What is the relation between time, frequency, spatial and spectral domains?
I think that time and spatial domains are the "original" domains (e.g. if the signal is a greyscale image, then the domain would e.g. be all possible grey intensities for all pixels), whereas the frequency and spectral domains are the "Fourier" domains, that is, the domains of the functions after having applied the Fourier transform to the original function or signal. Is this right?
I also think that we use spatial when the input, in the original domain, are images, whereas we use "time" in a more general sense, but maybe we should be using it only when the original domain only represents time (we could say a similar thing regarding the frequency domain). The spectral domain, I think, is a more general term, which refers to the domain after having applied the Fourier transform, so it can e.g. refer to the frequency domain. Is this right?
I am more interested in knowing the meaning of these concepts in the context of image processing and computer vision. I think it would be interesting to have a diagram that explains the transitions between these domains (using e.g. the FT).