Identifiability of motion parameters under perspective stereo vision

We consider a problem of recovering motion of 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. It is shown that the parameters are identifiable genetically. Moreover, the only cases where the parameters can not be determined uniquely imply very much restrictive motions, confined either in certain planes or lines, in which case any identification algorithms will fail. Moreover whenever the parameters can be determined uniquely, the parameters can be recovered from stereo image data over any time interval of arbitrary length. The problem is also analyzed in discrete-time settings, which can be used for the case of continuous-time motion with discrete-time observations.