An algorithm for matching spatial objects of different-scale maps based on topological data analysis

Abstract

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.

Strategies for generating panoramic video images without information about scene correspondences for multispectral distributed aperture systems

“… подход 1, основанный на поиске сюжетных соответствий путём выделения особых точек (ОТ), опи-сании их окрестностей с использованием дескрипторов, автоматическом поиске пар соответствий по дескрипторам (либо по топологическим особенностям [5], либо по морфологическим коэффициентам диффузной корреляции [6], либо по нормализованным взаимным корреляционным функциям [7,8]) и оценке по ним матриц гомографии (либо непосредственно матриц внутренних и внешних параметров [9]) для перехода от системы координат одной камеры к системе координат другой камеры [10 -13]; данная стратегия не требует априорных сведений о камерах;  подход 2, основанный на предварительной фотограмметрической калибровке камер СТЗ с РА и оценке матрицы гомографии по априорной информации о матрицах внутренних и внешних параметров камер, дальности до объекта съёмки и ракурсе съёмки [14 -16]. Подход 2 целесообразно применять, когда взаимное пространственное положение камер при съёмке не изменяется.…”