Errors in Movement
To see the illusion in Figure 1, look at the black dot in the center of the image and move your head towards and away from the screen. You will experience a rotational movement of the inner ring -- clockwise as you move away and counter clockwise otherwise.
Since the boxes are tilted in different ways in the inner and outer ring, there are different normal flow vectors and as a result, different optical flow estimates (because of different biases) in the two rings. The difference is tangential to the circles and thus experienced as rotation.
Actually, the estimation is somewhat more elaborate. The vision system not only computes normal flow and flow on the basis of the raw image. But it also smoothes, or blurs, the image and computes normal flow and flow from the blurred image. We say the vision system computes flow at different levels of resolution. The final estimate is an average of the flow estimates at the individual resolutions.
Based on the understanding of how the illusion works, we can increase and decrease the effect by changing the texture. For example by inserting small diagonals in the boxes, we make the normal flow distribution in the inner and outer ring about the same. This greatly reduces the illusion.