Retrieval of Euler rotation angles from 3D similarity transformation based on quaternions

ABSTRACT

Recently, it has been shown how quaternion-based representation of a rotation matrix has advantages over conventional Eulerian representation in 3D similarity transformations. The iterative estimation procedure in similarity transformations based on quaternions results in translations and (scaled) quaternion elements. One needs, therefore, an additional procedure for evaluating the rest of the transformation parameters (translation, scale factor and rotation angles) after this solution.This contribution shows how to evaluate the rotation angles and the full covariance matrix of the transformation parameters from the estimation results in asymmetric and symmetric 3D similarity transformations based on quaternions.

KEYWORDS:

• 3D similarity transformation
• quaternion
• euler rotation angle
• covariance matrix
• total least squares

Acknowledgments

We thank the Editor and three anonymous reviewers for their constructive comments and remarks which clearly helped to improve this study. Furthermore, the second author is thankful to YTU Rectorate for providing Academic licence for Matlab-2017a.

Disclosure statement

No potential conflict of interest was reported by the authors.

Supplemental Material

Supplemental data for this article can be accessed here