Slavik O. Mathematical Modeling of Surfaces by the Methods of Interstripation of Functions on Incomplete Information About It

The object of research is the process of processing remote sensing data of the planet. The purpose of the work is to build mathematical models of surfaces of three-dimensional bodies taking into account data about them on different systems of strips based on the use of operators of interstripation of functions. Research methods are based on the complex use of new information operators, methods of mathematical analysis and mathematical modeling: to build mathematical models of the surfaces of the object – the theory of approximation of functions of two variables using interlination operators; for segmentation of the surface of the object – methods of detecting edges in digital images; for the construction of discontinuous splines – methods of approximation by interpolation operators. The scientific novelty of the work lies in the following: the method of surface restoration according to the data on it on the system of strips located at any angle is proposed and substantiated; for the first time a mathematical model of the body surface was built on the basis of data on it on a system of strips with curvilinear boundaries; the method of surface restoration according to the data on it on the system of strips taking into account the structure of the body is developed and investigated; the method of finding discontinuity lines of functions (one or two variables) or their derivatives of some order is improved. The practical significance of the obtained results lies in the possibility of using the proposed interstripation operators for automatic restoration of the surface between the strips on the basis of remote sensing of the Earth, aerial photography, seismic tomography, etc. In addition, the developed mathematical model of the surface can be used to recover two-dimensional signals damaged by errors in data transmission over the network or its overloading. Estimation of the true values of the lost data is necessary in most tasks of digital image processing or, for example, in tasks of processing archival documents in the form of graphic images, which having various distortions (scratches, stains, dust, unnecessary inscriptions, fold lines, etc.); when restoring damaged paintings, portraits, images, etc. The results of the dissertation research were introduced into the educational process of the Ukrainian Engineering and Pedagogical Academy when teaching the course "Information Technologies in Research" for graduate students of the Ukrainian Engineering and Pedagogical Academy.