Scale using a black and white image

I want to scale a lot of objects in a scene from the center to the edge. I saw someone do that using a black and white image, where the center was black (simple round gradiant), and by scaling this image, he used an expression for the scale of all the objetcs to scale using the black as guide.

I don't know if it seems complicated, but it's a lot of little balls spaced alike, and they have to scale from the center of the comp to the edge, from 0% to 100%, and I remember that way of doing but I don`t know if the best. 

(doing it manually is the last resorce)