With the rapid development of remote sensing technology, efficiently extracting useful information from large-scale remote sensing image data has become one of the core challenges in the field. However, traditional target recognition methods face difficulties when dealing with complex backgrounds, dynamic scenes, multi-angle targets, and so on.

This study proposes an innovative approach based on topological data analysis (TDA), introducing persistent homology and mapper analysis to model and analyze infrared remote sensing images at multiple scales. The remote sensing image is mapped to a point cloud structure in a high-dimensional topological space, and then persistent homology analysis or mapper analysis is used to extract the simplified topological structure of the point cloud data, forming a persistence diagram or a complex network structure. The network exhibits strong global properties, robustness, and excellent visualization characteristics, and can effectively capture the geometric and topological structures in the data while highlighting subtle differences. In previous experiments conducted on public datasets for airplane and automobile classification, the proposed method achieved a 1.5% improvement in accuracy compared to using convolutional neural networks (CNNs). And for ship classification, the method successfully categorized four types of ships, which shows strong applicability in target recognition and classification tasks.

The rotational invariance of topological data analysis effectively addresses the challenges in target recognition caused by changes in observation angles, thereby improving recognition and classification accuracy. It provides a new approach for infrared target recognition and classification， and also shows potential in the large-scale processing and pattern recognition of remote sensing data. Additionally, the method holds significant importance and practical value in fields such as military applications, urban management, climate change research, and disease detection.