Which Algorithm for Motion Detection Between Consecutive Images?

[whatta]

there seem to be no forum for applied math on PF, but can anyone here point me to simplest yet efficient yet not covered by evil patents algorithm for motion detection between two/more consecutive images?

 

[whatta]

it might help if I say what is this for. for example, http://www.imagehosting.com/out.php/i276617_motion.GIF "white" represents background, "gray" is round moving object in two frames, and "dim gray" is area that we have no background information for. for "gray" areas it should be possible to restore background, but we need some way to tell which data is background data in each frame. I can see that, subtracting images, I can find these areas, but how do I guess the direction of motion?