Geometric understanding of rigid body transformations

It has been demonstrated by Chasles over a century ago that any given displacement of a rigid body can be effected by a single rotation around an axis combined with a translation parallel to that axis. In this paper, we first describe geometric properties of image correspondence vectors. We then formalise such properties by extending Chasles´ work and put forward a new general theoretical framework for the analysis of rigid body transformations in 2D and in 3D. We then propose two novel algorithms to calibrate rigid body transformation parameters which are validated through experiments. Our analysis addresses central issues to computer vision applications as it provides closed form solutions for all calibrated parameters and an accurate insight into the number of calibration solutions