Parallax geometry of smooth surfaces in multiple views

This paper investigates the multiple view geometry of smooth surfaces and a plane, where the plane provides a planar homography mapping between the views. Innovations are made in three areas: first, new solutions are given for the computation of epipolar and trifocal geometry for this type of scene. In particular it is shown that the epipole may be determined from bitangents between the homography registered occluding contours, and a new minimal solution is given for computing the trifocal tensor: Second, algorithms are demonstrated for automatically estimating the fundamental matrix and trifocal tensor from images of such scenes. Third, a method is developed for estimating camera matrices for a sequence of images of these scenes. These three areas are combined in a "freehand scanner" application where 3D texture-mapped graphical models of smooth objects are acquired directly from a video sequence of the object and plane.