In this paper we consider the images taken from pairs of parabolic catadioptric cameras separated by discrete motions. Despite the nonlinearity of the projection model, the epipolar geometry arising from such a system, like the perspective case, can be encoded in a bilinear form, the catadioptric fundamental matrix. We show that all such matrices have equal Lorentzian singular values, and they define a nine-dimensional manifold in the space of 4 /spl times/ 4 matrices. Furthermore, this manifold can be identified with a quotient of two Lie groups. We present a method to estimate a matrix in this space, so as to obtain an estimate of the motion. We show that the estimation procedures are robust to modest deviations from the ideal assumptions.
Mirrors in motion: epipolar geometry and motion estimation
2003-01-01
734365 byte
Conference paper
Electronic Resource
English
Mirrors in Motion: Epipolar Geometry and Motion Estimation
British Library Conference Proceedings | 2003
|3D Motion Recovery via Affine Epipolar Geometry
British Library Online Contents | 1995
|Real-Time Estimation of Head Motion Using Weak Perspective Epipolar Geometry
British Library Conference Proceedings | 1998
|Epipolar geometry of catadioptric stereo systems with planar mirrors
British Library Online Contents | 2009
|