New 2D discrete Fourier transforms in image processing

Artyom M. Grigoryan; Sos S. Agaian

doi:10.1117/12.2083389

16 March 2015 New 2D discrete Fourier transforms in image processing

Artyom M. Grigoryan, Sos S. Agaian

Proceedings Volume 9399, Image Processing: Algorithms and Systems XIII; 939910 (2015) https://doi.org/10.1117/12.2083389
Event: SPIE/IS&T Electronic Imaging, 2015, San Francisco, California, United States

Abstract

In this paper, the concept of the two-dimensional discrete Fourier transformation (2-D DFT) is defined in the general case, when the form of relation between the spatial-points (x, y) and frequency-points (ω₁, ω₂) is defined in the exponential kernel of the transformation by a nonlinear form L(x, y; ω₁, ω₂). The traditional concept of the 2-D DFT uses the Diaphanous form xω₁ +yω₂ and this 2-D DFT is the particular case of the Fourier transform described by the form L(x, y; ω₁, ω₂). Properties of the general 2-D discrete Fourier transform are described and examples are given. The special case of the N × N-point 2-D Fourier transforms, when N = 2^r, r > 1, is analyzed and effective representation of these transforms is proposed. The proposed concept of nonlinear forms can be also applied for other transformations such as Hartley, Hadamard, and cosine transformations.

Citation Download Citation

Artyom M. Grigoryan and Sos S. Agaian "New 2D discrete Fourier transforms in image processing", Proc. SPIE 9399, Image Processing: Algorithms and Systems XIII, 939910 (16 March 2015); https://doi.org/10.1117/12.2083389

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