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I am working on a Fourier Ptychography problem. My research problem requires me to shift the Fourier spectrum of an image by a floating-point value. For a real-valued image, we can simply use cv2.warpAffine to shift the image by floating-point values (aka subpixel shifting).

Taking fourier transform of an image produces a complex matrix. The problem is, cv2.warpAffine does not support complex matrices, and so I cannot use it on them. I tried searching for alternatives, but none of them seem to work. I came across numpy.roll, but the problem is, it does not support subpixel shifting. Rounding off the shifting values translates to loss of information in my case. Is there a solution in python, that allows for subpixel shifting on complex matrices?

Thanks.

EDIT: Based on Marcus' answer, I did some digging and implemented a nifty little script for subpixel shifting in python based on a Matlab script for the same.

Here's the link to the script. Hope it helps!

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You'd not do it in frequency domain at all. Use the shift property of the discrete Fourier transform!

Simply multiply the rows of your original image with an $e^{j2\pi \Delta f_x x/W}$ pointwise ($x$: pixel index in that row, $W$: width of image) before transforming to frequency domain to shift by $\Delta f_x$ in row direction. Same for shifts in column direction; multiply columns with $e^{j2\pi \Delta f_y y/H}$ pointwise ($y$: pixel index in that column, $H$: height of image). There's no restrictions on the "fineness" of $\Delta f$ in either direction, and any 2D shift can be understood as a shift in row and one in column direction.

If necessary, transform your image from frequency to spatial domain, do the multiplications, and transform back.

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  • $\begingroup$ Oh, that seems easy to implement by myself! I really wonder how none of the major python number-crunching libraries have this tiny little function implemented yet. Thank you for your help! Hadn't thought about it that way. $\endgroup$ Apr 28 '20 at 21:07
  • $\begingroup$ @SuyogJadhav why should they? It's not hard to implement oneself, and image processing people usually don't care about complex numbers :) $\endgroup$ Apr 29 '20 at 7:17
  • $\begingroup$ Yeah true. One doesn't usually need to do a shifting on complex matrices. $\endgroup$ Apr 29 '20 at 10:08

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