If you are going to be doing this type of image  manipulation you are
probably better off using Java 2D to draw the whole thing yourself or
perhaps you can use some other graphic toolkit on top  of 2D. I would
avoid using AWT/Swing and its layout  managers for this type of application.

here is an idea:
try to make images instead of icons, use the
g.drawImage function to locate those images over the
map and make a function that responds to the user
click on a x,y point, something like this:

//area:x,y,width,height
//i asume that u have various areas
int[][]
area={{20,20,20,20},{50,80,60,10},{10,10,10,10}};

//function returns the area clicked
//x,y are given by a mousemotionlistener

int usr_click(x,y){
int z=0;
while(z<area.length){
if(x>=area[z][0]&&x<=(area[z][0]+area[z][2])&&y>=area[z][1]&&x<=(area[z][0]+area\
[z][3])){
return(z);
}
z++;}
return(-1);//no area found, default  action
}

Sorry, I have never met with such a problem before. Because I am using another image processing tool. You can google it and choose one to have a try.
http://www.rasteredge.com/how-to/csharp-imaging/