The geometry of dynamic scenes—On coplanar and convergent linear motions embedded in 3D static scenes

In this paper, we consider structure and motion recovery for scenes consisting of static and dynamic features. More particularly, we consider a single moving uncalibrated camera observing a scene consisting of points moving along straight lines converging to a unique point and lying on a motion plane. This scenario may describe a roadway observed by a moving camera whose motion is unknown. We show that there exist matching tensors similar to fundamental matrices. We derive the link between dynamic and static structure and motion and show how the equation of the motion plane (or equivalently the plane homographies it induces between images) may be recovered from dynamic features only. Experimental results on real images are provided, in particular on a 60-frames video sequence.