The lossy Geometry-based Point Cloud Compression (G-PCC) inevitably impairs the geometry information of point clouds, which deteriorates the quality of experience (QoE) in reconstruction and/or misleads decisions in tasks such as classification. To tackle it, this work proposes GRNet for the geometry restoration of G-PCC compressed large-scale point clouds. By analyzing the content characteristics of original and G-PCC compressed point clouds, we attribute the G-PCC distortion to two key factors: point vanishing and point displacement. Visible impairments on a point cloud are usually dominated by an individual factor or superimposed by both factors, which are determined by the density of the original point cloud. To this end, we employ two different models for coordinate reconstruction, termed Coordinate Expansion and Coordinate Refinement, to attack the point vanishing and displacement, respectively. In addition, 4-byte auxiliary density information is signaled in the bitstream to assist the selection of Coordinate Expansion, Coordinate Refinement, or their combination. Before being fed into the coordinate reconstruction module, the G-PCC compressed point cloud is first processed by a Feature Analysis Module for multiscale information fusion, in which kNN-based Transformer is leveraged at each scale to adaptively characterize neighborhood geometric dynamics for effective restoration. Following the common test conditions recommended in the MPEG standardization committee, GRNet significantly improves the G-PCC anchor and remarkably outperforms state-of-the-art methods on a great variety of point clouds (e.g., solid, dense, and sparse samples) both quantitatively and qualitatively. Meanwhile, GRNet runs fairly fast and uses a smaller-size model when compared with existing learning-based approaches, making it attractive to industry practitioners.

Although the multiscale sparse tensor using stacked convolutions has attained noticeable gains for lossy compression of point cloud geometry (PCG), its capability suffers because convolutions with fixed receptive field and fixed weights after training cannot aggregate sufficient information collection due to the extremely sparse and unevenly distributed nature of points. To best tackle the sparsity and adaptively exploit inter-point correlations, we apply local self-attention on$k$nearest neighbors (kNN) that are instantaneously formed for each point, with which attention-based mechanism can effectively characterize and embed spatial information conditioned on the dynamic neighborhood. This kNN self-attention is implemented using the prevalent Transformer architecture and stacked with sparse convolutions to capture neighborhood information in a progres-sively re-sampling framework, referred to as the PCGFormer. Compared with the MPEG standard Geometry-based PCC (G-PCC) using the latest octree codec, the proposed PCGFormer provides more than 90% and 87% BD-rate (Bjøntegaard Delta Rate) reduction in average across three different object point cloud datasets for point-to-point (D1) and point-to-plane (D2) distortion measures. Compared with the state-of-the-art learning-based approach, the PCGFormer achieves 17.39% and 15.75% BD-rate gains on D1 and D2, respectively.