Motion Estimation for Nonoverlapping Multicamera Rigs: Linear Algebraic and L∞ Geometric Solutions

• Published in: IEEE transactions on pattern analysis and machine intelligence Vol. 32; no. 6; pp. 1044 - 1059
• Main Authors: Jae-Hak Kim, Hongdong Li, Hartley, Richard
• Format: Journal Article
• Language: English
• Published: Los Alamitos, CA IEEE 01.06.2010; IEEE Computer Society
• Subjects: Applied sciences; Artificial intelligence; branch and bound; Cameras; Computer science; control theory; systems; Computer vision; Context modeling; Data acquisition; epipolar equation; Equations; Exact sciences and technology; generalized camera; Iterative algorithms; Linear programming; Motion estimation; Multicamera rigs; Pattern recognition. Digital image processing. Computational geometry; Stereo vision; Vehicles; Motion estimation; Optimal algorithm; Branch and bound method; Epipolar geometry; Linear programming; branch and bound; Modeling; Hartley transformation; Multiple view; Computational geometry; Multicamera rigs; Optimal solution; Algebraic method; Stereopsis; Measurement error; generalized camera; epipolar equation
• ISSN: 0162-8828; 1939-3539
• DOI: 10.1109/TPAMI.2009.82

We investigate the problem of estimating the ego-motion of a multicamera rig from two positions of the rig. We describe and compare two new algorithms for finding the 6 degrees of freedom (3 for rotation and 3 for translation) of the motion. One algorithm gives a linear solution and the other is a geometric algorithm that minimizes the maximum measurement error-the optimal L ∞ solution. They are described in the context of the General Camera Model (GCM), and we pay particular attention to multicamera systems in which the cameras have nonoverlapping or minimally overlapping field of view. Many nonlinear algorithms have been developed to solve the multicamera motion estimation problem. However, no linear solution or guaranteed optimal geometric solution has previously been proposed. We made two contributions: 1) a fast linear algebraic method using the GCM and 2) a guaranteed globally optimal algorithm based on the L ∞ geometric error using the branch-and-bound technique. In deriving the linear method using the GCM, we give a detailed analysis of degeneracy of camera configurations. In finding the globally optimal solution, we apply a rotation space search technique recently proposed by Hartley and Kahl. Our experiments conducted on both synthetic and real data have shown excellent results.