Motion recovery of moving objects under perspective stereo vision

We consider a problem of recovering motion of an object moving in space under perspective observation. It is assumed that the motion equation is described by a linear system with unknown constant motion parameters and that a single feature point on the object is perspectively observed by two cameras. Then we analyze the identifiability of motion parameters from the stereo image data observed over an interval of time. The identifiability problem is solved by employing theories on linear dynamical systems, and the condition, established as a necessary and sufficient condition, turns out to be the controllability of a modified linear system. Such an analysis is essential when we develop and use any algorithms involving motion parameter identification. Finally, we include numerical results by employing the extended Kalman filter.