I am facing the following problem: I have an image and a contrast sentivity function (CSF). The CSF is a function defined in the frequency domain and it is just a band-pass filter. The problem is that it is a 1D filter so I do not know how to apply it to the Fourier transform of the image.

I thought about creating a 2D filter based on the revolution around the zero frequency of the 1D filter but I do not know if it is mathematically correct or if it is the common procedure.

Thanks in advance!


1 Answer 1


I believe what you want to do is take your 1D filter column vector, call it $x$, and create a 2D filter with $xx^T$. The result of this outer product (column vector times row vector) is a matrix that you can use to do element-wise multiplication with the 2D Fourier transform of the image.

  • $\begingroup$ I am sorry. I accepted your answer but I realized that it is not what I wanted. If you do the outer product you do not get the revolution of the 1D function but only in the quartes. Nevertheless, I give you up vote for the idea (EDIT: It seems I am not allowed :S). $\endgroup$
    – DOMiguel
    Commented Aug 5, 2015 at 7:23
  • $\begingroup$ Perhaps I don't understand what you are trying to do... it sounds like you want to rotate a vector in a polar coordinate system? $\endgroup$ Commented Aug 5, 2015 at 15:36
  • $\begingroup$ That's it, but with outer product you do not get an exact rotation. For example, the outer product of the function $y=x^2$ defined over the region $[-1,1]$ is not a paraboloid of revolution. $\endgroup$
    – DOMiguel
    Commented Aug 5, 2015 at 15:47

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