energy: Energy Function of a Camera Estimation Problem

Description Usage Author(s) References Examples

Description

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)=āˆ‘_{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.

Usage

1

Author(s)

Samuel Gerber

References

Peter Lindstrom and Mark Duchaineau, Factoring Algebraic Error for Relative Pose Estimation, Lawrence Livermore National Laboratory, LLNL-TR-411194, Mar. 2009

Examples

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data(camera_estimation)
summary(energy)

msr documentation built on May 30, 2017, 4:23 a.m.