GIMP :: Break Up Political Map Into Individual Images

I have an image of political boundary map that I want to break up so that I have an individual image for each unit, such that I could combine them back together and get the original map. For purpose of illustration, let's say it's a US state map.

I know that I could take the original image, erase everything but Washington State to alpha, save that as Washington, then undo back to the beginning, erase everything but Oregon to alpha, save that as Oregon, undo, etc, until I had all 50 states, all in the same position as on the original map. I could then easily create images of arbitrary groups of states by just combining the images of the individual states I wanted to be in the group.

But getting to that point would take 50 manual erasing for a state map, and many more on my actual map. Is there a way to break up the map in an automated way?

The map image has the boundary all in one color that isn't otherwise present in the image, so it's easy enough to select just the boundary .