Multi-Scale Structured Dictionary Learning for 3-D Point Cloud Attribute Compression

Abstract

Existing 3-D point cloud attribute compression methods are rigid for complex signals defined in spatially irregular domain, as they solely depend on geometric information or adopt pre-defined analytic bases for transform. In this article, we propose a multi-scale structured dictionary learning algorithm for 3-D point cloud attribute compression. The proposed multi-scale dictionary leverages hierarchical sparsity within signals by adapting atoms in an arborescent structure. It supports hierarchical sparse transform for encoding voxelized point cloud attributes with progressive refinement of high-frequency details from coarser to finer scales. To represent spatial blocks with varying amounts of occupied voxels, a non-uniform binary weight matrix is incorporated in dictionary learning to characterize the dimensional irregularity of signals. To guarantee optimal approximation with improved efficiency, alternating optimizations including Alternating Direction Method of Multipliers and Gauss-Seidel iterations are adopted for the weighted mixed $\ell _{2}/\ell _{1}$ -minimization. Furthermore, we develop a lossy attribute compression framework by integrating sparse transform based prediction with dedicated quantization and entropy coding routines. Experimental results demonstrate that the proposed framework outperforms the state-of-the-art transform-based coding methods and is competitive with the most recent MPEG PCC test models in point cloud attribute compression.