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Proceedings Paper

Fast and accurate computation of the Fourier transform of an image
Author(s): Gregory Beylkin
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Paper 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(ND)+ O(N2logN) operations, where ND 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.

Paper Details

Date Published: 25 October 1994
PDF: 9 pages
Proc. SPIE 2277, Automatic Systems for the Identification and Inspection of Humans, (25 October 1994); doi: 10.1117/12.191887
Show Author Affiliations
Gregory Beylkin, Univ. of Colorado/Boulder (United States)


Published in SPIE Proceedings Vol. 2277:
Automatic Systems for the Identification and Inspection of Humans
Richard J. Mammone; J. David Murley, Editor(s)

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