chinu1310: Thank you for reply! I tested on that code before. Only enlarge is not enough for this question. I need more explanation theoretically.
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Resize image by FFT
Hello everyone:
I have another question about FFT resize image.
I have an image and calculate its FFT, question is if I enlarge or reduce images size, how can I get its new FFT base on previous FFT? I do not want to re-calculate FFT again.
Matlab code would be good for testing! Thanks in advance!
Chao
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Answers
An intensity in the frequency domain is basically a histogram bin.
Consider what it means to resize an image:
Doubling its size will effectively halve all frequencies.
Halving its size will effectively double all frequencies.
Also, the "histogram bins" must be rescaled according to the new total "energy" in the image (the next to last code line above).
Ugumba: if you double the size, i think what you double, for a same image, the sample frequency, so low frequencies are the same but higher frequencies are absent, because we cant reconstruct details that weren't present at original image.
For doubling from FFT, what i would do create a double size all Zeros FFT table and fill the low frequency coefficients by copying from the original FFT, and keep zero the high frequency coefficients.
For halving, just filter with a cut frequency of pi/2 the first half coefficients with a FIR filter to remove aliasing, then truncate the FFT to half the size (in the case of 2D FFT, a quarter the size).
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by: chinu1310Posted on 2007-06-29 at 15:08:25ID: 19393926
here is example code of how to enlarge an image using an FFT:
% Copyright: Joseph O'Ruanaidh 2003, All Rights Reserved
% Disclaimer: not to be used for air traffic control
function y=fftResize(x, l)
ff=fft2(x);
[m,n]=size(ff);
ml = floor((l-1)*m/2)*2
mm = m + 2*ml
nl = floor((l-1)*n/2)*2
nn = n + 2*nl
% what will soon be the new transform
qq = zeros(mm, nn);
% The following indices copy from the original FFT to the new FFT if mod(m, 2)==0
xr = [1:m/2 ml+m/2+1 2*ml+((m/2+2):m)]
else
xr = [1:((m+1)/2) 2*ml+(((m+3)/2):m)]
end
if mod(n, 2)==0
yr = [1:n/2 nl+n/2+1 2*nl+((n/2+2):n)]
else
yr = [1:((n+1)/2) 2*nl+(((n+3)/2):n)]
end
% Do the copying and rescale the indices
qq(xr, yr) = ff*(mm*nn)/(m*n);
% And don't forget the most important part
y=ifft2(qq);