Normalization of 2D Images “in Terms of Level” Based on Cosine and Hadamard Transform

Олександр Іванович Рибін, Сергій Миколайович Літвінцев, Ірина Олександрівна Сушко


Background. The problem of pattern recognition is considered in this paper. We propose to use orthogonal basis functions for pattern recognition of 2D signals.

Objective. The aim of this paper is investigation of pattern recognition problem of 2D images based on cosine and Hadamard transforms.

Methods. Pre-processing of signals is proposed to reduce the number of spectral components in the orthogonal series of signal decomposition. Normalization of a reference signal “in terms of level” allows comparing reference and tested signals by means of transform coefficient calculation. This coefficient is a match criterion of these signals.

Results. Theoretical information used for proposed classification method is described. The normalization algorithms of the reference and tested signals, which have to perform before determining similarity of images, are proposed. Transformation of a reference signal to two-dimensional basic function is fundamental point. This basic function is based on selected 2D orthogonal transform. Complete cycle of calculation for pattern recognition of some 2D images is executed. The calculations were performed using Hadamard and cosine transforms. 2D images of obtained spectra are given.

Conclusions. As a result, this research shows that we can perform pattern recognition of normalized 2D images based on calculation of transform coefficient. The analysis of calculation results shows that classification of signals based on transform coefficient values is possible. Development of matching classifiers is the aim of the next research.


normalization in terms of level; image classification; Hadamard transform; cosine transform; pattern recognition


V.G. Abakumov and A.I. Rybin, Biomedical Signals (Genesis, Treatment, Monitoring).Kyiv,Ukraine: Nora-Print, 2001, 516 p. (in Ukrainian).

A.N. Prodeus and Ye.N. Zakhrabova, Expert Systems in Medicine.Kyiv,Ukraine: VEK+, 1998, 320 p. (in Russian).

W. Ouyang et al., “Fast pattern matching using orthogonal Haar transform”, in Proc. of IEEE Conf. on Computer Vision and Pattern Recognition, San Francisco, CA, USA, June 13–18, 2010, pp. 3050–3057. doi: 10.1109/CVPR.2010.5540058

A.I. Rybin et al., “Transform coefficients of normalized orthogonal transformations and diagnosis of pulsegrams”, Visnyk NTUU KPI. Ser. Radiotehnika. Radioaparatobuduvannya, no. 30, pp. 148–156, 2005.

A.I. Rybin and A.D. Melnyk, “Matched normalized signal filtering”, Izv. Vysh. Uchebn. Zaved. Radioelektron., vol. 51, no. 2, pp. 112–114, 2008. doi: 10.3103/S0735272708020106

A.I. Rybin, “Normalization of discrete orthogonal transformations by a test signal”, Izv. Vysh. Uchebn. Zaved. Radioelektron., vol. 47, no. 7, pp. 27–31, 2004.

A.I. Rybin and Yu.Kh. Nizhebetskaya, “Analysis of images similarity and difference using normal orthogonal conversion”, Izv. Vysh. Uchebn. Zaved. Radioelektron., vol. 53, no. 3, pp. 167–172, 2010. doi: 10.3103/S0735272710030076

GOST Style Citations

  1. Абакумов В.Г., Рибін О.І. Біомедичні сигнали (генезис, обробка, моніторинг). – К.: Нора-Прінт, 2001. – 516 с.

  2. Продеус А.Н., Захрабова Е.Н. Экспертные системы в медицине. – К.: ВЕК+, 1998. – 318 с.

  3. Ouyang W., Zhang R., Cham W.-K. Fast pattern matching using orthogonal Haar transform // IEEE Conf. Computer Vision and Pattern Recognition, 13–18 June 2010,San Francisco,CA,USA. – San Francisco, 2010. – P. 3050–3057. doi: 10.1109/CVPR.2010.5540058

  4. Коэффициенти трансформант нормализованных ортогональних преобразований и диагностика пульсограм / А.И. Рыбин, О.Б. Шарпан, Т.В. Сакалош, Е.Г. Григоренко // Вісник НТУУ “КПІ”. Сер. Приладобудування. – 2005. – Вип. 30. – С. 148–156.

  5. Рыбин А.И., Мельник А.Д. Согласованная нормализованная фильтрация сигналов // Радиоэлектроника. – 2008. –  51, № 2. – С. 77–80. – (Известия вузов). doi: 10.20535/S0021347008020106

  6. Рыбин А.И. Нормализация дискретных ортогональных преобразований тестовым сигналом // Радиоэлектроника. – 2004. – 47, № 7. – С. 39–46. – (Известия вузов).

  7. Рыбин А.И., Нижебецкая Ю.Х. Анализ подобия и различия образов с использованием нормального ортогонального преобразования // Радиоэлектроника. – 2010. – 53, № 3. – С. 58–64. – (Известия вузов). doi: 10.20535/S0021347010030076

Copyright (c) 2017 NTUU KPI