Abstract

In this paper, we present a new algorithm for fifinding all intersections of three quadrics. The proposed method is algebraic in nature and it is considerably more effificient than the Grobner basis and resultant-based solutions pre- ¨ viously 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 signifificantly outperform the state-of-theart in speed.