Like in any other kind of signal processing, the relationship is Nyquist's theorem. An image is a discrete sequence of samples of a continuous signal. If the original signal has frequency components higher than half the sampling rate, then there will be aliasing. To put that another way, if you look at the real-world size of a pixel, any details smaller than two pixels wide will be aliased. This applies to synthetic images as well as to photographs. If you define a procedural texture via a mathematical function, the function is continuous but you only evaluate it at certain points.
The problem is, of course, if you only have the sampled image and not the original signal, the high-frequency components have already been aliased, so you can't measure them directly. You have to use statistical techniques to guess which details in your aliased image were originally higher-frequency signals.