  Group contraction is an algebraic map that relates two classes of Lie groups
by a limiting process. We utilize this notion for the compactification of the
class of Cartan motion groups. The compactification process is then applied to
reduce a non-compact synchronization problem to a problem where the solution
can be obtained by means of a unitary, faithful representation. We describe
this method of synchronization via contraction in detail and analyze several
important aspects of this application. One important special case of Cartan
motion groups is the group of rigid motions, also called the special Euclidean
group. We thoroughly discuss the synchronization over this group and show
numerically the advantages of our approach compared to some current
state-of-the-art synchronization methods on both synthetic and real data.
