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Computational and Mathematical Methods in Medicine
Volume 2015, Article ID 450341, 23 pages
http://dx.doi.org/10.1155/2015/450341
Review Article

MRI Segmentation of the Human Brain: Challenges, Methods, and Applications

Department of Telecommunications and Information Processing TELIN-IPI-iMinds, Ghent University, St-Pietersnieuwstraat 41, 9000 Ghent, Belgium

Received 27 June 2014; Revised 11 September 2014; Accepted 1 October 2014

Academic Editor: Rafael M. Luque-Baena

Copyright © 2015 Ivana Despotović et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. D. L. Pham, C. Xu, and J. L. Prince, “Current methods in medical image segmentation,” Annual Review of Biomedical Engineering, vol. 2, no. 2000, pp. 315–337, 2000. View at Publisher · View at Google Scholar · View at Scopus
  2. J. Ashburner and K. J. Friston, “Unified segmentation,” NeuroImage, vol. 26, no. 3, pp. 839–851, 2005. View at Publisher · View at Google Scholar · View at Scopus
  3. Y. Zhang, M. Brady, and S. Smith, “Segmentation of brain MR images through a hidden Markov random field model and the expectation-maximization algorithm,” IEEE Transactions on Medical Imaging, vol. 20, no. 1, pp. 45–57, 2001. View at Publisher · View at Google Scholar · View at Scopus
  4. S. Z. Li, Markov Random Field Modeling in Computer Vision, Springer, New York, NY, USA, 1995.
  5. R. M. Haralick, K. Shanmugam, and I. Dinstein, “Textural features for image classification,” IEEE Transactions on Systems, Man and Cybernetics, vol. 3, no. 6, pp. 610–621, 1973. View at Publisher · View at Google Scholar · View at Scopus
  6. P. Yan, S. Xu, B. Turkbey, and J. Kruecker, “Discrete deformable model guided by partial active shape model for trus image segmentation,” IEEE Transactions on Biomedical Engineering, vol. 57, no. 5, pp. 1158–1166, 2010. View at Publisher · View at Google Scholar · View at Scopus
  7. O. Ecabert, J. Peters, H. Schramm et al., “Automatic model-based segmentation of the heart in CT images,” IEEE Transactions on Medical Imaging, vol. 27, no. 9, pp. 1189–1201, 2008. View at Publisher · View at Google Scholar · View at Scopus
  8. J. Yang and J. S. Duncan, “3D image segmentation of deformable objects with joint shape-intensity prior models using level sets,” Medical Image Analysis, vol. 8, no. 3, pp. 285–294, 2004. View at Publisher · View at Google Scholar · View at Scopus
  9. X. Tao, J. L. Prince, and C. Davatzikos, “Using a statistical shape model to extract sulcal curves on the outer cortex of the human brain,” IEEE Transactions on Medical Imaging, vol. 21, no. 5, pp. 513–524, 2002. View at Publisher · View at Google Scholar · View at Scopus
  10. N. Duta and M. Sonka, “Segmentation and interpretation of MR brain images: an improved active shape model,” IEEE Transactions on Medical Imaging, vol. 17, no. 6, pp. 1049–1062, 1998. View at Publisher · View at Google Scholar · View at Scopus
  11. R. Davies, C. Twining, and C. Taylor, Statistical Models of Shape Optimisation and Evaluation, Springer, London, UK, 2008.
  12. R. C. Gonzalez and R. E. Woods, Digital Image Processing, Pearson Education, 2008.
  13. J. Rogowska, “Overview and fundamentals of medical image segmentation,” in Handbook of Medical Image Processing and Analysis, I. Bankman, Ed., Elsevier, Amsterdam, The Netherlands, 2000. View at Google Scholar
  14. J. Canny, “A computational approach to edge detection,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 8, no. 6, pp. 679–698, 1986. View at Google Scholar · View at Scopus
  15. D. Marr and E. Hildreth, “Theory of edge detection,” Proceedings of the Royal Society of London—Biological Sciences, vol. 207, no. 1167, pp. 187–217, 1980. View at Publisher · View at Google Scholar · View at Scopus
  16. P. Kovesi, “Image feature from phase congurency,” Journal of Computer Vision Research, vol. 1, no. 3, pp. 1–26, 1999. View at Google Scholar
  17. P. Kovesi, “Edges are not just steps,” in Proceedings of the 5th Asian Conference on Computer Vision (ACCV '02), pp. 822–827, Melbourne, Australia, 2002.
  18. M. C. Morrone and R. A. Owens, “Feature detection from local energy,” Pattern Recognition Letters, vol. 6, no. 5, pp. 303–313, 1987. View at Publisher · View at Google Scholar · View at Scopus
  19. H. Gudbjartsson and S. Patz, “The Rician distribution of noisy MRI data,” Magnetic Resonance in Medicine, vol. 34, no. 6, pp. 910–914, 1995. View at Publisher · View at Google Scholar · View at Scopus
  20. D. Salas-González, J. M. Górriz, J. Ramírez, M. Schloegl, E. W. Lang, and A. Ortiz, “Parameterization of the distribution of white and grey matter in MRI using-stable distribution,” Computers in Biology and Medicine, vol. 43, pp. 559–567, 2013. View at Google Scholar
  21. B. Fischl, D. H. Salat, E. Busa et al., “Whole brain segmentation: automated labeling of neuroanatomical structures in the human brain,” Neuron, vol. 33, no. 3, pp. 341–355, 2002. View at Publisher · View at Google Scholar · View at Scopus
  22. P. Maillard, N. Delcroix, F. Crivello et al., “An automated procedure for the assessment of white matter hyperintensities by multispectral (T1, T2, PD) MRI and an evaluation of its between-centre reproducibility based on two large community databases,” Neuroradiology, vol. 50, no. 1, pp. 31–42, 2008. View at Publisher · View at Google Scholar · View at Scopus
  23. A. Mayer and H. Greenspan, “An adaptive mean-shift framework for MRI brain segmentation,” IEEE Transactions on Medical Imaging, vol. 28, no. 8, pp. 1238–1250, 2009. View at Publisher · View at Google Scholar · View at Scopus
  24. C. R. Traynora, G. J. Barkerb, W. R. Crumb, S. C. R. Williamsb, and M. P. Richardsona, “Segmentation of the thalamus in MRI based on T1 and T2,” NeuroImage, vol. 56, no. 1, pp. 939–950, 2011. View at Publisher · View at Google Scholar
  25. C. M. Collins, W. Liu, W. Schreiber, Q. X. Yang, and M. B. Smith, “Central brightening due to constructive interference with, without, and despite dielectric resonance,” Journal of Magnetic Resonance Imaging, vol. 21, no. 2, pp. 192–196, 2005. View at Publisher · View at Google Scholar · View at Scopus
  26. J. G. Sied, A. P. Zijdenbos, and A. C. Evans, “A nonparametric method for automatic correction of intensity nonuniformity in MRI data,” IEEE Transactions on Medical Imaging, vol. 17, no. 1, pp. 87–97, 1998. View at Publisher · View at Google Scholar · View at Scopus
  27. E. B. Lewis and N. C. Fox, “Correction of differential intensity inhomogeneity in longitudinal MR images,” NeuroImage, vol. 23, no. 1, pp. 75–83, 2004. View at Publisher · View at Google Scholar · View at Scopus
  28. D. W. Shattuck, S. R. Sandor-Leahy, K. A. Schaper, D. A. Rottenberg, and R. M. Leahy, “Magnetic resonance image tissue classification using a partial volume model,” NeuroImage, vol. 13, no. 5, pp. 856–876, 2001. View at Publisher · View at Google Scholar · View at Scopus
  29. M. S. Cohen, R. M. DuBois, and M. M. Zeneih, “Rapid and effective correction of RF inhomogeneity for high field magnetic resonance imaging,” Human Brain Mapping, vol. 10, no. 4, pp. 204–211, 2000. View at Publisher · View at Google Scholar
  30. W. M. Wells III, W. E. L. Crimson, R. Kikinis, and F. A. Jolesz, “Adaptive segmentation of MRI data,” IEEE Transactions on Medical Imaging, vol. 15, no. 4, pp. 429–442, 1996. View at Publisher · View at Google Scholar · View at Scopus
  31. K. Van Leemput, F. Maes, D. Vandermeulen, and P. Suetens, “Automated model-based bias field correction of MR images of the brain,” IEEE Transactions on Medical Imaging, vol. 18, no. 10, pp. 885–896, 1999. View at Publisher · View at Google Scholar · View at Scopus
  32. J.-F. Mangin, “Entropy minimization for automatic correction of intensity nonuniformity,” in Proceedings of the IEEE Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA '00), pp. 162–169, Hilton Head Island, SC, USA, June 2000. View at Publisher · View at Google Scholar · View at Scopus
  33. A. C. Evans, D. L. Collins, S. R. Mills, E. D. Brown, R. L. Kelly, and T. M. Peters, “3D statistical neuroanatomical models from 305 MRI volumes,” in Proceedings of the IEEE Nuclear Science Symposium & Medical Imaging Conference, pp. 1813–1817, November 1993. View at Scopus
  34. J. V. Hajnal, D. L. G. Hill, and D. J. Hawkes, Medical Image Registration, CRC Press, New York, NY, USA, 2001.
  35. D. Shen and C. Davatzikos, “HAMMER: hierarchical attribute matching mechanism for elastic registration,” IEEE Transactions on Medical Imaging, vol. 21, no. 11, pp. 1421–1439, 2002. View at Publisher · View at Google Scholar · View at Scopus
  36. E. D'Agostino, F. Maes, D. Vandermeulen, and P. Suetens, “A viscous fluid model for multimodal non-rigid image registration using mutual information,” in Proceedings of the Medical Image Computing and Computer Assisted Intervention (MICCAI '02), pp. 541–548, 2002.
  37. J. Ashburner and K. J. Friston, “Nonlinear spatial normalization using basis functions,” Human Brain Mapping, vol. 7, no. 4, pp. 254–266, 1999. View at Publisher · View at Google Scholar
  38. D. Rueckert, L. I. Sonoda, C. Hayes, D. L. Hill, M. O. Leach, and D. J. Hawkes, “Nonrigid registration using free-form deformations: application to breast mr images,” IEEE Transactions on Medical Imaging, vol. 18, no. 8, pp. 712–721, 1999. View at Publisher · View at Google Scholar · View at Scopus
  39. J. M. Fitzpatrick, D. L. G. Hill, and C. R. Maurer, “Image registration,” in Handbook of Medical Imaging: Medical Image Processing and Analysis, M. Sonka and J. M. Fitzpatrick, Eds., vol. 2, SPIE Publications, 2004. View at Google Scholar
  40. W. R. Crum, T. Hartkens, and D. L. G. Hill, “Non-rigid image registration: theory and practice,” British Journal of Radiology, vol. 77, no. 2, pp. S140–S153, 2004. View at Publisher · View at Google Scholar · View at Scopus
  41. B. Zitová and J. Flusser, “Image registration methods: a survey,” Image and Vision Computing, vol. 21, no. 11, pp. 977–1000, 2003. View at Publisher · View at Google Scholar · View at Scopus
  42. H. Xue, L. Srinivasan, S. Jiang et al., “Automatic segmentation and reconstruction of the cortex from neonatal MRI,” NeuroImage, vol. 38, no. 3, pp. 461–477, 2007. View at Publisher · View at Google Scholar · View at Scopus
  43. S. M. Smith, “Fast robust automated brain extraction,” Human Brain Mapping, vol. 17, no. 3, pp. 143–155, 2002. View at Publisher · View at Google Scholar · View at Scopus
  44. M. Battaglini, S. M. Smith, S. Brogi, and N. de Stefano, “Enhanced brain extraction improves the accuracy of brain atrophy estimation,” NeuroImage, vol. 40, no. 2, pp. 583–589, 2008. View at Publisher · View at Google Scholar · View at Scopus
  45. N. R. Pal and S. K. Pal, “A review on image segmentation techniques,” Pattern Recognition, vol. 26, no. 9, pp. 1277–1294, 1993. View at Publisher · View at Google Scholar · View at Scopus
  46. T. F. Chan and L. A. Vese, “Active contours without edges,” IEEE Transactions on Image Processing, vol. 10, no. 2, pp. 266–277, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  47. Y. Boykov and G. Funka-Lea, “Graph cuts and efficient N-D image segmentation,” International Journal of Computer Vision, vol. 70, no. 2, pp. 109–131, 2006. View at Publisher · View at Google Scholar · View at Scopus
  48. R. Unnikrishnan, C. Pantofaru, and M. Hebert, “Toward objective evaluation of image segmentation algorithms,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 29, no. 6, pp. 929–944, 2007. View at Publisher · View at Google Scholar · View at Scopus
  49. W. Cai, S. Chen, and D. Zhang, “Fast and robust fuzzy c-means clustering algorithms incorporating local information for image segmentation,” Pattern Recognition, vol. 40, no. 3, pp. 825–838, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  50. M. Prastawa, An MRI segmentation framework for brains with anatomical deviations [Ph.D. thesis], University of North Carolina at Chapel Hill, 2007.
  51. F. Shi, D. Shen, P.-T. Yap et al., “CENTS: cortical enhanced neonatal tissue segmentation,” Human Brain Mapping, vol. 32, no. 3, pp. 382–396, 2011. View at Publisher · View at Google Scholar · View at Scopus
  52. L. Wang, F. Shi, G. Li et al., “Segmentation of neonatal brain MR images using patch-driven level sets,” NeuroImage, vol. 84, pp. 141–158, 2014. View at Publisher · View at Google Scholar · View at Scopus
  53. N. I. Weisenfeld and S. K. Warfield, “Automatic segmentation of newborn brain MRI,” NeuroImage, vol. 47, no. 2, pp. 564–572, 2009. View at Publisher · View at Google Scholar · View at Scopus
  54. J. C. Moreno, V. B. Surya Prasath, H. Proença, and K. Palaniappan, “Fast and globally convex multiphase active contours for brain MRI segmentation,” Computer Vision and Image Understanding, vol. 125, pp. 237–250, 2014. View at Publisher · View at Google Scholar · View at Scopus
  55. D. M. Greig, B. T. Porteous, and A. H. Seheult, “Exact maximum a posteriori estimation for binary images,” Journal of the Royal Statistical Society B, vol. 51, no. 2, pp. 271–279, 1989. View at Google Scholar
  56. J. de Oliveira and W. Pedrycz, Advances in Fuzzy Clustering and Its Applications, John Wiley & Sons, New York, NY, USA, 2007.
  57. I. Despotovíć, E. Vansteenkiste, and W. Philips, “Spatially coherent fuzzy clustering for accurate and noise-robust image segmentation,” IEEE Signal Processing Letters, vol. 20, no. 4, pp. 295–298, 2013. View at Publisher · View at Google Scholar · View at Scopus
  58. D. C. Collier, S. S. C. Burnett, M. Amin et al., “Assessment of consistency in contouring of normal-tissue anatomic structures,” Journal of Applied Clinical Medical Physics, vol. 4, no. 1, pp. 17–24, 2003. View at Google Scholar · View at Scopus
  59. E. Vansteenkiste, Quantitative analysis of ultrasound images of the preterm brain [Ph.D. dissertation], Ghent University, 2007.
  60. M. Murgasova, Segmentation of brain MRI during early childhood [Ph.D. thesis], Imperial College London, 2008.
  61. P. A. Yushkevich, J. Piven, H. C. Hazlett et al., “User-guided 3D active contour segmentation of anatomical structures: significantly improved efficiency and reliability,” NeuroImage, vol. 31, no. 3, pp. 1116–1128, 2006. View at Publisher · View at Google Scholar · View at Scopus
  62. ITK-SNAP, 2009, http://www.itksnap.org/.
  63. M. Sezgin and B. Sankur, “Survey over image thresholding techniques and quantitative performance evaluation,” Journal of Electronic Imaging, vol. 13, no. 1, pp. 146–168, 2004. View at Publisher · View at Google Scholar · View at Scopus
  64. R. M. Haralick and L. G. Shapiro, “Image segmentation techniques,” Computer Vision, Graphics, and Image Processing, vol. 29, no. 1, pp. 100–132, 1985. View at Publisher · View at Google Scholar · View at Scopus
  65. N. Passat, C. Ronse, J. Baruthio, J.-P. Armspach, C. Maillot, and C. Jahn, “Region-growing segmentation of brain vessels: an atlas-based automatic approach,” Journal of Magnetic Resonance Imaging, vol. 21, no. 6, pp. 715–725, 2005. View at Publisher · View at Google Scholar · View at Scopus
  66. T. Weglinski and A. Fabijanska, “Brain tumor segmentation from MRI data sets using region growing approach,” in Proceedings of the 7th International Conference on Perspective Technologies and Methods in MEMS Design (MEMSTECH '11), pp. 185–188, May 2011. View at Scopus
  67. M. del Fresno, M. Vénere, and A. Clausse, “A combined region growing and deformable model method for extraction of closed surfaces in 3D CT and MRI scans,” Computerized Medical Imaging and Graphics, vol. 33, no. 5, pp. 369–376, 2009. View at Publisher · View at Google Scholar · View at Scopus
  68. R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification, John Wiley & Sons, New York, NY, USA, 2nd edition, 2001. View at MathSciNet
  69. S. K. Warfield, F. A. Kaus, M. Jolesz, and R. Kikinis, “Adaptive template moderated spatially varying statistical classification,” in Proceedings of the Medical Image Computing and Computer Assisted Intervention (MICCAI '98), pp. 431–438, 1998.
  70. C. A. Cocosco, A. P. Zijdenbos, and A. C. Evans, “A fully automatic and robust brain MRI tissue classification method,” Medical Image Analysis, vol. 7, no. 4, pp. 513–527, 2003. View at Publisher · View at Google Scholar · View at Scopus
  71. K. M. Pohl, J. Fisher, W. E. L. Grimson, R. Kikinis, and W. M. Wells, “A Bayesian model for joint segmentation and registration,” NeuroImage, vol. 31, no. 1, pp. 228–239, 2006. View at Publisher · View at Google Scholar · View at Scopus
  72. C. W. Therrien, Decision, Estimation, and Classification: An Introduction to Pattern Recognition and Related Topics, John Wiley & Sons, New York, NY, USA, 1989. View at MathSciNet
  73. G. B. Coleman and H. C. Andrews, “Image segmentation by clustering,” Proceedings of the IEEE, vol. 67, no. 5, pp. 773–785, 1979. View at Publisher · View at Google Scholar · View at Scopus
  74. J. C. Dunn, “A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters,” Journal of Cybernetics: Transactions of the American Society for Cybernetics, vol. 3, no. 3, pp. 32–57, 1973. View at Google Scholar · View at MathSciNet · View at Scopus
  75. J. C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press, New York, NY, USA, 1981. View at MathSciNet
  76. L. A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, no. 3, pp. 338–353, 1965. View at Google Scholar
  77. M. N. Ahmed, S. M. Yamany, N. Mohamed, A. A. Farag, and T. Moriarty, “A modified fuzzy C-means algorithm for bias field estimation and segmentation of MRI data,” IEEE Transactions on Medical Imaging, vol. 21, no. 3, pp. 193–199, 2002. View at Publisher · View at Google Scholar · View at Scopus
  78. J.-H. Xue, A. Pizurica, W. Philips, E. Kerre, R. van de Walle, and I. Lemahieu, “An integrated method of adaptive enhancement for unsupervised segmentation of MRI brain images,” Pattern Recognition Letters, vol. 24, no. 15, pp. 2549–2560, 2003. View at Publisher · View at Google Scholar · View at Scopus
  79. S. Chen and D. Zhang, “Robust image segmentation using FCM with spatial constraints based on new kernel-induced distance measure,” IEEE Transactions on Systems, Man, and Cybernetics Part B: Cybernetics, vol. 34, no. 4, pp. 1907–1916, 2004. View at Publisher · View at Google Scholar · View at Scopus
  80. S. Shen, W. Sandham, M. Granat, and A. Sterr, “MRI fuzzy segmentation of brain tissue using neighborhood attraction with neural-network optimization,” IEEE Transactions on Information Technology in Biomedicine, vol. 9, no. 3, pp. 459–467, 2005. View at Publisher · View at Google Scholar · View at Scopus
  81. K.-S. Chuang, H.-L. Tzeng, S. Chen, J. Wu, and T.-J. Chen, “Fuzzy c-means clustering with spatial information for image segmentation,” Computerized Medical Imaging and Graphics, vol. 30, no. 1, pp. 9–15, 2006. View at Publisher · View at Google Scholar · View at Scopus
  82. Z. M. Wang, Y. C. Soh, Q. Song, and K. Sim, “Adaptive spatial information-theoretic clustering for image segmentation,” Pattern Recognition, vol. 42, no. 9, pp. 2029–2044, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  83. I. Despotović, B. Goossens, E. Vansteenkiste, and W. Philips, “T1- and T2-weighted spatially constrained fuzzy C-means clustering for brain MRI segmentation,” in Medical Imaging: Image Processing, Proceedings of SPIE, p. 9, San Diego, Calif, USA, February 2010. View at Publisher · View at Google Scholar · View at Scopus
  84. B. N. Li, C. K. Chui, S. Chang, and S. H. Ong, “Integrating spatial fuzzy clustering with level set methods for automated medical image segmentation,” Computers in Biology and Medicine, vol. 41, no. 1, pp. 1–10, 2011. View at Publisher · View at Google Scholar · View at Scopus
  85. K. M. Pohl, W. M. Wells, A. Guimond et al., “Incorporating non-rigid registration into expectation maximization algorithm to segment MR images,” in Proceedings of the Medical Image Computing and Computer Assisted Intervention (MICCAI '02), pp. 564–572, 2002.
  86. K. M. Pohl, Prior information for brain parcellation [Ph.D. thesis], Massachusetts Institute of Technology, 2005.
  87. E. D'Agostino, F. Maes, D. Vandermeulen, and P. Suetens, “Non-rigid atlas-to-image registration by minimization of class-conditional image entropy,” in Proceedings of the 7th International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI '04), pp. 745–753, September 2004. View at Scopus
  88. M. Prastawa, J. H. Gilmore, W. Lin, and G. Gerig, “Automatic segmentation of MR images of the developing newborn brain,” Medical Image Analysis, vol. 9, no. 5, pp. 457–466, 2005. View at Publisher · View at Google Scholar · View at Scopus
  89. M. Kuklisova-Murgasova, P. Aljabar, L. Srinivasan et al., “A dynamic 4D probabilistic atlas of the developing brain,” NeuroImage, vol. 54, no. 4, pp. 2750–2763, 2011. View at Publisher · View at Google Scholar · View at Scopus
  90. C. Li, R. Huang, Z. Ding, J. C. Gatenby, D. N. Metaxas, and J. C. Gore, “A level set method for image segmentation in the presence of intensity inhomogeneities with application to MRI,” IEEE Transactions on Image Processing, vol. 20, no. 7, pp. 2007–2016, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  91. D. Rivest-Hénault and M. Cheriet, “Unsupervised MRI segmentation of brain tissues using a local linear model and level set,” Magnetic Resonance Imaging, vol. 29, no. 2, pp. 243–259, 2011. View at Publisher · View at Google Scholar · View at Scopus
  92. M. Kass, A. Witkin, and D. Terzopoulos, “Snakes: active contour models,” International Journal of Computer Vision, vol. 1, no. 4, pp. 321–331, 1988. View at Publisher · View at Google Scholar · View at Scopus
  93. D. Terzopoulos, A. Witkin, and M. Kass, “Constraints on deformable models: recovering 3D shape and nonrigid motion,” Artificial Intelligence Journal, vol. 36, no. 1, pp. 91–123, 1988. View at Publisher · View at Google Scholar · View at Scopus
  94. L. D. Cohen and I. Cohen, “Finite-element methods for active contour models and balloons for 2-D and 3-D images,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 11, pp. 1131–1147, 1993. View at Publisher · View at Google Scholar · View at Scopus
  95. S. Kichenassamy, A. Kumar, P. Olver, A. Tannenbaum, and A. Yezzy, “Gradient flows and geometric active contour models,” in Proceedings of the 5th International Conference on Computer Vision (ICCV '95), pp. 810–815, 1995.
  96. R. Malladi, J. A. Sethian, and B. C. Vemuri, “Shape modeling with front propagation: a level set approach,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 17, no. 2, pp. 158–175, 1995. View at Publisher · View at Google Scholar · View at Scopus
  97. V. Caselles, R. Kimmel, and G. Sapiro, “Geodesic active contours,” International Journal of Computer Vision, vol. 22, no. 1, pp. 61–79, 1997. View at Publisher · View at Google Scholar · View at Scopus
  98. D. Mumford and J. Shah, “Optimal approximations by piecewise smooth functions and associated variational problems,” Communications on Pure and Applied Mathematics, vol. 42, no. 5, pp. 577–685, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
  99. A. Huang, R. Abugharbieh, and R. Tam, “A hybrid geometricstatistical deformable model for automated 3-D segmentation in brain MRI,” IEEE Transactions on Biomedical Engineering, vol. 56, no. 7, pp. 1838–1848, 2009. View at Publisher · View at Google Scholar · View at Scopus
  100. R. Kimmel, “Fast edge integration,” in Geometric Level Set Methods in Imaging, Vision, and Graphics, S. Osher and N. Paragios, Eds., Springer, New York, NY, USA, 2003. View at Google Scholar
  101. C. Sagiv, N. A. Sochen, and Y. Y. Zeevi, “Integrated active contours for texture segmentation,” IEEE Transactions on Image Processing, vol. 15, no. 6, pp. 1633–1646, 2006. View at Publisher · View at Google Scholar · View at Scopus
  102. P. Mesejo, A. Valsecchi, L. Marrakchi-Kacem, S. Cagnoni, and S. Damas, “Biomedical image segmentation using geometric deformable models and metaheuristics,” Computerized Medical Imaging and Graphics, 2014. View at Publisher · View at Google Scholar · View at Scopus
  103. L. Wang, F. Shi, W. Lin, J. H. Gilmore, and D. Shen, “Automatic segmentation of neonatal images using convex optimization and coupled level sets,” NeuroImage, vol. 58, no. 3, pp. 805–817, 2011. View at Publisher · View at Google Scholar · View at Scopus
  104. L. A. Vese and T. F. Chan, “A multiphase level set framework for image segmentation using the Mumford and Shah model,” International Journal of Computer Vision, vol. 50, no. 3, pp. 271–293, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  105. E. S. Brown, T. F. Chan, and X. Bresson, “Completely convex formulation of the Chan-Vese image segmentation model,” International Journal of Computer Vision, vol. 98, no. 1, pp. 103–121, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  106. M. S. Keegan, B. Sandberg, and T. F. Chan, “A multiphase logic framework for multichannel image segmentation,” Inverse Problems and Imaging, vol. 6, no. 1, pp. 95–110, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  107. S. H. Kang and R. March, “Existence and regularity of minimizers of a functional for unsupervised multiphase segmentation,” Nonlinear Analysis: Theory, Methods & Applications, vol. 76, pp. 181–201, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  108. L. Wang, C. Li, Q. Sun, D. Xia, and C.-Y. Kao, “Active contours driven by local and global intensity fitting energy with application to brain MR image segmentation,” Computerized Medical Imaging and Graphics, vol. 33, no. 7, pp. 520–531, 2009. View at Publisher · View at Google Scholar · View at Scopus
  109. T. F. Chan, S. Esedoglu, and M. Nikolova, “Algorithms for finding global minimizers of image segmentation and denoising models,” SIAM Journal on Applied Mathematics, vol. 66, no. 5, pp. 1632–1648, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  110. A. Chambolle, D. Cremers, and T. Pock, “A convex approach to minimal partitions,” SIAM Journal on Imaging Sciences, vol. 5, no. 4, pp. 1113–1158, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  111. E. Bae, J. Yuan, and X.-C. Tai, “Global minimization for continuous multiphase partitioning problems using a dual approach,” International Journal of Computer Vision, vol. 92, no. 1, pp. 112–129, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  112. T. Kapur, W. Eric, L. Grimson, W. M. Wells III, and R. Kikinis, “Segmentation of brain tissue from magnetic resonance images,” Medical Image Analysis, vol. 1, no. 2, pp. 109–127, 1996. View at Publisher · View at Google Scholar · View at Scopus
  113. Y. Masutani, T. Schiemann, and K. H. Hohne, “Vascular shape segmentation and structure extraction using a shape-based region-growing model,” in Medical Image Computing and Computer-Assisted Interventation—MICCAI'98: Proceedings of the 1st International Conference Cambridge, MA, USA, October 11–13, 1998, vol. 1496 of Lecture Notes in Computer Science, pp. 1242–1249, Springer, Berlin, Germany, 1998. View at Publisher · View at Google Scholar
  114. Z. Tu, K. L. Narr, P. Dollar, I. Dinov, P. M. Thompson, and A. W. Toga, “Brain anatomical structure segmentation by hybrid discriminative/generative models,” IEEE Transactions on Medical Imaging, vol. 27, no. 4, pp. 495–508, 2008. View at Publisher · View at Google Scholar · View at Scopus
  115. I. Despotovic, E. Vansteenkiste, and W. Philips, “Brain volume segmentation in newborn infants using multi-modal MRI with a low inter-slice resolution,” in Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC '10), pp. 5038–5041, Buenos Aires, Argentina, September 2010. View at Publisher · View at Google Scholar · View at Scopus
  116. J. M. Lötjönen, R. Wolz, J. R. Koikkalainen et al., “Fast and robust multi-atlas segmentation of brain magnetic resonance images,” NeuroImage, vol. 49, no. 3, pp. 2352–2365, 2010. View at Publisher · View at Google Scholar · View at Scopus
  117. C. Vijayakumar and D. Gharpure, “Development of image-processing software for automatic segmentation of brain tumors in MR images,” Journal of Medical Physics, vol. 36, no. 3, pp. 147–158, 2011. View at Publisher · View at Google Scholar · View at Scopus
  118. L. Gui, R. Lisowski, T. Faundez, P. S. Hüppi, F. Lazeyras, and M. Kocher, “Morphology-driven automatic segmentation of MR images of the neonatal brain,” Medical Image Analysis, vol. 16, no. 8, pp. 1565–1579, 2012. View at Publisher · View at Google Scholar · View at Scopus
  119. A. Ortiz, J. M. Gorriz, J. Ramirez, and D. Salas-Gonzalez, “Improving MR brain image segmentation using self-organising maps and entropy-gradient clustering,” Information Sciences, vol. 262, pp. 117–136, 2014. View at Publisher · View at Google Scholar · View at Scopus
  120. S. K. Warfield, M. Kaus, F. A. Jolesz, and R. Kikinis, “Adaptive, template moderated, spatially varying statistical classification,” Medical Image Analysis, vol. 4, no. 1, pp. 43–55, 2000. View at Publisher · View at Google Scholar · View at Scopus
  121. A. Ortiz, A. A. Palacio, J. M. Górriz, J. Ramírez, and D. Salas-González, “Segmentation of brain MRI using SOM-FCM-based method and 3D statistical descriptors,” Computational and Mathematical Methods in Medicine, vol. 2013, Article ID 638563, 12 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  122. K. Van Leemput, F. Maes, D. Vandermeulen, and P. Suetens, “A unifying framework for partial volume segmentation of brain MR images,” IEEE Transactions on Medical Imaging, vol. 22, no. 1, pp. 105–119, 2003. View at Publisher · View at Google Scholar · View at Scopus
  123. P. Santago and D. H. Gage, “Quantification of MR brain images by mixture density and partial volume modeling,” IEEE Transactions on Medical Imaging, vol. 12, no. 3, pp. 566–574, 1993. View at Publisher · View at Google Scholar · View at Scopus
  124. L. Nocera and J. C. Gee, “Robust partial volume tissue classification of cerebral MRI scans,” in Medical Imaging: Image Processing, vol. 3034 of Proceedings of SPIE, pp. 312–322, February 1997. View at Publisher · View at Google Scholar · View at Scopus
  125. D. L. Collins, A. P. Zijdenbos, V. Kollokian et al., “Design and construction of a realistic digital brain phantom,” IEEE Transactions on Medical Imaging, vol. 17, no. 3, pp. 463–468, 1998. View at Publisher · View at Google Scholar · View at Scopus
  126. IBSR, “The Internet Brain Segmentation Repository,” 2013, http://www.nitrc.org/projects/ibsr.
  127. L. R. Dice, “Measures of the amount of ecologic association between species,” Ecology, vol. 26, no. 3, pp. 297–302, 1945. View at Google Scholar
  128. W. R. Crum, O. Camara, and D. L. G. Hill, “Generalized overlap measures for evaluation and validation in medical image analysis,” IEEE Transactions on Medical Imaging, vol. 25, no. 11, pp. 1451–1461, 2006. View at Publisher · View at Google Scholar · View at Scopus