A quantitative approach to camera fixation

The quantitative aspects of camera fixation for a static scene are addressed. In general, when the camera undergoes translation and rotation, there is an infinite number of points that produce equal optical flow for any instantaneous point in time. Using a camera-centered spherical coordinate system, it is shown how to find these points in space. For the case where the rotation axis of the camera is perpendicular to the instantaneous translation vector, these points lie on cylinders. If the elevation component of the optical flow is set to zero then these points form a circle (called the equal flow circle or simply EFC) and a line, i.e. all points that lie on this circle or line are observed as having the same azimuthal optical flow. A special case of the EFCs is the zero flow circle (ZFC) where both components of the optical flow are equal to zero. A fixation point is the intersection of all the ZFCs. Points inside and outside the ZFC can be quantitatively mapped using the EFCs. It is shown how the concept of the EFC and ZFC can be used to explain the optical flow produced by points near the fixation point