A Nine-point Algorithm for Estimating Para-Catadioptric Fundamental Matrices

We present a minimal-point algorithm for finding fundamental matrices for catadioptric cameras of the parabolic type. Central catadioptric cameras-an optical combination of a mirror and a lens that yields an imaging device equivalent within hemispheres to perspective cameras-have found wide application in robotics, tele-immersion and providing enhanced situational awareness for remote operation. We use an uncalibrated structure-from-motion framework developed for these cameras to consider the problem of estimating the fundamental matrix for such cameras. We present a solution that can compute the para-catadioptirc fundamental matrix with nine point correspondences, the smallest number possible. We compare this algorithm to alternatives and show some results of using the algorithm in conjunction with random sample consensus (RANSAC).