Fast and accurate computation of the Fourier transform of an image

Gregory Beylkin

doi:10.1117/12.191887

25 October 1994 Fast and accurate computation of the Fourier transform of an image

Gregory Beylkin

Proceedings Volume 2277, Automatic Systems for the Identification and Inspection of Humans; (1994) https://doi.org/10.1117/12.191887
Event: SPIE's 1994 International Symposium on Optics, Imaging, and Instrumentation, 1994, San Diego, CA, United States

Abstract

We use the Battle-Lemarie scaling function in an algorithm for fast computation of the Fourier transform of a piecewise smooth function f. Namely, we compute for -N <EQ m,n <EQ N (with a given accuracy (epsilon) ) the integrals f(m,n) equals (integral) ¹₀ (integral) ¹₀ f(x,y)e^-2(pi imx)e^-2(pi iny)dxdy (0.1) in O(N_D)+ O(N²logN) operations, where N_D is the number of subdomains where the function f is smooth. We consider an application of this algorithm to image processing. Notwithstanding that it might be advantageous to consider an image as a piecewise smooth function f, it is a common practice in image processing to simply take the FFT of the pixel values of the image in order to evaluate the Fourier transform. We propose our algorithm as a tool for the accurate computation of the Fourier transform of an image since the direct evaluation of (0.1) is very costly.

Citation Download Citation

Gregory Beylkin "Fast and accurate computation of the Fourier transform of an image", Proc. SPIE 2277, Automatic Systems for the Identification and Inspection of Humans, (25 October 1994); https://doi.org/10.1117/12.191887

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