Yibing Yang, Alan Yuille
The instantaneous image motion field due to a camera moving through a static environment encodes information about ego-motion and environmental layout. For pure translational motion, the motion field has a unique point termed focus of expansion/contraction where the image velocity vanishes. We reveal the fact that for an arbitrary 3D motion the zero-velocity points, whose number can be large, have the regularity of being approximately cocircular. More generally, all the image points with the same velocity u are located approximately on a circle (termed the iso-velocity circle (IVC)) determined solely by u and the ego-motion, except for the pathological cases in which the circle degenerates into a straight line. While IVCs can be recovered from 3 or more pairs of iso-velocity points in the motion field using a linear method, estimating ego-motion reduces to solving systems of linear equations constraining iso-velocity point pairs (Yang 1992).