I suppose it seemed simple for me since I'm done it with AWT before.
Basically, you build up a Polygon object with vertices. You pass it to the
Graphics.draw method to display it (or not if you want an invisible hit test
layer over the image). You intercept click or touch events and use the
Polygon's inside() or contains() method to do the hit test.

Depending on the complexity and display size of the image, you may run into
some hit test accuracy issues due to the touch UI.

If you have the original artwork in Adobe Illustrator, you ought to be able
to get a vertex list therefrom. If not, google for a raster-to-vector tool
of your choice, for example:
http://freegeographytools.com/2007/converting-raster-area-images-into-polygon-shapefiles

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