1D FFT on rotated image column by column

Question

I am facing a problem: performing 1D FFT on a rotated column by column on a rotated image, described as following:

Original Image:

Rotated Image:

What I have:

• original image
• convolution kernel for the rotated image.

what I'd like to do:

• perform the 1D FFT (image domain convolution, or frequency domain multiplication) on the ROTATED image.

Something like this:

However, from implementation point of view, then I need to do image rotation, then apply the 1D FFT, and it is an expensive implementation and execution at run time.

So, I am wondering, instead of rotating the image, how can I change my convolution kernel such that I can apply it to the original image? can I rotate the 1D FFT convolution kernel? If so, should I do it in frequency domain, or image domain? And how? Or any resources and literatures? Thanks a lot.

Answer 1

I eventually rotated the image, then performed the 1D fft column by column.