On unified optical flow field

A new approach to motion analysis from a sequence of stereo images has been developed recently (C. Q. Shu and Y. Q. Shi, A new approach to motion analysis from a sequence of stereo images, Technical Report No. 18, Electronic Imaging Laboratory, Department of Electrical and Computer Engineering, New Jersey Institute of Technology, Newark, NJ, 1990) in which the optical flow determined by B. K. P. Horn and B. G. Schunck (Determining optical flow, Artif. Intell. 17, 185-203, 1981) is extended to a spatial image sequence resulting in a unified optical flow field (UOFF). A set of equations is established to characterize the UOFF. Another set of equations is derived from which 3D motion can be recovered based on the UOFF. There is no need for feature correspondence in the approach. The recovered 3D motion is for a whole continuous field. It is therefore a purely optical flow approach. In this paper, the new concept of the UOFF is presented in a more general and compact manner. This paper discusses two main aspects about the UOFF. Firstly, the brightness function of an image is considered as not only a function of time but also a function of sensor's spatial position. The concept of imaging space is presented as an accurate description of the set of all possible brightness functions. Secondly, the brightness invariance is recognized not only for the time variation but also for the space variation so that the brightness invariance equations for both time and space domains are established. It is noted that the optical flow discussed in Horn and Schunck (1981) and the optical flow for a spatial image sequence developed in Shu and Shi (1990) are both special cases within the framework of the UOFF.