Chirality

• Authors: Richard I. Hartley
• Venue: International Journal of Computer Vision
• Year: 1998

It is known that a set of points in three-dimensions is determinedup to projectivity from two views with uncalibrated cameras. It is shown inthis paper that this result may be improved by distinguishing between pointsin front of and behind the camera. Any point that lies in an image must liein front of the camera producing that image. Using this idea, it is shownthat the scene is determined from two views up to a more restricted class ofmappings known as quasi-affine transformations, which are precisely thoseprojectivities that preserve the convex hull of an object of interest. Aninvariant of quasi-affine transformation known as the chiral sequence of aset of points is defined and it is shown how the chiral sequence may becomputed using two uncalibrated views. As demonstrated theoretically and byexperiment the chiral sequence may distinguish between sets of points thatare projectively equivalent. These results lead to necessary and sufficientconditions for a set of corresponding pixels in two images to be realizableas the images of a set of points in three dimensions.Using similar methods,a necessary and sufficient condition is given for the orientation of a setof points to be determined by two views. If the perspective centres are notseparated from the point set by a plane, then the orientation of the set ofpoints is determined from two views.