For this kind of thing we use an image used as a mask, with transparent/opaque or black/white pixels. The masks aren't drawn, but are conceptually "placed" over the map region they cover.
When you get a click, first check the bounding box of the image. If it's outside, the player didn't click the region. If it's inside, check the pixel. If it's transparent/black, the player didn't click the region. Otherwise, he did.
If memory usage is a serious concern, you can use half-sized images and apply the appropriate screen to image coordinate conversion. You won't get pixel-perfect detection but you probably don't need it in this case.
Also, if you go transparent/opaque, either save the masks as PNG (or any other lossless compression scheme) or use a high threshold (alpha > 128 instead of alpha > 0). Otherwise, JPEG artifacts may cause some of the transparent pixels to appear not so transparent (say alpha = 1 or 2 instead of alpha = 0)