Detecting Static Footage in FCP

I'd like to strip out all footage in screen captures where there is no onscreen motion or changes. These are screen captures of non-motion video sources like leaderboards in a game. I would think there are two ways to do this: one would be to get my Mac to act like a security cam with a motion-detector, and only record when there are screen changes. The other way, which I'll probably have to resort to if I can, is to detect when frames change, and introduce cuts. But I can't find a way to do either. I use Final Cut Pro, and DaVinci. Any thoughts?