Bayesian Segmentation of Magnetic Resonance Images Using the α-Stable Distribution

  • Diego Salas-Gonzalez
  • Matthias Schlögl
  • Juan M. Górriz
  • Javier Ramírez
  • Elmar Lang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6678)


In this work, a segmentation method of Magnetic Resonance images (MRI) is presented. On the one hand, the distribution of the grey (GM) and white matter (WM) are modelled using a mixture of α-stable distributions. A Bayesian α-stable mixture model for histogram data is used and the unknown parameters are sampled using the Metropolis-Hastings algorithm, therefore, voxel intensity information is included in the model via a parameterized mixture of α-stable distribution which allows us to calculate the likelihood. On the other hand, spatial information is also included: the images are registered to a common template and a prior probability is given to each intensity value using a normalized segmented tissue probability map. Both informations, likelihood and prior values, are combined using the Bayes’ Rule. Performance of the segmentation approaches using spatial prior information, intensity values via the likelihood and combining both using the Bayes’ Rule are compared. Better segmentation results are obtained when the latter is used.


Magnetic Resonance Imaging Image Segmentation α-Stable Distribution Mixture Model 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abraham, A., Corchado, E., Corchado, J.M.: Hybrid learning machines. Neurocomputing 72(13-15), 2729–2730 (2009)CrossRefGoogle Scholar
  2. 2.
    Ashburner, J., Friston, K.: Unified segmentation. NeuroImage 26, 839–851 (2005)CrossRefGoogle Scholar
  3. 3.
    Clarke, L.R., Velthuizen, R.R., Camacho, M.A., Heine, J.J., Vaidyanathan, M., Hall, L.O., Thatcher, R.W., Silbiger, M.L.: Mri segmentation: methods and applications. Magnetic Resonance Imaging 13(3), 334–368 (1995)CrossRefGoogle Scholar
  4. 4.
    Corchado, E., Abraham, A., de Carvalho, A.: Hybrid intelligent algorithms and applications. Information Sciences 180(14), 2633–2634 (2010)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Derrac, J., Garca, S., Herrera, F.: Algorithms for instance and feature selection. In: Corchado, E., Wu, X., Oja, E., Herrero, Á., Baruque, B. (eds.) HAIS 2009. LNCS, vol. 5572, pp. 557–564. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  6. 6.
    García-Sebastián, M., Fernández, E., Grana, M., Torrealdea, F.J.: A parametric gradient descent mri intensity inhomogeneity correction algorithm. Pattern Recognition Letters 28(13), 1657–1666 (2007)CrossRefGoogle Scholar
  7. 7.
    García-Sebastián, M., González, A.I., Graña, M.G.: An adaptive field rule for non-parametric mri intensity inhomogeneity estimation algorithm. Neurocomputing 72, 3556–3569 (2009)CrossRefGoogle Scholar
  8. 8.
    Górriz, J.M., Lassl, A., Ramírez, J., Salas-Gonzalez, D., Puntonet, C.G., Lang, E.W.: Automatic selection of rois in functional imaging using gaussian mixture models. Neuroscience Letters 460(2), 108–111 (2009)CrossRefGoogle Scholar
  9. 9.
    Greenspan, H., Ruf, A., Goldberger, J.: Constrained gaussian mixture model framework for automatic segmentation of mr brain images. IEEE Transactions on Medical Imaging 25(9), 1233–1245 (2006)CrossRefGoogle Scholar
  10. 10.
    Merisaari, H., Parkkola, R., Alhoniemi, E., Teräs, M., Lehtonen, L., Haataja, L., Lapinleimu, H., Nevalainen, O.S.: Gaussian mixture model-based segmentation of mr images taken from premature infant brains. Journal of Neuroscience Methods 182(1), 110–122 (2009)CrossRefGoogle Scholar
  11. 11.
    Pham, D.L., Xu, C., Prince, J.L.: Current methods in medical image segmentation. Annual Review of Biomedical Engineering 2(1), 315–337 (2000)CrossRefGoogle Scholar
  12. 12.
    Salas-Gonzalez, D., Kuruoglu, E.E., Ruiz, D.P.: Bayesian estimation of mixtures of skewed alpha stable distributions with an unknown number of components. In: Proceedings of the 14th European Signal Processing Conference (EUSIPCO 2006), Florence, Italy, September 4-8 (2006)Google Scholar
  13. 13.
    Salas-Gonzalez, D., Kuruoglu, E.E., Ruiz, D.P.: Estimation of mixtures of symmetric alpha stable distributions with an unknown number of components. In: Proceedings. 2006 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2006, France, May 14-19, pp. 545–548 (2006)Google Scholar
  14. 14.
    Salas-Gonzalez, D., Kuruoglu, E.E., Ruiz, D.P.: Finite mixture of stable distributions. Digital Signal Processing 19(2), 250–264 (2009)CrossRefGoogle Scholar
  15. 15.
    Salas-Gonzalez, D., Kuruoglu, E.E., Ruiz, D.P.: Modelling with mixture of symmetric stable distributions using gibbs sampling. Signal Processing 90(3), 774–783 (2010)CrossRefzbMATHGoogle Scholar
  16. 16.
    Segovia, F., Górriz, J.M., Ramírez, J., Salas-Gonzalez, D., Álvarez, I., López, M., Chaves, R., Padilla, P.: Classification of functional brain images using a gmm-based multi-variate approach. Neuroscience Letters 474(1), 58–62 (2010)CrossRefGoogle Scholar
  17. 17.
    da Silva, A.R.F.: Bayesian mixture models of variable dimension for image segmentation. Computer Methods and Programs in Biomedicine 94, 1–14 (2009)CrossRefGoogle Scholar
  18. 18.
    Suetens, P., Bellon, E., Vandermeulen, D., Smet, M., Marchal, G., Nuyts, J., Mortelman, L.: Image segmentation: methods and applications in diagnostic radiology and nuclear medicine. European Journal of Radiology 17, 14–21 (1993)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Diego Salas-Gonzalez
    • 1
  • Matthias Schlögl
    • 1
  • Juan M. Górriz
    • 1
  • Javier Ramírez
    • 1
  • Elmar Lang
    • 2
  1. 1.Dpt. Signal Theory, Networking and CommunicationsETSIIT-UGR, University of GranadaGranadaSpain
  2. 2.Institute of BiophysicsUniversity of RegensburgRegensburgGermany

Personalised recommendations