Generalized essential matrix: Properties of the singular value decomposition

When considering non-central imaging devices, the computation of the relative pose requires the estimation of the rotation and translation that transform the 3D lines from one coordinate system to the second. In most of the state-of-the-art methods, this transformation is estimated by the computing a 6 × 6 matrix, known as the generalized essential matrix. To allow a better understanding of this matrix, we derive some properties associated with its singular value decomposition.