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.

翻译：本文研究了以下核心问题：“能否对高精度三维表示进行压缩，并直接用于点云配准？”通过有符号距离场的张量列分解，可实现场景地图压缩，其数据压缩量由张量列秩调控。基于该表示，我们提出TT-SDF2PC算法，通过利用张量列域中高效的导数计算，能够直接实现点云与压缩有符号距离场的配准，从而节省计算与内存资源。在合成数据集与真实数据集上，我们将TT-SDF2PC与现有先进的局部与全局配准方法进行对比，结果表明在性能相当的前提下，该方法所需资源显著更少。