How to get the center of FFT spot

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I'd like to the exact position of FFT spot. I can firstly give a rough position to the script, and then the script will extract a box with defined size. Then I'd like to automatically get the exact position of the spot center. I think I need to use 2D gaussian to fit the spot, or use centroid algorithm. Is there any good idea?

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This question is more about a specific algorithm than about the program language and as such not really on topic here. Both your suggestions sound fine to me. To my knowledge, no special "command" or simple shortcut for your task exists in current GMS scripting, but you might be able to find some Python library that does it and thus could be called from GMS.