Abstract
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
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