An Investigation of Smoothness Constraints for the Estimation of Displacement Vector Fields from Image Sequences

A mapping between one frame from an image sequence and the preceding or following frame can be represented as a displacement vector field. In most situations, the mere gray value variations do not provide sufficient information in order to estimate such a displacement vector field. Supplementary constraints are necessary, for example the postulate that a displacement vector field varies smoothly as a function of the image position. Taken as a general requirement, this creates difficulties at gray value transitions which correspond to occluding contours. Nagel therefore introduced the ``oriented smoothness´´ requirement which restricts variations of the displacement vector field only in directions with small or no variation of gray values. This contribution reports results of an investigation about how such an ``oriented smoothness´´ constraint may be formulated and evaluated.