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This paper addresses the following research question: ``can one compress adetailed 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. Itregulates the amount of data reduced by the so-called TT-ranks.  Using this representation we have proposed an algorithm, the TT-SDF2PC, thatis capable of directly registering a PC to the compressed SDF by making use ofefficient calculations of its derivatives in the TT domain, saving computationsand memory. We compare TT-SDF2PC with SOTA local and global registrationmethods in a synthetic dataset and a real dataset and show on par performancewhile requiring significantly less resources.

TT-SDF2PC: Registration of Point Cloud and Compressed SDF Directly in the Memory-Efficient Tensor Train Domain