Identifying the projective group for patterns by developing the camera model, the projective Fourier transform and its inverse are obtained in analogy with the classical, that is, Euclidean Fourier analysis. Projectively adapted properties are demonstrated in a numerical test. Using the expression of the projective Fourier integral by a standard Fourier integral in the coordinates given by the complex principal logarithm, the discrete projective Fourier transform and its inverse are constructed showing that FFT algorithms can be adapted for their computations.
Jacek Turski, Jacek Turski,
"Projective Fourier analysis in computer vision: theory and computer simulations", Proc. SPIE 3168, Vision Geometry VI, (20 October 1997); doi: 10.1117/12.279657; https://doi.org/10.1117/12.279657