  This paper addresses the following research question: ``can one compress a
detailed 3D representation and use it directly for point cloud registration?''.
Map compression of the scene can be achieved by the tensor train (TT)
decomposition of the signed distance function (SDF) representation. It
regulates the amount of data reduced by the so-called TT-ranks.
  Using this representation we have proposed an algorithm, the TT-SDF2PC, that
is capable of directly registering a PC to the compressed SDF by making use of
efficient calculations of its derivatives in the TT domain, saving computations
and memory. We compare TT-SDF2PC with SOTA local and global registration
methods in a synthetic dataset and a real dataset and show on par performance
while requiring significantly less resources.
