On the estimation of optical flow: Relations between different approaches and some new results

A common basis is suggested for the optical flow estimation approaches of Nagel (1983), Haralick and Lee (1983) and Tretiak and Pastor (1984). Based on a discussion of these approaches, an exact solution for the system of partial differential equations proposed by Horn and Schunck (1981) is given at gray value corners and extrema. The insight gained by this solution results in a modification of the “oriented smoothness” approach of Nagel (1983) which thereby becomes considerably simpler. In addition, the optical flow estimation approach of Hildreth (1983, 1984) can be shown to represent a kind of special case of this modified “oriented smoothness” approach in a more direct manner than discussed in Nagel (1984).