I understand how a 1D Fourier transform separates a signal into its component frequencies, but I'm having difficulty understanding how a 2D Fourier transform affects a 2D image.
From another question, John Calsbeek linked to an interesting paper about measuring the quality of noise functions. This showed various noise functions and the Fourier transform of each.
Is this a discrete transform of the pixel data, or a continuous transform of the continuous interpolating function which is used to generate the noise at arbitrary points?
Is the annular shape analagous to taking 1D Fourier transforms of the line through the centre of the image at every possible angle? Or is the transform for each possible angle also measured across the whole 2D space rather than only along a line through the centre? I'm trying to get an intuitive feel for what changes in the input image correspond to what changes in the Fourier transform.