In an experiment aimed at studying the integration of local velocity measurements Nakayama and Silverman [21] found that smooth curves may be perceived to deform non-rigidly when translated in the image plane. Their experiment on moving sinusoids is shown below.

The main difference in the two curves lies in the size of the regions where flow estimates are heavily biased.

   

Figure 2

Figure 2 shows the flow derived using least squares estimation within small regions. Bias occurs in the regions next to the inflexion points, and these regions are much larger for the low amplitude sinusoid than for the high amplitude sinusoid. A more general flow model must include constraints allowing the flow to smoothly vary from point to point. This smoothness constraints propagate the bias. As a result the low amplitude sinusoid has flow which is upward in one half of the curve and downward in the other. In comparison, the deviation from the veridical is much less in the high amplitude curve as shown in Figure 3.