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Fast Fourier Transform (FFT) for images

Posted 9 years ago
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Hi friends, I am trying to do a FFT of the images using Mathematica and found there exists a package called "ImageProcessing" :
http://reference.wolfram.com/legacy/applications/digitalimage/UsersGuide/ImageTransforms/8.2.html.

However the package is not implemented in the Mathematica and I could not find a place to download such a package either. Has anyone of you used this for Fourier and Inverse Fourier transformation of images? Thanks a lot for your help!
4 Replies
You can often find old packages or information about old packages in the Wolfram Library Archive: http://library.wolfram.com/

In particular please see: http://library.wolfram.com/infocenter/Conferences/350/

The package you mention appears to have been an add-on package avaialble for purchase for Mathematica 4. If you would like the package, please search the Archive for more content or contact the package's maker.

In recent versions of Mathematica, you can use ImageData to get a matrix of the pixel values of the image (reference.wolfram.com/mathematica/ref/ImageData.html). This matrix can then be used in additional proccessing for functions like Fourier.

Instead of the Fourier transform, you may consider using Wavelets: http://reference.wolfram.com/mathematica/guide/Wavelets.html
People also find ImageConvolve useful for many applications where they would have used the fourier transform of the image: http://reference.wolfram.com/mathematica/ref/ImageConvolve.html
Posted 9 years ago
Thanks! It's of great help!
You could just run:
Fourier[ImageData[insert image here]]
and then run:
Abs[Fourier[ImageData[insert image here]]]
to get a rational version.

Finally you can run:
Image[Abs[Fourier[ImageData[insert image here]]]]
to get an image back.


Also on a side note in computer programs fourier transforms are not run in either the old method (slow fourier transforms?) or with fast fourier transforms but with a completely different algorithm.
You can use ImagePeriodogram to compute the power spectrum of an image.
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