TY - CHAP A1 - Schmidt, Jochen A1 - Niemann, H. T1 - Using Quaternions for Parametrizing 3D Rotations in Unconstrained Nonlinear Optimization T2 - Vision, Modeling, and Visualization 2001, pages 399-406, Stuttgart, Germany N2 - In this paper we address the problem of using quaternions in unconstrained nonlinear optimization of 3-D rotations. Quaternions representing rotations have four elements but only three degrees of freedom, since they must be of norm one. This constraint has to be taken into account when applying e.g. the Levenberg-Marquardt algorithm, a method for unconstrained nonlinear optimization widely used in computer vision. We propose an easy to use method for achieving this. Experiments using our parametrization in photo grammetric bündle -adjustment are presented at the end of the paper. KW - 3D Rotations KW - Pattern recognition KW - Unconstrained NonlinearOptimization Y1 - 2002 ER -