Rate-Distortion Optimized Skip Coding of Region Adaptive Hierarchical Transform Coefficients for MPEG G-PCC

TL;DR

The paper tackles bitrate inefficiency in Region-Adaptive Hierarchical Transform (RAHT) within MPEG G-PCC by introducing an adaptive skip coding scheme for RAHT residuals. It develops a rate–distortion (RD) framework with an adaptive Lagrange multiplier to decide, per color component, whether to skip residuals in the last $k\in\{1,2,3,4\}$ RAHT layers, computing distortion in the transform domain via Parseval. Experimental results on GeS-TM v4.0 under MPEG CTC show notable BD-rate reductions, especially under inter-frame prediction, with average improvements of $-3.50\%$, $-5.56\%$, and $-4.18\%$ for Luma, Cb, Cr respectively. The approach yields substantial bitrate savings at low bitrates (e.g., CGI sequence queen) while incurring minimal decoding overhead, indicating practical impact for dynamic point cloud compression.

Abstract

Three-dimensional (3D) point clouds are becoming more and more popular for representing 3D objects and scenes. Due to limited network bandwidth, efficient compression of 3D point clouds is crucial. To tackle this challenge, the Moving Picture Experts Group (MPEG) is actively developing the Geometry-based Point Cloud Compression (G-PCC) standard, incorporating innovative methods to optimize compression, such as the Region-Adaptive Hierarchical Transform (RAHT) nestled within a layer-by-layer octree-tree structure. Nevertheless, a notable problem still exists in RAHT, i.e., the proportion of zero residuals in the last few RAHT layers leads to unnecessary bitrate consumption. To address this problem, we propose an adaptive skip coding method for RAHT, which adaptively determines whether to encode the residuals of the last several layers or not, thereby improving the coding efficiency. In addition, we propose a rate-distortion cost calculation method associated with an adaptive Lagrange multiplier. Experimental results demonstrate that the proposed method achieves average Bjøntegaard rate improvements of -3.50%, -5.56%, and -4.18% for the Luma, Cb, and Cr components, respectively, on dynamic point clouds, when compared with the state-of-the-art G-PCC reference software under the common test conditions recommended by MPEG.

Figures (9)

• Figure 1: G-PCC encoding and decoding frameworks. The yellow, green, and blue colors represent data processing, geometry processing, and attribute processing, respectively.
• Figure 2: The process of RAHT. Take the points in the current node as an example, first, a 3D Haar Wavelet transform is performed along with the Y direction to obtain 3 immediate DC coefficients and 2 AC coefficients; second, the 3 immediate DC coefficients are further transformed along with the Z direction to obtain 2 immediate DC coefficients and 1 AC coefficients; third, the 2 immediate DC coefficients are transformed along with the X direction to obtain 1 DC coefficient and 1 AC coefficient. The DC coefficient in the third stage and the AC coefficients in all the three stages are then quantized and entropy encoded.
• Figure 3: Illustration of RAHT: (a) transform order of sub-blocks in a layer according to Morton code, (b) Morton code-based order, (c) transform results of a sub-block.
• Figure 4: The proportion of zero residuals to be encoded in each RAHT layer at different bitrates.
• Figure 5: The procedure of encoding and bitrate estimation of quantized coefficient' residuals.