IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v56y2012i1p49-61.html
   My bibliography  Save this article

Bayesian multiscale analysis of images modeled as Gaussian Markov random fields

Author

Listed:
  • Thon, Kevin
  • Rue, Håvard
  • Skrøvseth, Stein Olav
  • Godtliebsen, Fred

Abstract

A Bayesian multiscale technique for the detection of statistically significant features in noisy images is proposed. The prior is defined as a stationary intrinsic Gaussian Markov random field on a toroidal graph, which enables efficient computation of the relevant posterior marginals. Hence the method is applicable to large images produced by modern digital cameras. The technique is demonstrated in two examples from medical imaging.

Suggested Citation

  • Thon, Kevin & Rue, Håvard & Skrøvseth, Stein Olav & Godtliebsen, Fred, 2012. "Bayesian multiscale analysis of images modeled as Gaussian Markov random fields," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 49-61, January.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:1:p:49-61
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947311002635
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Godtliebsen, Fred & Oigard, Tor Arne, 2005. "A visual display device for significant features in complicated signals," Computational Statistics & Data Analysis, Elsevier, vol. 48(2), pages 317-343, February.
    2. Oigard, Tor Arne & Rue, Havard & Godtliebsen, Fred, 2006. "Bayesian multiscale analysis for time series data," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1719-1730, December.
    3. Holmström, Lasse & Pasanen, Leena & Furrer, Reinhard & Sain, Stephan R., 2011. "Scale space multiresolution analysis of random signals," Computational Statistics & Data Analysis, Elsevier, vol. 55(10), pages 2840-2855, October.
    4. Ian L. Dryden & Mark R. Scarr & Charles C. Taylor, 2003. "Bayesian texture segmentation of weed and crop images using reversible jump Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(1), pages 31-50, January.
    5. J. Polzehl & V. G. Spokoiny, 2000. "Adaptive weights smoothing with applications to image restoration," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 335-354.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lasse Holmström & Leena Pasanen, 2017. "Statistical Scale Space Methods," International Statistical Review, International Statistical Institute, vol. 85(1), pages 1-30, April.
    2. Hotz, Thomas & Marnitz, Philipp & Stichtenoth, Rahel & Davies, Laurie & Kabluchko, Zakhar & Munk, Axel, 2012. "Locally adaptive image denoising by a statistical multiresolution criterion," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 543-558.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Cheolwoo Park & Yongho Jeon & Kee-Hoon Kang, 2016. "An exploratory data analysis in scale-space for interval-valued data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(14), pages 2643-2660, October.
    2. Huh, Jib & Park, Cheolwoo, 2015. "Theoretical investigation of an exploratory approach for log-density in scale-space," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 272-279.
    3. Park, Cheolwoo & Huh, Jib, 2013. "Statistical inference and visualization in scale-space using local likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 336-348.
    4. Emilio Augusto Coelho-Barros & Jorge Alberto Achcar & Josmar Mazucheli, 2010. "Longitudinal Poisson modeling: an application for CD4 counting in HIV-infected patients," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(5), pages 865-880.
    5. Geffray, S. & Klutchnikoff, N. & Vimond, M., 2016. "Illumination problems in digital images. A statistical point of view," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 191-213.
    6. Billé, AG & Salvioni, C. & Benedetti, R., 2015. "Spatial Heterogeneity In Production Functions Models," 150th Seminar, October 22-23, 2015, Edinburgh, Scotland 212662, European Association of Agricultural Economists.
    7. Čížek, Pavel & Koo, Chao Hui, 2021. "Jump-preserving varying-coefficient models for nonlinear time series," Econometrics and Statistics, Elsevier, vol. 19(C), pages 58-96.
    8. Timmermans, Catherine & Fryzlewicz, Piotr, 2012. "Shah: Shape-Adaptive Haar Wavelet Transform For Images With Application To Classification," LIDAM Discussion Papers ISBA 2012015, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. Sørbye, Sigrunn H. & Hindberg, Kristian & Olsen, Lena R. & Rue, Håvard, 2009. "Bayesian multiscale feature detection of log-spectral densities," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3746-3754, September.
    10. Helbing, Georg & Shen, Zhiwei & Odening, Martin & Ritter, Matthias, 2017. "Estimating Location Values of Agricultural Land," German Journal of Agricultural Economics, Humboldt-Universitaet zu Berlin, Department for Agricultural Economics, vol. 66(3), September.
    11. M. Simona Andreano & Roberto Benedetti & Paolo Postiglione, 2017. "Spatial regimes in regional European growth: an iterated spatially weighted regression approach," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(6), pages 2665-2684, November.
    12. Sadick Mohammed & Awudu Abdulai, 2022. "Do Egocentric information networks influence technical efficiency of farmers? Empirical evidence from Ghana," Journal of Productivity Analysis, Springer, vol. 58(2), pages 109-128, December.
    13. Jens Kolbe & Rainer Schulz & Martin Wersing & Axel Werwatz, 2012. "Location, location, location: Extracting location value from house prices," SFB 649 Discussion Papers SFB649DP2012-040, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    14. N. Friel & A. N. Pettitt, 2008. "Marginal likelihood estimation via power posteriors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(3), pages 589-607, July.
    15. Anna Gloria Billé & Roberto Benedetti & Paolo Postiglione, 2017. "A two-step approach to account for unobserved spatial heterogeneity," Spatial Economic Analysis, Taylor & Francis Journals, vol. 12(4), pages 452-471, October.
    16. Polzehl, Jörg & Tabelow, Karsten, 2007. "Adaptive Smoothing of Digital Images: The R Package adimpro," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 19(i01).
    17. Holmström, Lasse & Pasanen, Leena & Furrer, Reinhard & Sain, Stephan R., 2011. "Scale space multiresolution analysis of random signals," Computational Statistics & Data Analysis, Elsevier, vol. 55(10), pages 2840-2855, October.
    18. Baiguo An & Beibei Zhang, 2020. "Logistic regression with image covariates via the combination of L1 and Sobolev regularizations," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-18, June.
    19. Jorge Alberto Achcar & Edilberto Cepeda-Cuervo & Eliane R. Rodrigues, 2012. "Weibull and generalised exponential overdispersion models with an application to ozone air pollution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(9), pages 1953-1963, May.
    20. J. Polzehl & V. Spokoiny & C. Starica, 2004. "When did the 2001 recession really start?," Econometrics 0411017, University Library of Munich, Germany.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:56:y:2012:i:1:p:49-61. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.