Possible to seperate out transparent background of flat image in node editor?

Hi,
I am trying to use the node editor Material Index to change color and other attributes of a flat 2D image. Is there a way to separate out the transparent background so as to just work on the opaque parts of the image? I am experimenting with the ID Mask as factor to the Alpha Over node, then original image and Invert to its two Image sockets. I succeeded only in changing the color of the sun – not in getting rid of the transparent background. (Please see my screen capture.) Is there a way to get rid of the image’s transparent background? Thanks.
Zaffer