Эволюция применения геометрических преобразований в фотограмметрии

摘要

The issues of development and improvement of the mathematical apparatus of processing digital images in photogrammetric methods are considered. Having stated that only euklidean, affine, projective transformations and their combinations are used in photogrammetry, it is possible to analyze the features of their use at different stages of photogrammetry development. At the first stage the position of objects was determined using photographs and via graphical constructions performed using elementary calculations. In this case Euclidean transformations were sufficient. Later, when analog methods of image processing had come into operation the usage of affine geometry grew more urgent. With the development of analytical photogrammetry and its practical implementation in technical solutions and in equalization calculations, the need to apply projective trans-formations has arisen. Occurrence of digital photogrammetric images caused the urgent need to improve automatic digital photogrammetry technologies. Solely the handling of new approaches using modern methods of applied mathematics allowed achieving positive results in the performing of projective transformations, especially in the auto-implemented algorithms. It is believed that the theoretical foundations of such algorithms are put in computer vision (CV), which has much in common with photogrammetry, since the reconstruction of a scene from two-dimensional overlapping digital images in CV is nothing but the construction of a geometric (photogrammetric) terrain model via digital stereo pairs snapshots. Therefore, the developments of computer vision are also used in photogrammetry, which provided short initial impulses for its development. Unfortunately, this area of science, which the best mathematicians had chosen, was underestimated by the Russian photogrammetry scientists. Several works were rather an exception. Moreover they did not reveal the underlying conceptions of application of projective transformations in photogrammetry. The authors of this article set themselves the goal to restore this gap to a certain extent.%С развитием аналитической фотограмметрии проявилась необходимость в применении проективных преобразований. С появлением цифровых фотограмметрических снимков это проявилось как острая необходимость совершенствования автоматических цифровых технологий фотограмметрии. Считается, что теоретические основы для решения этой задачи были заложены в компьютерном зрении, которое имеет много общего с фотограмметрией. Однако этому направлению в отечественной фотограмметрии не уделялось достаточного внимания. Восстановить этот пробел и поставили своей целью авторы настоящей статьи.