Using Quaternions for Parametrizing 3-D Rotations in Unconstrained Nonlinear Optimization
Jochen Schmidt, Heinrich Niemann · 2001
In this paper we address the problem of using quaternions in unconstrained nonlinear optimiza-tion of 3-D rotations. Quaternions representing ro-tations 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 ap-plying 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. Experi-ments using our parametrization in photogrammet-ric bundle-adjustment are presented at the end of the paper. 1