There is no possible equation for it. Whether something is foreground or background is dependent on the purpose for which the equation is being processed, rather than on any inherent property in the image.
For example if you are doing detection of comets in near-solar orbit, then images of the Sun itself are background and tiny tiny objects are the foreground, but if you are doing analysis of solar flares then you examine exactly the same images ignoring all those tiny dots and looking at the bright bright object that needs to be ignored in the comet detection task.
