Skip to main content

Advertisement

SpringerLink
Log in

Weighted model-based clustering for remote sensing image analysis

  • Original paper
  • Published:
Computational Geosciences Aims and scope Submit manuscript

Abstract

We introduce a weighted method of clustering the individual units of a segmented image. Specifically, we analyze geologic maps generated from experts’ analysis of remote sensing images and provide geologists with a powerful method to numerically test the consistency of a mapping with the entire multidimensional dataset of that region. Our weighted model-based clustering method (WMBC) employs a weighted likelihood and assigns fixed weights to each unit corresponding to the number of pixels located within the unit. WMBC characterizes each unit by the means and standard deviations of the pixels within that unit and uses the expectation-maximization algorithm with a weighted likelihood function to cluster the units. With both simulated and real data sets, we show that WMBC is more accurate than standard model-based clustering. Specifically, we analyze Magellan data from a large, geologically complex region of Venus to validate the mapping efforts of planetary geologists.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Fraley, C., Raftery, A.E.: How many clusters? Which clustering method? Answers via model-based cluster analysis. Comput. J. 41(8), 378–388 (1998)

    Article  Google Scholar 

  2. Banfield, J.D., Raftery, A.E.: Model-based Gaussian and non-Gaussian clustering. Biometrics 49, 803–821 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  3. Fraley, C., Raftery, A.E.: Model-based clustering, discriminant analysis, and density estimation. J. Am. Stat. Assoc. 97(458), 611–631 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  4. Campbell, J.G., Fraley, C., Murtagh, F., Raftery, A.E.: Linear flaw detection in woven textiles using model-based clustering. Pattern Recogn. Lett. 18, 1539–1548 (1997)

    Article  Google Scholar 

  5. Wehrens, R., Buydens, L.M.C., Fraley, C., Raftery, A.E.: Model-based clustering for image segmentation and large datasets via sampling. J. Classif. 21, 231–253 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  6. U.S. Geological Survey: USGS National Geologic Map Database. U.S. Geological Survey, Reston (2005)

    Google Scholar 

  7. Grosfils, E.B., Drury, D.E., Hurwitz, D.M., Kastl, B., Long, S.M., Richards, J.W., Venechuk, E.M.: Geological evolution of the Ganiki Planitia Quadrangle (V14) on Venus, abstract no. 1030. In: Lunar and Planetary Science Conference, vol. XXXVI (2005)

  8. Celeux, G., Govaert, G.: Gaussian parsimonious clustering models. Pattern Recogn. 28, 781–793 (1995)

    Article  Google Scholar 

  9. Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the EM algorithm. J. R. Stat. Soc. Ser. B Stat. Methodol. 39(1), 1–38 (1977)

    MATH  MathSciNet  Google Scholar 

  10. McLachlan, G.J., Krishnan, T.: The EM Algorithm and Extensions. Wiley, New York (1997)

    MATH  Google Scholar 

  11. Wu, C.F.J.: On the convergence properties of the EM algorithm. Ann. Stat. 11(1), 91–103 (1983)

    Article  Google Scholar 

  12. Billingsley, P.: Probability and Measure, 3rd edn. Wiley-Interscience, New York (1995)

    MATH  Google Scholar 

  13. Hu, F., Zidek, J.V.: The weighted likelihood. Can. J. Stat. 30(3), 347–371 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  14. Wang, X., van Eeden, C., Zidek, J.V.: Asymptotic properties of maximum weighted likelihood estimators. J. Stat. Plan. Inference 119, 37–54 (2004)

    Article  MATH  Google Scholar 

  15. Markatou, M.: Mixture models, robustness, and the weighted likelihood methodology. Biometrics 56, 483–486 (2000)

    Article  MATH  Google Scholar 

  16. Markatou, M., Basu, A., Lindsay, B.G.: Weighted likelihood equations with bootstrap root search. J. Am. Stat. Assoc. 93(442), 740–750 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  17. Saunders, R.S., Spear, S.J., Allin, P.C., Austin, R.S., Berman, A.L., Chandlee, R.C., Clark, J., deCharon, A.V., De Jong, E.M., Griffith, D.G., Gunn, J.M., Hensley, S., Johnson, W.T.K., Kirby, C.E., Leung, K.S., Lyons, D.T., Michaels, G.A., Miller, J., Morris, R.B., Morrison, A.D., Piereson, R.G., Scott, J.F., Shaffer, S.J., Slonski, J.P., Stofan, E.R., Thompson, T.W., Wall, S.D.: Magellan mission summary. J. Geophys. Res. 97(E8), 13067–13090 (1992)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Joseph W. Richards

  2. Department of Mathematics, Pomona College, Claremont, CA, 91711, USA

    Johanna Hardin

  3. Department of Geology, Pomona College, Claremont, CA, 91711, USA

    Eric B. Grosfils

Authors
  1. Joseph W. Richards
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Johanna Hardin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Eric B. Grosfils
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Joseph W. Richards.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Richards, J.W., Hardin, J. & Grosfils, E.B. Weighted model-based clustering for remote sensing image analysis. Comput Geosci 14, 125–136 (2010). https://doi.org/10.1007/s10596-009-9136-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10596-009-9136-z

Keywords

Search

Navigation