APPROXIMATION OF IMAGES GEOMETRICAL TRANSFORMATIONS WITH POLYNOMIALS
Tolkachev Danil Sergeevich
Engineering-Technological Academy of Southern Federal University
Abstract. In the article the approximation of the two-dimensional pictures of images geometrical transformation with polynomials is suggested. Approximation method according to the technique of least squares is introduced. The schemes of polynomial evaluation with Horner’s and finite difference methods are described. Such approximation correctness with regard to the problem of camera lens geometrical distortions correction has been tested.
Key words and phrases: геометрическое преобразование изображений, коррекция геометрических искажений, дисторсия, схема Горнера, метод конечных разностей, images geometrical transformation, geometrical distortions correction, distortion, Horner’s method, finite difference method
Open the whole article in PDF format. Free PDF-files viewer can be downloaded here.
References:
Beklemishev D. V. Dopolnitel'nye glavy lineinoi algebry. M.: Nauka (Glavnaya redaktsiya fiziko-matematicheskoi literatury), 1983. 336 s.
Kakhaner D., Mouler K., Nesh S. Chislennye metody i matematicheskoe obespechenie / per. s angl. M.: Mir, 1998. 575 s.
Korn G., Korn T. Spravochnik po matematike (dlya nauchnykh rabotnikov i inzhenerov). M.: Nauka, 1973. 832 s.
Levitin A. Algoritmy: vvedenie v razrabotku i analiz / per. s angl. M.: Izdatel'skii dom "Vil'yams", 2006. 576 s.
Yane B. Tsifrovaya obrabotka izobrazhenii. M.: Tekhnosfera, 2007. 584 s.
Bradski G., Kaehler A. Learning OpenCV. Sebastopol: O’Reilly, 2008. 555 p.
Szeliski R. Image Alignment and Stitching: a tutorial // Foundations and Trends® in Computer Graphics and Vision. 2006. Vol. 2. № 1. P. 1-104.