Generalized convolution for extraction of image features in the primary domain

• Autorzy: Korohoda P. , Dąbrowski A.
• Języki publikacji: EN

Abstrakty

EN

In this paper, a class of techniques for flexible extraction of image features is proposed. These techniques are based on the convolution type filtering in the primary domain. The mentioned flexibility results from the fact that any discrete transform suitable for the analysis of desired image features (as, e.g., the Karhunen-Loeve transform) may be designed and the filter with the assumed transform-domain properties may be applied straightforwardly in the image (i.e., primary) domain. The proposed solution creates an entirely new approach to image filtering. After recalling the concept referred to by the authors as generalized convolution and extending it to the 2-dimensional case, the theoretical results are illustrated with several examples based on filtering of the test image with filters designed in the Haar, Hadamard and the DCT II domains. Finally, it is explained how the proposed approach indicates several possible ways for further developments towards the design of image-and-feature based tools.

Słowa kluczowe

EN

generalized convolution; discrete transforms; image decomposition; image filtering

• Wydawca: Institute of Information Technology of the Warsaw University of Life Sciences – SGGW
• Czasopismo: Machine Graphics and Vision
• Rocznik: 2008
• Tom: Vol. 17, No. 3
• Strony: 279--297
• Opis fizyczny: Bibliogr. 18 poz., rys., wykr.

Twórcy

autor

Korohoda P.

autor

Dąbrowski A.

• AGH Univesity of Science and Technology, Institute of Electronics,

Bibliografia

• [1] Aizenberg N. N.: Spectrum of the convolution of the discrete signals in an arbitrary basis.(In Russian) Rep. Acad. Science USSR (Doklady Akademii Nauk SSSR), 241(3), 551-554, 1978.
• [2] Aizenberg N. N., Trofimiuk O. T.: Shift, convolution and correlation function of the discrete signals in an arbitrary basis. (In Russian) Rep. Acad. Science USSR (Doklady Akademii Nauk SSSR.), 250 (1), 47-51, 1980.
• [3] Clarke R. J.: Transform coding of images, Academic Press 1985.
• [4] Tadeusiewicz R., Korohoda P.: Computer based analysis and processing of images.(in Polish) Wyd. Fundacji Postepu Telekomunikacji, Cracow, Poland, 1997.
• [5] Margrave G. F.: Theory of nonstationary linear filtering in the Fourier domain with application time-variant filtering. Geophysics, 63 (1), 244-259, 1998.
• [6] Mitra S. K.: Digital Signal Processing: A Computer Based Approach. McGraw-Hill, 1998.
• [7] Bovik A. (ed.): Handbook of image and video processing. Academic Press, 2000.
• [8] Bracewell R. N.: The Fourier transform and Its Applications. McGraw-Hill, 2000.
• [9] Korohoda P., Dąbrowski A.: Generalized primary domain interpretation of product filtering of digital signals in the transform domain. Proc. of the IEEE Workshop gn Signal Processing, (Poznan, Poland) Oct., 75-80, 2003.
• [10] Korohoda P., Dąbrowski A.: Generalized convolution concept based on DCT. Proc. of the 12th European Signal Processing Conference - EUSIPCO’O4, (Vienna, Austria), Sep., 973-976, 2004.
• [12] Korohoda P.: Equivalent of impulse response notion for selected discrete transformations. (in Polish) Automatyka, AGH University of Science and Technology of Cracow, Poland, 8 (3), 351-359, 2004.
• [13] Tadousiewicz R., Ogiela M.: Medical Image Understanding Technology. Springer -Verlag, Berlin Heidelberg, 2004.
• [14] Jaworska T.: Amplitude elimination for stereo image matching based on the wavelet approach. MGV, 14(1), Warsaw, Poland, 103-120, 2005.
• [15] Korohoda., Dabrowski A.: Generalized convolution concept extension to multidimensional signals. Proc. of the IEEE Workshop on Multidimensional Signal Processing, (Wuppertal, Germany), July, 187-192, 2005.
• [16] Korohoda P., Dąbrowski A.: Approximation of the generalized convultion - case study example. Proc. of the IEEE Workshop on Signal Processing, (Poznan, Poland), Sep., 41-44, 2005.
• [17] Aizenberg I., Astola J. T.: Discrete generalized Fresnel functions and transform in an arbitrary discrete basis. IEEE Trans. on Signal Processing, 54 (11), Nov., 4261-4270, 2006.
• [18] Korohoda P., Dabrowski A: Some Further Study on the Concept ofthe Generalized Convolution. Elektronika, 48(4), Apr., 16-20, 2007.