This page gives the foundations of panoramic stereo vision by presenting the analysis of epipolar geometry for panoramic cameras. The panoramic cameras with convex hyperbolic or parabolic mirror, so called central panoramic cameras, allow the epipolar geometry as perspective cameras.
Using standard perspective (pinhole) cameras the motion estimation algorithm cannot, in some cases, well distinguish a small pure translation of the camera from a small rotation. The confusion can be removed if a camera with large field of view is used. Ideally one would like to use a panoramic camera which has complete 360° field of view and sees to all directions. It can be imagined as a pinhole camera with a spherical imaging surface (instead of planar one as it is usual) centered at the focal point of the pinhole camera. Panoramic camera can, in principle, obtain correspondences from everywhere independently of the direction of motion.
Motion estimation from panoramic images requires to:
We do not consider here panoramic vision systems with moving parts since they are not applicable for real time imaging. The panoramic camera covering almost the whole imaging sphere can be obtained by combining a classical perspective (pinhole) camera with a convex mirror.
|Spherical mirror. The reflected optical rays do not intersect in a unique point. Spherical aberration.||Hyperbolic mirror. The reflected optical rays intersect in the focus of the hyperboloid. The center of camera projection coincides with the second mirror focus.||Parabolic mirror. The reflected optical rays intersect in the focus of the paraboloid when orthographic projection is assumed. The second mirror focus goes to the infinity.|
Epipolar geometry geometry of two perspective cameras
assigns to each point q1 in one image an
epipolar line l2 in the second image. The
mathematical expression of the epipolar geometry is
Each epipolar plane intersects the mirror in a planar conic. To a
point q1 in the first image a conic in the