Detection of Repeated Structures in an Image Based on Topological Data Analysis

A problem for detecting repeated structures in images is considered in the article. A method that is based on topological properties of objects is proposed to solve the problem. Topological data analysis represents the information about objects in the form of a barcode. The proposed method creates a tree based on the barcode and finds subtrees with the same properties. The found subtrees correspond to repeated structures. The research was conducted on satellite images that contain repeated and near repeated spatial objects.