Description Usage Author(s) References Examples
Given two images with point correspondences, the goal is to estimate the translation and rotation of two calibrated cameras. This problem can be formulated as a minimization of the total squared algebraic error:
h(R,t)=f(E)=ā_{i} (x_{i}^{T}Ex'_{i})^2
with x_i=[x_{i1}x_{i2}1]^T and x'_i=[x'_{i1}x'_{i2}1]^T being corresponding points on the image plane defined in the respective camera coordinates. The essential matrix E=[t]_{x} R is a 3 x 3 rank-2 matrix. In this formulation, the translation between the two cameras is described by the unit vector t, and the relative camera orientation is defined by the orthogonal rotation matrix R. Both t and R are expressed in the coordinate frame of x. Due to the formulation of the problem, E is guaranteed to have only 5 degrees of freedom: 3 to describe the rotation and 2 to determine the translation up to scale. Hence, h is defined on a 5D manifold embedded in 9D space. For more detailed information on the definition of this problem, see the manuscript by.
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Samuel Gerber
Peter Lindstrom and Mark Duchaineau, Factoring Algebraic Error for Relative Pose Estimation, Lawrence Livermore National Laboratory, LLNL-TR-411194, Mar. 2009
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