Dual quaternions for absolute orientation and hand-eye calibration
Many computer vision problems involving three dimensional motion necessitate an efficient representation for 3D displacement that enhances the understanding of the problem and facilitates linear solutions of low complexity. The most common representation is a rotation about an axis through the origin followed by a translation and represented by an orthogonal matrix and a vector, respectively. An alternative representation to orthogonal matrices are the unit quaternions already used in several vision algorithms  which still use the translation as a separate unknown. From Chasles’ theorem  it is known that a rigid transformation can be modeled as a rotation about an axis not through the origin and a translation along this axis. This well known screw transformation can be algebraically modeled using dual vectors, matrices or quaternions .
KeywordsScalar Part Rigid Transformation Dual Vector Unit Quaternion Screw Axis
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