Lyubchenko V. Mathematical models and methods of normalization of projective transformations in the systems of image processing

The thesis is devoted to the development of the mathematical methods of the visual perception and the image normalization based on the projective geometry in the systems of image processing. The thesis suggests new mathematical methods of the projective distortions normalization using the successive procedure. For this purpose several decompositions of the full projective group on their own basic subgroups were developed and mathematically based that allow technical realization (displacement, compressions, oblique displacements, turns, perspective transformations and so on). When analyzing the developed decompositions it was proved, that the perspective transformation is the transformation, that binds the affine and projective geometry. Normalization methods were developed basing on the properties of the perspective transformations. That are the base of the algorithms of the projective normalizations, developed for the systems of technical vision.