Laplacian Matrix Learning for Point Cloud Attribute Compression with Ternary Search-Based Adaptive Block Partition

Graph Fourier Transform (GFT) has demonstrated significant effectiveness in point cloud attribute compression task. However, existing graph modeling methods are based on the geometric relationships of the points, which leads to reduced efficiency of graph transforms in cases where the correlation between attributes and geometry is weak. In this paper, we propose a novel graph modeling method based on attribute prediction values. Specifically, we utilize Gaussian priors to model prediction values, then use maximum a posteriori estimation to learn the Laplacian matrix that best fits the prediction values in order to conduct separate graph transforms on prediction values and ground truth values to derive residuals, and subsequently perform quantization and entropy coding on these residuals. Additionally, since the partitioning of point clouds directly affects the coding performance, We design an adaptive block partitioning method based on ternary search, which selects reference points using distance threshold r and performs block partitioning and non-reference point attribute prediction based on these reference points. By conducting ternary search on distance threshold r, we rapidly identify the optimal block partitioning strategy. Moreover, we introduce an efficient residual encoding method based on Morton codes for the attributes of reference points while the prediction attributes of non-reference points are modeled using the proposed graph-based modeling approach. Experimental results demonstrate that our method significantly outperforms two attribute compression methods employed by Moving Picture Experts Group (MPEG) in lossless geometry based attribute compression tasks, with an average of 30.57% BD-rate gain compared to Predictive Lifting Transform (PLT), and an average of 33.54% BD-rate gain compared to Region-Adaptive Hierarchical Transform (RAHT), which exhibits significantly improved rate-distortion performance over the current state-of-the-art method based on GFT.