Computer Vision algorithm to tell if camera is moving?
Use background detection algorithm, say Gaussian Mixture-based background detection (present in OpenCv) and then make some assumption - say backround takes more than 60% of image.
Then convert frames to color model which keeps luminance as separate component. Compare consecutive frames with small tolerance per color per pixel and bigger tolerance per light (to take into account shadows). If your camera is not really stationary, check by movement algorithm if frame is shifted by some distance (camera may move slightly even if it stands still), in that case compare it with shifted frame after detecting shift.

Now gather frames with some tolerance, say 95% of frames match background in at least 60% of pixels with slight shifts (it depends on distance from camera to background).
If it matches, camera was still, if not then either parameters were too big or it was moving.
Adjust parameters, done.