Interpretation of conic motion and its applications

摘要

The indeterminacy of conic motion is analyzed in terms of Lie group theory. It is shown that an image motion of a conic is associated with a group ofinvisible motions that do not cause a visible change of the conic. All such groups are isomorphic to the group associated with a special conic called thestandard circle, for which the group of invisible motions is the (three-dimensional)Lorentz group. Similar results are obtained forinvisible optical flows. Finally, our analysis is extended toconic stereo: the 3-D position and orientation of a conic in the scene are computed from two projections. This algorithm also works with one camera if a circular pattern is projected from a light source.