Stereo with Oblique Cameras

Mosaics acquired by pushbroom cameras, stereo panoramas, omnivergent mosaics, and spherical mosaics can be viewed as images taken by non-central cameras, i.e. cameras that project along rays that do not all intersect at one point. It has been shown that in order to reduce the correspondence search in mosaics to a one-parametric search along curves, the rays of the non-central cameras have to lie in double ruled epipolar surfaces. In this work, we introduce the oblique stereo geometry, which has non-intersecting double ruled epipolar surfaces. We analyze the configurations of mutually oblique rays that see every point in space. These configurations, called oblique cameras, are the most non-central cameras among all cameras. We formulate the assumption under which two oblique cameras posses oblique stereo geometry and show that the epipolar surfaces are non-intersecting double ruled hyperboloids and two lines. We show that oblique cameras, and the correspondingoblique stereo geometry, exist and give an example of a physically realizable oblique stereo geometry. We introduce linear oblique cameras as those which can be generated by a linear mapping from points in space to camera rays and characterize those collineations which generate them. We show that all linear oblique cameras are obtained by a collineation from one example of an oblique camera. Finally, we relate oblique cameras to spreads known from incidence geometries.