| Errors in Movement
The spiral above, if rotating around its center, does not give rise to the
perception of circular motion but appears to contract or expand. This is predicted by the
large bias in the estimation.
For a rotation around the spiral's center, every point on the spiral traces a circle. Thus, the motion vectors are tangential to circles. Figure 1 shows in red the motion vectors for a counter-clockwise rotation. The corrsponding normal flow vectors, shown in blue, are close to the radial direction.
Such a configuration gives rise to very large bias in the regional estimation of flow and thus flow in the radial direction is computed as shown in Figure 2.
Figure 2: Flow field computed using LS estimation within small circular regions.