  We present a new solution to tracking and mapping with an event camera. The
motion of the camera contains both rotation and translation, and the
displacements happen in an arbitrarily structured environment. As a result, the
image matching may no longer be represented by a low-dimensional homographic
warping, thus complicating an application of the commonly used Image of Warped
Events (IWE). We introduce a new solution to this problem by performing
contrast maximization in 3D. The 3D location of the rays cast for each event is
smoothly varied as a function of a continuous-time motion parametrization, and
the optimal parameters are found by maximizing the contrast in a volumetric ray
density field. Our method thus performs joint optimization over motion and
structure. The practical validity of our approach is supported by an
application to AGV motion estimation and 3D reconstruction with a single
vehicle-mounted event camera. The method approaches the performance obtained
with regular cameras, and eventually outperforms in challenging visual
conditions.
