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

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dc.creatorBoutin, Mireille
dc.creatorKemper, Gregor
dc.date2003-11-02
dc.date.accessioned2026-07-07T05:02:25Z
dc.date.available2026-07-07T05:02:25Z
dc.descriptionIn 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.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/math/0311004
dc.identifierhttp://arxiv.org/abs/math/0311004
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69045
dc.subjectMetric Geometry
dc.subjectComputer Vision and Pattern Recognition
dc.subjectCommutative Algebra
dc.subjectAlgebraic Geometry
dc.subject68U;14L
dc.titleWhich Point Configurations are Determined by the Distribution of their Pairwise Distances?
dc.typetext

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