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

We study the problem of lossy attribute compression, given encoded 3D point cloud geometry available at the decoder, in a multi-resolution B-spline projection framework. A target continuous 3D attribute function is first projected onto a sequence of nested subspaces ${\mathcal {F}}^{(p)}_{l_{0}} \subseteq \cdots \subseteq {\mathcal {F}} ^{(p)}_{L}$ , where ${\mathcal {F}}^{(p)}_{l}$ 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 $F_{l}^{*}$ are computed via 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.