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A new algorithm for the small-field astrometric point-pattern matching problem

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Abstract

The small-field astrometric point-pattern matching problem is a fundamental problem in astronomy, that although considered a long time ago still lacks a formal definition. It can be textually stated as: given two lists of positions of stars, find the common stars between these lists, taking into account rotation, translation, reflection and scaling operations. It is expected that there might be missing stars between the lists. In this work, we give the astronomical context, review some heuristic methods adopted in the literature, present distance matrix formulations for the problem and propose a new algorithm to solve it.

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References

  1. Groombridge, S., Airy, G.B.: A Catalogue of Circumpolar Stars. BiblioBazaar, Charleston (2009)

    Google Scholar 

  2. Groth, E.J.: A pattern-matching algorithm for two-dimensional coordinate lists. Astron. J. 91(5), 1244–1248 (1986)

    Article  Google Scholar 

  3. Howard, A.W., Marcy, G.W., Fischer, D.A., Isaacson, H., Muirhead, P.S., Henry, G.W., Boyajian, T.S., Braun, K., Becker, J.C., Wright, J.T.: The NASA-UC-UH ETA-earth program. IV. A low-mass planet orbiting an M dwarf 3.6 PC from earth. Astrophys. J. 794(1), 51–59 (2014)

    Article  Google Scholar 

  4. Lang, D., Hogg, D.W., Mierle, K., Blanton, M., Roweis, S.: Astrometry.net: blind astrometric calibration of arbitrary astronomical images. Astron. J. 139, 1782–1800 (2010)

    Article  Google Scholar 

  5. Liberti, L., Lavor, C., Maculan, N., Mucherino, A.: Euclidean distance geometry and applications. SIAM Rev. 56(1), 3–69 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  6. Meyer, C.D.: Matrix Analysis and Applied Linear Algebra. SIAM, Philadelphia (2000)

    Book  Google Scholar 

  7. Murtagh, F.: A new approach to point-pattern matching. Publ. Astron. Soc. Pac. 104, 301–307 (1992)

    Article  Google Scholar 

  8. Pal, A., Bakos, G.: Astrometry in wide-field surveys. Publ. Astron. Soc. Pac. 118(848), 1474–1483 (2006)

    Article  Google Scholar 

  9. Stetson, P.B.: The techniques of least squares and stellar photometry with CCDs. Vth IAG-USP Advanced School of Astrophysics (1989). http://nedwww.ipac.caltech.edu/level5/Stetson/Stetson5_2.html. Accessed Feb 2017

  10. Tabur, V.: Fast algorithms for matching CCD images to a stellar catalogue. Publ. Astron. Soc. Austral. 24, 189–198 (2007)

    Article  Google Scholar 

  11. Valdes, F.G., Campusano, L.E., Velasquez, J.D., Stetson, P.B.: FOCAS automatic catalog matching algorithm. Publ. Astron. Soc. Pac. 107, 1119–1128 (1995)

    Article  Google Scholar 

Download references

Acknowledgements

This work was performed under the auspices of the US Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. We also thank the support of the Brazilian Agencies CNPq, FAPESP, and FAPERJ. We would like to thank the anonymous reviewers for the helpful comments provided on earlier drafts of the manuscript.

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Authors and Affiliations

  1. Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, CA, 94550, USA

    Cláudio P. Santiago

  2. University of Campinas (IMECC - UNICAMP), Campinas, SP, 13083-859, Brazil

    Carlile Lavor

  3. UFRJ - Federal University of Rio de Janeiro, Rio de Janeiro, RJ, 23035-380, Brazil

    Sérgio Assunção Monteiro

  4. SIM - Universidade de Lisboa, 1749-016, Lisboa, Portugal

    Alberto Kroner-Martins

Authors
  1. Cláudio P. Santiago
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  2. Carlile Lavor
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  3. Sérgio Assunção Monteiro
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  4. Alberto Kroner-Martins
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Correspondence to Sérgio Assunção Monteiro.

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Santiago, C.P., Lavor, C., Monteiro, S.A. et al. A new algorithm for the small-field astrometric point-pattern matching problem. J Glob Optim 72, 55–70 (2018). https://doi.org/10.1007/s10898-018-0653-y

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  • DOI: https://doi.org/10.1007/s10898-018-0653-y

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