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 photogrammetric bundle-adjustment are presented
at the end of the paper.
