Determining generic point configurations from unlabeled path or loop lengths

Authors: Ioannis Gkioulekas, Steven J. Gortler, Louis Theran, and Todd Zickler
Preprint: 1709.03936, 2017
Full text: arXiv

In this paper we study the problem of reconstructing a configuration of points in dimensions from an unlabeled sequence of Euclidean lengths arising under an ensemble of paths or loops. We provide a sufficient trilateration-based condition for the reconstruction to be uniquely determined and a numerical procedure for performing this reconstruction.

Our results are obtained by completely characterizing the linear automrophisms of the “unsquared measurement variety” of points in dimensions for all and . The special case of and corresponds to the well known Regge symmetries of the tetrahedron.