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

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 F(p)l0 subseteq cdots subseteq F(p)L, where 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 Fl^* 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 ℓ1-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.