Efficient Intersection of Three Quadrics and Applications in Computer Vision

In this paper, we present a new algorithm for finding all intersections of three quadrics. The proposed method is algebraic in nature and it is considerably more efficient than the Gröbner basis and resultant-based solutions previously used in computer vision applications. We identify several computer vision problems that are formulated and solved as systems of three quadratic equations and for which our algorithm readily delivers considerably faster results. Also, we propose new formulations of three important vision problems: absolute camera pose with unknown focal length, generalized pose-and-scale, and hand-eye calibration with known translation. These new formulations allow our algorithm to significantly outperform the state-of-the-art in speed.