Towards an understanding of camera fixation

A fixation point is a point in 3-D space that projects to zero optical flow in an image over some period of time while the camera is moving. Quantitative aspects of fixation for a static scene are treated. For the case where the rotation axis of the camera is perpendicular to the instantaneous translation vector, it is shown that there is an infinite number of points that produce zero instantaneous optical flow. These points lie on a circle (called the zero flow circle, or ZFC) and a line. The ZFC changes its location and radius as a function of time, and the intersection of all the ZFCs is a fixation point. Points inside the ZFC produce optical flow that is opposite in sign to those that are outside the ZFC. This fact explains in a more quantitative way phenomena due to fixation. In particular, points in the neighborhood of the fixation point may change the sign of their optical flow as the camera moves. In a set of experiments, it is shown how the concept of the ZFC can be used to explain the optical flow produced by 3-D points near the fixation point