## 1 Introduction  
Human action recognition aims to help computers understand human behavior semantics from various data recorded by the acquisition devices. Particularly, 3D action recognition is dedicated to mining action patterns from 3D data involving human movements. It has attracted increasing attention due to its widespread applications, such as public safety monitoring, performance appraisal, military reconnaissance, and intelligent transportation [1]. The current mainstream 3D action recognition methods can be classified into depth-based methods (including depth maps and point cloud sequences) [2; 3; 4] and skeleton-based methods [5; 6] depending on the data type employed. Limited by the accuracy pose estimation algorithm--the unavoidable upstream task--skeleton-based methods face computational consumption and robustness challenges. By contrast, depth-based methods are more task-independent and have attracted widespread attention. Existing depth-based 3D action recognition approaches mainly fall into two main categories. The first one is to encode 3D motions into one or more images [2; 3; 7; 8] and utilize CNNs [9] for action recognition. However, the 2D image plane cannot fully characterize the 3D dynamics because human actions are concurrently spatiotemporal and conducted in the 3D space. The other is to transform the depth video into a point cloud sequence [10], which records the 3D coordinates of points in space at multiple time instances. Thus, compared with images, point cloud sequences have the advantage of retaining 3D appearance and geometry dynamics over time, enabling advanced analysis and understanding of human actions. In addition, point clouds can be obtained using various devices such as laser scanners, radars, depth sensors, and RGB+D cameras, which can be mounted on drones, street lights, vehicles, and surveillance aircraft, expanding the application scope of action recognition. However, due to the complex structure and massive volume of the point cloud, the existing 3D action recognition methods based on it have the following challenges. Firstly, point cloud sequences always have massive points proportional to the time dimension, and the data processing schema is time-consuming. Therefore, developing an efficient and lightweight point cloud sequence model is pivotal for 3D action recognition. Secondly, the points in the sequences are irregular, exhibiting unordered intra-frame spatial information and ordered inter-frame temporal details, making it challenging to analyze the underlying movement patterns. However, existing point cloud processing methods usually perform undifferentiated downsampling of the overall point clouds, resulting in uniform loss of essential and subtle information. In addition, existing point cloud analysis schemes ignore the critical body parts contributing to the actions, resulting in the lack of nuances of the extracted action features, which finally limits the performance of action recognition. To solve these problems, we propose a deep learning framework called the Symmetric Fine-coarse Neural Network (SFCNet) that symmetrically combines the analysis of motion features from local and global perspectives, as shown in Figure 1. Firstly, to save computational costs, we reduce the points by frame sampling and farthest point sampling. Next, the sampled point clouds are transformed into 3D voxels to create a compact point cloud representation. The original 3D positions are then attached with an interval-frequency descriptor to depict the overall spatial configuration and facilitate the identification of essential body parts, allowing us to divide the point cloud sequences into local fine space and global coarse space. We treat the voxels involved in these two spaces as points and employ PointNet++[11] to extract features in an end-to-end manner. Finally, our feature fusion module combines the global appearance and local details to obtain discriminative features for 3D action recognition.