The graph convolution algorithm currently suffers from the drawback of not fusing point cloud information and point cloud topology structure information based on visual selectivity features and using absolute quantities like distance as features, resulting in the algorithm losing geometric invariance. This information serves as the foundation for the "Graph Convolution Algorithm Based on Visual Selectivity and Application of Point Cloud Analysis". In order to propose a graph convolutional kernel and its design method based on visual selectivity, the algorithm analyzes the global characteristics of the point cloud "close in the vicinity and sparse in the distance," the local selectivity of the point cloud topology structure in the neighborhood, and the consistency between features and visual selectivity of primates. By combining point cloud information with point cloud topology structure information features, a graph convolution computation method was built, and the algorithm's geometric invariance was confirmed. The recognition and semantic segmentation performances of the approach in this study were verified using the ModelNet40 and ShapeNetPart data sets in comparison to the PointNet, PointNet++, DGCNN, KPConv, and 3D-GCN algorithms. The experimental design demonstrates that the algorithm presented in this research is accurate and practical, has geometric invariance, and performs better at semantic segmentation and recognition than conventional algorithms.