# Affinity-Point Graph Convolutional Network for 3D Point Cloud Analysis
## 1 Introduction  
With the developments of 3D acquisition equipment, 3D data have played an important role in practical applications. As the foundation of current point cloud analysis algorithms, 3D shape representation learning is important for tackling 3D computer vision tasks, including 3D reconstruction [1, 2], shape synthesis and modeling [3, 4], 3D object classification and segmentation [5, 6, 7], as well as graphics applications such as virtual avatars [8, 9].  
Since Convolutional Neural Networks (CNNs) have achieved great success in numerous areas, recent research has attempted to extend it from the regular date domain (such as image, voice signal, and video data) to unorganized 3D point clouds [6, 7, 8, 9, 10, 11, 12, 13]. However, it is challenging to apply CNN directly to 3D geometric data since they do not possess a regular Euclidean structure. A regular receptive field is required for the standard convolution kernels to extract features, since the convolution weights are fixed at a specific position of the convolution area. To solve this problem, regularization methods rasterize the irregular point clouds into probabilistic occupancy in 3D space [14, 15, 16] or project it into several 2D images [12, 13]. However, this kind of transformation always introduces loss of information during the quantization procedure. Meanwhile, this kind of position-determined weight results in isotropy of the convolution kernel to the features of neighboring points.  
Inspired by the great success of graph neural networks (GNNs) in other fields, some researchers tried to use it to handle 3D point cloud tasks [17, 18, 19, 20, 21]. They represented 3 Dpoint clouds as graphs, in which the number and orientation of each node's neighbors varied from one to another (node inconsistency). Then, an effective convolution operation similar to the traditional operation was defined, which was defined on Euclidean structured data for 3D shape representation learning. Many graph convolutional neural networks have been developed to deal with irregular point cloud data and have achieved promising results. However, they still obtain isotropic features, as they simply and roughly connect the neighbor to form the graph structure.  
To solve this problem, we designed a method that was motivated from the idea that the feature can be used to shield partial convolution weights according to the characteristics of the neighbors. Therefore, the actual receptive field of a point cloud convolution kernel is no longer a regular three-dimensional box but a shape that dynamically adapts to the structure of the object. In addition, as an important part of the graph, edges are used to enrich the features obtained.  
In summary, the contributions of this paper are as follows:  
(1) Affinity-Point Graph Convolutional Network (AP-GCN) is proposed for 3D point cloud analysis, which contains a graph neural network with a trainable neighbor structure. The neighbor selection method is used to replace the common spherical neighborhood and the k-NN (K-Nearest Neighbor) method.  
(2) Edge-conditioned convolution is designed according to the characteristics of message transmission on graph network.  
(3) A comparative 3D object classification accuracy is achieved based on the ModelNet40 classification benchmark [14] and the ShapeNet part benchmark [22].