Algorithm for selecting homogeneous regions from a set of spatial objects

Analysis of the topology of geographical objects is one of the main tasks of geoinformation systems. Objects that are not even explicitly connected, as a rule, make up structures. Based on these structures, we can search for homogeneous areas on the map. Homogeneous areas are entities that include similar objects, such as buildings, parks or parking lots. To implement the task, it is expedient to use the method of persistent homology. The objects on the map will be analyzed for location features relative to each other. Based on the analysis a bar code is compiled. Barcode displays the stable topological properties of structures from objects. Properties that are manifested in small ranges of distances are not considered. The method is represented as the implementation of two algorithms: the simplex search algorithm and the hole search algorithm. The study was conducted to identify homogeneous areas related to land. Individual sites represented as vector objects gradually merged into structural regions after increasing the radius of the search for neighboring structures. The analysis of the type of the shape of homogeneous structures is carried out. The algorithm can be used to automatically compare spatial objects on different-scale maps.