The recovery of motion for a class of movements in the space by using the perspective observation of one point, where the motion parameters are all time-varying, is considered in this paper. The motion equation can cover a wide class of practical movements in the space. The estimation of the position and the motion parameter 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. Finally, 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. Further, the occurrence of occlusion is considered in the recovery algorithm.