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I'm currently trying to compute the fft of an image via fftw_plan_dft_2d.

To use this function, I'm linearizing the image data into an in array and calling the function mentioned above (and detailed below)

ftw_plan fftw_plan_dft_2d(int n0, int n1,
                            fftw_complex *in, fftw_complex *out,
                            int sign, unsigned flags);

The func modifies a complex array, out, with a size equal to the number of pixels in the original image.

Do you know if this is the proper way of computing the 2D FFT of an image? If so, what does the data within out represent? IE Where are the high and low frequency values in the array?

Thanks, djs22

djs22
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2 Answers2

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A 2D FFT is equivalent to applying a 1D FFT to each row of the image in one pass, followed by 1D FFTs on all the columns of the output from the first pass.

The output of a 2D FFT is just like the output of a 1D FFT, except that you have complex magnitudes in x, y dimensions rather just a single dimension. Spatial frequency increases with the x and y index as expected.

There's a section in the FFTW manual (here) which covers the organisation of the real-to-complex 2D FFT output data, assuming that's what you're using.

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Paul R
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  • Thanks for the answer. The problem I'm having is that this 2D FFT returns a 1D array. Its easy enough to reconfigure it into the appropriately sized 2D array, but I'm still not quite sure how to work with the data.
    I'm pretty sure that would imply that my lowest frequency content would be in the upper left hand corner and higher freq content would be in the bottom right?
    With respect to the section in the manual; as you said that's explicitly for the real to complex function, but unfortunately I'm using the fftw_plan_dft_2d.     – djs22 Mar 16 '11 at 18:59
  • @djs22: OK - the array isn't really 1D, it's n0 x n1 in row major order - see section 2.2 of the FFTW manual. – Paul R Mar 16 '11 at 20:49
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It is. Try to compute 2 plans:

plan1 = fftw_plan_dft_2d(image->rows, image->cols, in, fft, FFTW_FORWARD, FFTW_ESTIMATE); 
plan2 = fftw_plan_dft_2d(image->rows, image->cols, fft, ifft, FFTW_BACKWARD, FFTW_ESTIMATE);

You'll obtain the original data in ifft.

Hope it helps :)

grc
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João Faria
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