Motion recovery for a class of movements under perspective observation

The recovery of motion for a class of movements in the space by using the perspective observation of one point is considered in this paper. The motion equation can cover a wide class of practical movements in the space. The estimations of the position and motion parameters which are all time-varying are simultaneously developed in the proposed algorithm. The formulated problem can be converted into the observation of a dynamical system with nonlinearities. The proposed observer is based on the second method of Lyapunov. First, the parameters relating to the rotation of the motion are identified, where only one camera is needed. Then the position of the moving object is identified, where the stereo vision is necessary. In the third step, the parameters relating to the straight movement are identified. The assumptions about the perspective system are reasonable, and the convergence conditions are intuitive and have apparently physical interpretations. The proposed method requires minor a priori knowledge about the system and can cope with a much more general class of perspective systems. Furthermore, the algorithm is modified to deal with the occlusion phenomenon.