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Issue No. 06 - June (2010 vol. 32)
ISSN: 0162-8828
pp: 1044-1059
Jae-Hak Kim , Queen Mary University of London, London
Hongdong Li , The Australian National University, Canberra
Richard Hartley , The Australian National University, Canberra
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_\infty 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_\infty 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.
Multicamera rigs, generalized camera, motion estimation, epipolar equation, branch and bound, linear programming.

R. Hartley, H. Li and J. Kim, "Motion Estimation for Nonoverlapping Multicamera Rigs: Linear Algebraic and {\rm L}_\infty Geometric Solutions," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 32, no. , pp. 1044-1059, 2009.
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