Motion analysis is a bit beyond what the Arduino is capable of and in any case where would you attach a webcam? I'm working on something similar with audio and I'm looking to use either a modulated infrared beam or, if I can't get the distance that way, some sort of ultrasound transciever. On the other hand, if you just want to detect motion in a room, passive infrared devices (PIR) are cheap (since they're widely used in security systems) and have a good range. They should also be "stable" in the sense that you can adjust them to prevent false positives.