# Variable Rate Point Cloud Attribute Compression with Non-Local Attention Optimization
## 1 Introduction  
Recent years have witnessed tremendous development of 3D capture devices and reconstruction technologies, and point clouds have become a crucial data structure for storage and transmission of 3D data. A point cloud is an unordered set of points in 3D space, usually represented by their coordinates, corresponding to the geometry, and each point may have its associated attributes, such as color and reflectance. Through these properties it can practically represent arbitrary 3D objects or scenes. As more and more point cloud content is made available and non-compressed point cloud requires a huge volume of data, the development of appropriate coding solutions becomes essential. Motivated by the huge success of deep neural networks (DNN)-based image and video compression [1; 2; 3; 4], several studies have been devoted to the use of deep learning for PCAC. Generally, they follow the VAE framework of image compression but in different point cloud representations to perform the attribute compression, such as the point-based PointNet series [5; 6] architecture in [7] (Deep-PCAC), voxel-based 3D dense convolutions in [8] and sparse convolution in [9] (SparsePCAC). Specially, [PERSON] et al. [10] builds a mapping between 3D point clouds and 2D grids, and utilizes the existing image compression method to encode and decode the 2D grids. However, the performance of these learning-based solutions still lags behind that of traditional G-PCC. How to develop the potential of learning-based approaches to outperform the traditional methods is still a challenging task. Point cloud compression can be divided into two main categories: geometry compression and attribute compression. Geometry compression involves compression of pointcoordinates in 3D space while attribute compression involves compression of point attributes. In this paper, we focus on point cloud attribute compression and assume the geometry information is known. Without loss of generality, we assume that the attributes are colors represented as (R, G, B) triplets in RGB color space. Considering the efficiency of sparse convolution processing sparsely distributed point clouds, we establish a PCAC framework on top of the sparse convolution [11] based VAE structure. It should be noted that, in the proposed framework, we overcome the defect of other learning-based methods in capturing the long range dependencies in the use of stacked convolution operations. The non-local attention mechanism module (NLAM) is introduced into the proposed VAE structure to capture both local and global correlations among voxels. The non-local attention masks are applied at different layers to distinguish the importance of latent features in both positions and channels dimensions for better compression. Furthermore, in the existing learning-based PCAC methods, the network parameters are learned by jointly minimizing bitrate and distortion at a particular trade-off. To this end each trade-off needs an independent model. Multiple independent models require large memory to store and transmission, which puts great limitations on the practical applications. Inspired by the variable bitrate compression methods of image compression [12; 13; 14], we propose a modulation network to adaptively modify the latent features of different layers. This modulation network is based on parameter sharing multilayer perceptron (MLP) and the modification is implemented by simple yet effective channel-wise production. Experimental results have shown that the proposed lightweight but effective modulation network successfully achieve variable bit compression in a single network with only acceptable performance loss. We evaluate the performance on voxelized 8i Voxelized Full Bodies (8 iVFB) [15] which has been adopted by MPEG as the standard test set and experiments are executed under common test conditions.