Duality, Rigidity and Planar Parallax

We i n vestigate the geometry of two views of seven points, four of which are coplanar, and the geometry of three views of six points, four of which are coplanar. We p r o ve that the two are dual, and that the fundamental geometric constraints in each case are encapsulated by a planar homology. The work uniies a number of previously diverse results related to planar parallax, duality and planar homologies. In addition, we m a k e a n umber of practical contributions, including for-mulae for computing the distance of the cameras from a distinguished world plane and formulae for structure computations. We s h o w that the trifocal tensor is obtained uniquely from three views of six points, four of which are coplanar, and give a simple interpretation of the trifocal geometry. We g i v e examples of these computations on real images.