driven manner.

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