When talking about Fourier transform for image processing, we often call the original image formed by pixels in the "time space".
I find it is difficult to understand it. why is it called the time space, where is time coming from?
I can understand if it is called screen space and image space. but why is it time space?
The original formulation of Fourier series was to take a signal, which is to say a function of amplitude values over time, and represent it as a combination of sinusoids, which is to say a function of amplitude values over a range of frequencies. So you would consider the original signal to be $f(t)$, defined over the domain of time $t$, and the Fourier transform $\mathcal{F(f)} = F(T)$, defined over the domain of frequency $T$.
Obviously in the case of image processing the analogy isn't great, since you now have a 2-dimensional "time domain", but it seems like the language has stuck despite that.