@article{fa3d0389f3564c70abdce2a26a4f6ee0,
title = "Synchronization over Cartan Motion Groups via Contraction",
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.",
keywords = "Cartan motion groups, Group contraction, Matrix motion group, Special Euclidean group, Synchronization",
author = "Onur {\"O}zye{\c s}il and Nir Sharon and Amit Singer",
note = "Funding Information: ∗Received by the editors December 1, 2016; accepted for publication (in revised form) January 9, 2018; published electronically April 17, 2018. http://www.siam.org/journals/siaga/2-2/M110605.html Funding: The authors were partially supported by award R01GM090200 from the NIGMS, FA9550-12-1-0317 and FA9550-13-1-0076 from AFOSR, the Simons Foundation Investigator Award and Simons Collaborations on Algorithms and Geometry, and the Moore Foundation Data-Driven Discovery Investigator Award. †INTECH Investment Management LLC, Princeton, NJ 08542 (oozyesil@intechjanus.com). ‡Program in Applied and Computational Mathematics (PACM), Princeton University, Princeton, NJ 08544-1000 (nsharon@math.princeton.edu). §Department of Mathematics and PACM, Princeton University, Princeton, NJ 08544-1000 (amits@math. princeton.edu). Funding Information: The authors were partially supported by award R01GM090200 from the NIGMS, FA9550-12-1-0317 and FA9550-13-1-0076 from AFOSR, the Simons Foundation Investigator Award and Simons Collaborations on Algorithms and Geometry, and the Moore Foundation Data-Driven Discovery Investigator Award. The authors thank Amit Bermano for many useful discussions regarding 3D registration. Publisher Copyright: Copyright {\textcopyright} by SIAM",
year = "2018",
doi = "10.1137/16M1106055",
language = "English (US)",
volume = "2",
pages = "207--241",
journal = "SIAM Journal on Applied Algebra and Geometry",
issn = "2470-6566",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "2",
}