# How to apply a 1D filter (CSF) to an image?

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.

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.
• 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. – DOMiguel Aug 5 '15 at 15:47