Issue No. 04 - April (2012 vol. 34)
J. Gallier , Dept. of Comput. & Inf. Sci., Univ. of Pennsylvania, Philadelphia, PA, USA
X. S. Zhou , Dept. of Comput. Sci. & Eng., Univ. of Minnesota, Minneapolis, MN, USA
O. Naroditsky , Dept. of Comput. & Inf. Sci., Univ. of Pennsylvania, Philadelphia, PA, USA
S. I. Roumeliotis , Dept. of Comput. Sci. & Eng., Univ. of Minnesota, Minneapolis, MN, USA
K. Daniilidis , Dept. of Comput. & Inf. Sci., Univ. of Pennsylvania, Philadelphia, PA, USA
This paper presents two new, efficient solutions to the two-view, relative pose problem from three image point correspondences and one common reference direction. This three-plus-one problem can be used either as a substitute for the classic five-point algorithm, using a vanishing point for the reference direction, or to make use of an inertial measurement unit commonly available on robots and mobile devices where the gravity vector becomes the reference direction. We provide a simple, closed-form solution and a solution based on algebraic geometry which offers numerical advantages. In addition, we introduce a new method for computing visual odometry with RANSAC and four point correspondences per hypothesis. In a set of real experiments, we demonstrate the power of our approach by comparing it to the five-point method in a hypothesize-and-test visual odometry setting.
vectors, computer vision, distance measurement, geometry, pose estimation, five-point method, visual odometry, directional correspondence, relative pose problem, image point correspondences, reference direction, three-plus-one problem, five-point algorithm, vanishing point, inertial measurement unit, robots, mobile devices, gravity vector, algebraic geometry, RANSAC, four point correspondences, Polynomials, Cameras, Noise, Vectors, Visualization, Sparse matrices, Groebner basis., Computer vision, structure from motion, visual odometry, minimal problems
J. Gallier, X. S. Zhou, O. Naroditsky, S. I. Roumeliotis and K. Daniilidis, "Two Efficient Solutions for Visual Odometry Using Directional Correspondence," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 34, no. , pp. 818-824, 2012.