Getting the intersection of two image files (as an image file)

[LogLady]

Let's say I have 2 same-size images, a and b. Image a is all red pixels; b is all blue. Both images top halves are a slightly lighter color than their bottom halves.

Is there a method of getting an image that is the intersection of the two images? For example, the desired result (based on the example) would be a new image, of the same size as a and b, whose bottom half is transparent and whose top half is white with <255 alpha.

Another example would be, comparing an all-red image with an all-blue image (no lighter halves or anything) would yield a fully transparent new image.

EDIT: Please keep in mind that the red and blue images are simply examples. I'm looking for a method that works with any two images of the same dimensions.