3-D MOTION ESTIMATION FROM MOTION FIELD

Several experiments suggest that the first stage of motion perception is the measurement of visual motion. The result of this stage is called the motion field, which assigns a velocity vector to each point in the image plane. The second stage involves interpreting the motion field in terms of objects and motion in the three-dimensional world. Recovering 3-D motion of the object from the motion field has been difficult owing to the nonlinear system of equations involved, and the sensitivity of the system to noise. The need for the stability of the system is essential as only the optical flow field can be recovered from a sequence of images, which is at best a crude approximation to the motion field. We define two sets of ''basic'' parameters, which can be recovered from the motion field by solving a linear system of equations. The relationship between the basic parameters and the motion parameter being one-to-one and linear, we obtain a closed form solution for the 3-D motion parameter by solving a system of linear equations only. We prove the correctness, completeness and robustness of the approach and in that sense the problem of recovering the motion parameter from the motion field may be said to be ''solved''. We present the results of extensive experimentation with real and simulated image sequences.