Which Point Configurations are Determined by the Distribution of their Pairwise Distances?

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

In a previous paper we showed that, for any $n \ge m+2$, most sets of $n$ points in $\RR^m$ are determined (up to rotations, reflections, translations and relabeling of the points) by the distribution of their pairwise distances. But there are some exceptional point configurations which are not reconstructible from the distribution of distances in the above sense. In this paper, we present a reconstructibility test with running time $O(n^{11})$. The cases of orientation preserving rigid motions (rotations and translations) and scalings are also discussed.
10 pages

Keywords

Metric Geometry, Computer Vision and Pattern Recognition, Commutative Algebra, Algebraic Geometry, 68U;14L

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/69045

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0311004
 http://arxiv.org/abs/math/0311004

Collections

arXiv