Method of iteratively compensating projective image distortions

Луцив В.Р. Метод итеративной компенсации проективных искажений изображений // Оптический журнал. 2009. Т. 76. № 7. С. 53–60.

Lutsiv V.R. Method of iteratively compensating projective image distortions [in Russian] // Opticheskii Zhurnal. 2009. V. 76. № 7. P. 53–60.

V.R. Lutsiv, "Method of iteratively compensating projective image distortions," Journal of Optical Technology. 76 (7), 417-422 (2009). https://doi.org/10.1364/JOT.76.000417

This paper presents a method of normalizing an image relative to a complete group of projective transformations on a plane, based on the iterative optimization of the solution in space of the two parameters of the projective transformation that distinguish it from an affine transformation. This pair of parameters is represented by a vector. Each iteration of the normalization is preceded by a measurement of the parameters and compensation of the affine transformation according to formulas derived and published earlier by the author. To partially compensate the projective transformation, the vector of a normalizing transformation is used at each iteration along such a direction that changing its direction to the opposite corresponds to the largest-in-modulus change of the displacement rate of the center of gravity of the image to be transformed. The iterative process reduces to an image state that is standard relative to the projective transformation for which a normalizing transformation vector of any direction causes a displacement of the center of gravity that is identical in modulus.