  This paper explores the use of an entropy-based technique for point cloud
reconstruction with the goal of calibrating a lidar to a sensor capable of
providing egomotion information. We extend recent work in this area to the
problem of recovering the $Sim(3)$ transformation between a 2D lidar and a
rigidly attached monocular camera, where the scale of the camera trajectory is
not known a priori. We demonstrate the robustness of our approach on realistic
simulations in multiple environments, as well as on data collected from a
hand-held sensor rig. Given a non-degenerate trajectory and a sufficient number
of lidar measurements, our calibration procedure achieves millimetre-scale and
sub-degree accuracy. Moreover, our method relaxes the need for specific scene
geometry, fiducial markers, or overlapping sensor fields of view, which had
previously limited similar techniques.
