I need get angle of object on picture, using Fourier transformation.
I have a picture object, that I rotated. There are no problems with the Fourier realization. It shows me good gradient lines that confirm the correct object angle.
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You don't show us the image or its transform, so I'll assume the gradient lines are indeed clear enough. In that case you'd use the Hough transform. Output is a set of lines, each with an angle.