Abstract

The geometry of two uncalibrated views obtained with a parabolic catadioptric device is the sub ject of this paper. We introduce the notion of circle space, a natural representation of line images, and the set of incidence preserving transformations on this circle space which happens to equal the Lorentz group. In this space, there is a bilinear con- straint on transformed image coordinates in two parabolic catadioptric views involving what we call the catadioptric fundamental matrix. We prove that the angle between corresponding epipolar curves is preserved and that the transformed image of the absolute conic is in the kernel of that matrix, thus enabling a Euclidean reconstruction from two views. We establish the necessary and suficient conditions for a matrix to be a catadioptric fundamental matrix.