The images consist of different types of objects of interest. Special attention is paid to the study of objects that are repeated in the images. The paper considers the problem and investigates possible methods to solve it for detecting regular structures. To solve the problem, we propose to use an approach that takes into account topological properties of objects. Nowadays topological data analysis is being actively developed. It allows us to reveal the structure of objects of any nature and to represent this information in the form of some topological characteristic called barcode. In this paper the study of topological structure of regular objects is carried out. The proposed method decomposes the image into connectivity components, analyzes dynamic information about their appearance and disappearance, calculates the barcode and finds subtrees with the same properties. It is shown that the found subtrees with the same structure correspond to regular objects. Satellite images that contain regular and almost regular spatial objects were used for the experiments. The results show that topological properties and structure of subtrees allow us to detect regular structures under their affine and deforming transformations.