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2dFFT & image processing

• To: mathgroup at smc.vnet.net
• Subject: [mg101500] 2dFFT & image processing
• From: "alexxx.magni at gmail.com" <alexxx.magni at gmail.com>
• Date: Thu, 9 Jul 2009 01:53:01 -0400 (EDT)

hi everybody,
I need to perform a high-pass filter on some images.

I know I can get a high pass filter doing a convolution of the image
with a predefined kernel, but for various reasons (and my learning
too) I wanted to follow the sequence:
1) fft
2) cut away central region (with a smooth edge)
3) fft again

but, due to my ignorance, I'm unable to accomplish the process:

given the image in a, I put:

f = Fourier[a[[1]]];
af = Abs@f;
Dimensions[f]
   {500,500}

and I can check the fft with Graphics[Raster[255*af/Max[af]]]

I then create the "hole" and apply it to the fft and invert again:

k = Table[1 - Exp[-(x^2 + y^2)/s], {x, -249, 250}, {y, -249, 250}] /.
s -> 1000.;
holed = af*k;
fholed = Abs[Fourier[holed]];

since the reconstructed image Graphics[Raster[255*fholed/Max[fholed]]]
is strongly fuzzed, whichever value I choose for the parameter s
above, I wanted to ask you if I completely misunderstood the process!

thank you,


alessandro

• Follow-Ups:
  • Re: Re: 2dFFT & image processing
    • From: Patrick Scheibe <pscheibe@trm.uni-leipzig.de>
  • Re: 2dFFT & image processing
    • From: Alessandro Magni <alexxx.magni@gmail.com>
  • Re: 2dFFT & image processing
    • From: Patrick Scheibe <pscheibe@trm.uni-leipzig.de>
  • Re: 2dFFT & image processing
    • From: Matthias Odisio <matthias@wolfram.com>
  • Re: 2dFFT & image processing
    • From: Sseziwa Mukasa <mukasa@jeol.com>