Structure and Motion for Dynamic Scenes - The Case of Points Moving in Planes

We consider dynamic scenes consisting of moving points whose motion is constrained to happen in one of a pencil of planes. This is for example the case when rigid objects move independently, but on a common ground plane (each point moves in one of a pencil of planes parallel to the ground plane). We consider stereo pairs of the dynamic scene, taken by a moving stereo system, that allow to obtain 3D reconstructions of the scene, for different time instants. We derive matching constraints for pairs of such 3D reconstructions, especially we introduce a simple tensor, that encapsulates parts of the motion of the stereo system and parts of the scene structure. This tensor allows to partially recover the dynamic structure of the scene. Complete recovery of structure and motion can be performed in a number of ways, e.g. using the information of static points or linear trajectories. We also develop a special self-calibration method for the considered scenario.