CHIRALITY

It is known that a set of points in three-dimensions is determined up to projectivity from two views with uncalibrated cameras. It is shown in this paper that this result may be improved by distinguishing betwe en points in front of and behind the camera. Any point that lies in an image must lie in front of the camera producing that image. Using thi s idea, it is shown that the scene is determined from two views up to a more restricted class of mappings known as quasi-affine transformati ons, which are precisely those projectivities that preserve the convex hull of an object of interest. An invariant of quasi-affine transform ation known as the chiral sequence of a set of points is defined and i t is shown how the chiral sequence may be computed using two uncalibra ted views. As demonstrated theoretically and by experiment the chiral sequence may distinguish between sets of points that are projectively equivalent. These results lead to necessary and sufficient conditions for a set of corresponding pixels in two images to be realizable as th e images of a set of points in three dimensions. Using similar methods , a necessary and sufficient condition is given for the orientation of a set of points to be determined by two views. If the perspective cen tres are not separated from the point set by a plane, then the orienta tion of the set of points is determined from two views.