When I first saw the problem description, I wanted to "amplify" the background image through movement in some way. For example, having sections of the image move around. I pondered movement with the foreground image and movement in the background image. I was compelled by movement of bodies in gravitational fields ... perhaps using the foreground image as a black hole or the background image as a white hole.
Then it occured to me to have movement in color space as opposed to physical space. This java applet is the result of this. Both RGB and HSB are multidimensional spaces and the applet moves the colors in the space while keeping the locations the same. I had no idea what this would look like before I implemented it, and I'm still quite puzzled by what it does.