Determining Velocity Map By 3-D Iterative Estimation

Velocity information is not only important for determining velocities and trajectories of objects but also important as a cue for image segmentation. It may be used to link adjacent but visually dissimilar surfaces or to divide surfaces not easily separable by static criteria alone[l]. A straightforward approach to obtaining velocity information is to find and track prominent features by a matching method from frame to frame[2,3]. These methods can estimate velocities of prominent points accurately; however, a problem of these methods is that velocities of only a sparsely sampled set of points can be obtained, which are not dense enough to be useful for tasks such as image segmentation. Another approach uses the fact that for images of moving objects the spatial and temporal intensity changes are not independent of each other and satisfy a relation Vx*Gx+Vy*Gy=-Dt (1) Here, (Vx,Vy) are the two components of the velocity vector, (Gx,Gy) represent the two components of the spatial intensity gradient, and Dt represents the gray value difference between consecutive frames, at a point (x,y). Since the single constraint of Eq. (1) does not allow one to determine both components (Vx,Vy) of the velocity, additional assumptions are necessary. Cafforio and Rocca[4] and Fennema and Thompson[5] assumed that the velocity is constant within a region corresponding to the image of a moving object, and applied a clustering approach to determine the dominant velocities in the scene. By this global method, they obtained accurate velocities of objects; however, with that assumption, the method is applicable only to objects which translate parallel to the image plane. Horn and Schunck[6] studied a more general assumption; namely that the velocity varies smoothly. This assumption is interesting because it constrains the variability of velocities between neighboring points and allows one to estimate the velocity of each point from local computation. However, the method seems to become more efficient and reliable if we have some initial estimates of velocities. There has been no attempt to try to combine or relate the matching method by which accurate estimation of velocities (although of only a sparsely sampled set of points) are obtained and the nonmatching method by which velocities of a dense set oi points can be estimated, but additional constraints are required. In this communication, we propose an approach which uses the velocity estimates of the prominent feature points as reliable initial estimates of velocities and propagates them to other points …