Synchronization over Cartan Motion Groups via Contraction

Onur Özyeşil, Nir Sharon, Amit Singer

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

Group contraction is an algebraic map that relates two classes of Lie groups by a limiting process. We utilize this notion for the compactification of the class of Cartan motion groups, which includes the important special case of rigid motions. The compactification process is then applied to reduce a noncompact synchronization problem to a problem where the solution can be obtained by means of a unitary, faithful representation. We describe this method of synchronization via contraction in detail and analyze several important aspects of this application. We then show numerically the advantages of our approach compared to some current state-of-the-art synchronization methods on both synthetic and real data.

Original languageEnglish (US)
Pages (from-to)207-241
Number of pages35
JournalSIAM Journal on Applied Algebra and Geometry
Volume2
Issue number2
DOIs
StatePublished - 2018

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Geometry and Topology
  • Applied Mathematics

Keywords

  • Cartan motion groups
  • Group contraction
  • Matrix motion group
  • Special Euclidean group
  • Synchronization

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