Exposing Digital Forgeries in Ballistic Motion

We describe a geometric technique to detect physically implausible trajectories of objects in video sequences. This technique explicitly models the three-dimensional ballistic motion of objects in free-flight and the two-dimensional projection of the trajectory into the image plane of a static or moving camera. Deviations from this model provide evidence of manipulation. The technique assumes that the object's trajectory is substantially influenced only by gravity, that the image of the object's center of mass can be determined from the images, and requires that any camera motion can be estimated from background elements. The computational requirements of the algorithm are modest, and any detected inconsistencies can be illustrated in an intuitive, geometric fashion. We demonstrate the efficacy of this analysis on videos of our own creation and on videos obtained from video-sharing websites.