Mathematical Model of Projective Transformations for Image Normalization Based on the Properties of Projective Geometry

Abstract

This paper focuses on the development of new mathematical model for image normalization base on the projective geometry. For this purpose several decompositions of full projective group and their subgroups were developed that allow technical realization such as: displacement, compressions, oblique displacements, turns, and perspective transformations. The developed decompositions had been proved through perspective transformation which binds the affine and projective geometry using properties of the perspective transformations.