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A problem of automatic comparison of spatial objects on maps with different scales for the same locality is considered in the article. It is proposed that this problem should be solved using methods of topological data analysis. The initial data of the algorithm are spatial objects that can be obtained from maps with different scales and subjected to deformations and distortions. Persistent homology allows us to identify the general structure of such objects in the form of topological features. The main topological features in the study are the connectivity components and holes in objects. The paper gives a mathematical description of the persistent homology method for representing spatial objects. A definition of a barcode for spatial data, which contains a description of the object in the form of topological features is given. An algorithm for comparing feature barcodes was developed. It allows us to find the general structure of objects. The algorithm is based on the analysis of data from the barcode. An index of objects similarity in terms of topological features is introduced. Results of the research of the algorithm for comparing maps of natural and municipal objects with different scales, generalization and deformation are shown. The experiments confirm the high quality of the proposed algorithm. The percentage of similarity in the comparison of natural objects, while taking into account the scale and deformation, is in the range from 85 to 92, and for municipal objects, after stretching and distortion of their parts, was from 74 to 87. Advantages of the proposed approach over analogues for the comparison of objects with significant deformation at different scales and after distortion are demonstrated.

In the article it is proposed to apply computer topology methods to create effective data structures that will allow storing and processing spatial scenes in n-dimensional space. The basis for the representation of nD-geoobjects is n-dimensional simplexes. For example, the representation of spatial data of high dimension will allow us to describe the topological relationships between 3D objects in time. The mathematical foundations and software for representation and processing of spatial data of high dimension are developed. The algorithm for encoding spatial objects nD in GIS will provide an opportunity to solve a wide range of tasks for processing complex graphic information.

Разработан метод кодирования топологических отношений между пространст-венными объектами. Информация о связях объектов содержится в их иденти-фикаторах. Показана возможность использования метода для обработки про-странственно связанных объектов.Ключевые слова: топологические отношения, идентификатор пространст-венного объекта, иерархия пространственных объектов.

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