Yes, in thinking about it its harder than I was expecting. Here is a Stack Overflow post with some good ideas:
Check out answer #2, it seems like with some tweaking something that could be made to work. The idea is calculate bytes per pixel in the original image and use that to scale the dimensions. But, smaller images often will use slightly more bytes per pixel so a fudge factor is needed. With a good formula the hope is only one iteration will be needed, bounding the time.