Structure and Motion From Uncalibrated Catadioptric Views

In this paper we present a new algorithm for structure from motion from point correspondences in images taken from uncalibrated catadioptric cameras with parabolic mirrors. We assume that the unknown intrinsic parameters are three: the combined focal length of the mirror and lens and the intersection of the optical axis with the image. We introduce a new representation for images of points and lines in catadioptric images which we call the circle space. This circle space includes imaginary circles, one of which is the image of the absolute conic. We formulate the epipolar constraint in this space and establish a new 4x4 catadioptric fundamental matrix. We show that the image of the absolute conic belongs to the kernel of this matrix. This enables us to prove that Euclidean reconstruction is feasible from two views with constant parameters and from three views with varying parameters. In both cases, it is one less than the number of views necessary with perspective cameras.