Abstract

Configurations of dynamic points viewed by one or more cameras have not been studied much. In this paper, we present sev- eral view and time-independent constraints on different configurations of points moving on a plane. We show that 4 points with constant inde- pendent velocities or accelerations under affine pro jection can be charac- terized in a view independent manner using 2 views. Under perspective pro jection, 5 coplanar points under uniform linear velocity observed for 3 time instants in a single view have a view-independent characteriza- tion. The best known constraint for this case involves 6 points observed for 35 frames. Under uniform acceleration, 5 points in 5 time instants have a view-independent characterization. We also present constraints on a point undergoing arbitrary planar motion under affine pro jections in the Fourier domain. The constraints introduced in this paper involve fewer points or views than similar results reported in the literature and are simpler to compute in most cases. The constraints developed can be applied to many aspects of computer vision. Recognition constraints for several planar point configurations of moving points can result from them. We also show how time-alignment of views captured independently can follow from the constraints on moving point configurations.