  In this paper we propose a new flexible method for hand-eye calibration. The
vast majority of existing hand-eye calibration techniques requires a
calibration rig which is used in conjunction with camera pose estimation
methods. Instead, we combine structure-from-motion with known robot motions and
we show that the solution can be obtained in linear form. The latter solves for
both the hand-eye parameters and for the unknown scale factor inherent with
structure-from-motion methods. The algebraic analysis that is made possible
with such a linear formulation allows to investigate not only the well known
case of general screw motions but also such singular motions as pure
translations, pure rotations, and planar motions. In essence, the robot-mounted
camera looks to an unknown rigid layout, tracks points over an image sequence
and estimates the camera-to-robot relationship. Such a self calibration process
is relevant for unmanned vehicles, robots working in remote places, and so
forth. We conduct a large number of experiments which validate the quality of
the method by comparing it with existing ones.
