Defining areas for mouselistener in Java?

Well, I have to code a risk clone in java (yes, fail) and I need the program to select the province when clicked on - so I need to define these areas some way. My idiot instructor suggested that I add every pixel manually, and I happen to prefer dying over it.

I am sure there is a more intelligent way, but does anyone know?

Use a bitmap with region 1 in colour 1, region 2 in colour 2, etc. for lookup. Polygons are fine, too.