Shape Analysis for Brain Structures

  • Bernard NgEmail author
  • Matthew Toews
  • Stanley Durrleman
  • Yonggang Shi
Part of the Lecture Notes in Computational Vision and Biomechanics book series (LNCVB, volume 14)


Advances in magnetic resonance imaging (MRI) have enabled non-invasive examination of brain structures in unprecedented details. With increasing amount of high resolution MRI data becoming available, we are at a position to make significant clinical contributions. In this chapter, we review the main approaches to shape analysis for brain structures. The purpose of this review is to provide methodological insights for pushing forward shape analysis research, so that we can better benefit from the available high resolution data. We describe in this review point-based, mesh-based, function-based, and medial representations as well as deformetrics. Their respective advantages and disadvantages as well as the implications of increasing resolution and greater sample sizes on these shape analysis approaches are discussed.


Brain Correspondence Shape representation Statistical analysis 


  1. 1.
    Dryden IL, Mardia KV (1998) Statistical Shape Analysis. Wiley, ChichesterzbMATHGoogle Scholar
  2. 2.
    Besl PJ, McKay ND (1992) A method for Registration of 3-D shapes. IEEE Trans Pattern Anal Mach Intel 14(2):239–256CrossRefGoogle Scholar
  3. 3.
    Bookstein FL (1997) Morphometric tools for landmark Data: geometry and biology. Cambridge University Press, CambridgeGoogle Scholar
  4. 4.
    Cootes TF, Taylor CJ, Cooper DH, Graham J (1995) Active shape models-their training and application. Comput Vis Image Underst 61(1):38–59CrossRefGoogle Scholar
  5. 5.
    Cootes TF, Edwards GJ, Taylor CJ (2001) Active appearance models. IEEE Trans Pattern Anal Mach Intel 23(6):681–685CrossRefGoogle Scholar
  6. 6.
    Rohr K (1997) On 3D differential operators for detecting point landmarks. Image Vis Comput 15(3):219–233CrossRefGoogle Scholar
  7. 7.
    Ono M, Kubik S, Abernathy CD (1990) Atlas of the cerebral sulci. Thieme Medical, New YorkGoogle Scholar
  8. 8.
    Duta N, Sonka M (1998) Segmentation and interpretation of MR Brain images. An improved active shape model. Imaging IEEE Trans Med 17(6):1049–1062CrossRefGoogle Scholar
  9. 9.
    Tao X, Prince JL, Davatzikos C (2002) Using a statistical shape model to extract sulcal curves on the outer cortex of the human brain. IEEE Trans Med Imaging 21(5):513–524CrossRefGoogle Scholar
  10. 10.
    Yushkevich PA, Piven J, Hazlett HC, Smith RG, Ho S, Gee JC, Gerig G (2006) User-guided 3D active contour segmentation of anatomical structures: significantly improved efficiency and reliability. Neuroimage 31(3):1116–1128CrossRefGoogle Scholar
  11. 11.
    Joshi S, Miller MI (2000) Landmark matching via large deformation diffeomorphisms. IEEE Trans Image Process 9(8):1357–1370CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Davies RH, Twining CJ, Cootes TF, Waterton JC, Taylor CJ (2002) A minimum description length approach to statistical shape modeling. IEEE Trans Med Imaging 21(5):525–537CrossRefGoogle Scholar
  13. 13.
    Brummer ME (1991) Hough transform detection of the longitudinal fissure in tomographic head images. IEEE Trans Med Imaging 10(1):74–81CrossRefGoogle Scholar
  14. 14.
    Harris C, Stephens M (1988) A combined corner and edge detector. In: Alvey vision conference, pp 147–151Google Scholar
  15. 15.
    Witkin A (1984) Scale-space filtering: a new approach to multi-scale description. IEEE Int Conf Acoust Speech Signal Process 9:150–153Google Scholar
  16. 16.
    Lindeberg T (1998) Feature detection with automatic scale selection. Int J Comput Vis 30(2):79–116CrossRefGoogle Scholar
  17. 17.
    Lowe DG (2004) Distinctive image features from scale-invariant keypoints. Int J Comput Vis 60(2):91–110CrossRefGoogle Scholar
  18. 18.
    Toews M, Wells WM III, Collins DL, Arbel T (2010) Feature-based morphometry: discovering group-related anatomical patterns. NeuroImage 49(3):2318–2327CrossRefGoogle Scholar
  19. 19.
    Burt P, Adelson E (1983) The Laplacian Pyramid as a compact image code. IEEE Trans Commun 31(4):532–540CrossRefGoogle Scholar
  20. 20.
    Toews M, Wells WM III (2013) Efficient and robust model-to-image alignment using 3D scale-invariant features. Med Image Anal 17(3):271–282CrossRefGoogle Scholar
  21. 21.
    Toews M, Wells III WM (2009) SIFT-rank: ordinal description for invariant feature correspondence. In: IEEE conference on computer vision and pattern recognition, pp 172–177Google Scholar
  22. 22.
    Toews M, Arbel T (2007) A statistical parts-based model of anatomical variability. IEEE Trans Med Imaging 26(4):497–508CrossRefGoogle Scholar
  23. 23.
    Toews M, Zöllei L, Wells WM III (2013) Invariant feature-based alignment of volumetric multi-modal images. In: Wells WM, Joshi S, Pohl KM (eds) IPMI 2013, LNCS, vol 7917. Springer, Berlin, pp 25–36Google Scholar
  24. 24.
    Gupta A, Toews M, Janardhana R, Rathi Y, Gilmore J, Escolar M, Styner M (2013) Fiber feature map based landmark initialization for highly deformable DTI registration. In: SPIE medical imaging, pp 866907–866907. International Society for Optics and PhotonicsGoogle Scholar
  25. 25.
    Toews M, Wells WM III, Zöllei L (2012) A feature-based developmental model of the infant brain in structural MRI. In: Ayache N, Delingette H, Golland P, Mori K (eds) MICCAI 2012, LNCS, vol 15. Springer, Berlin, pp 204–211Google Scholar
  26. 26.
    Uhlenbeck K (1976) Generic properties of eigenfunctions. Am J Math 98(4):1059–1078CrossRefzbMATHMathSciNetGoogle Scholar
  27. 27.
    Qiu A, Bitouk D, Miller MI (2006) Smooth functional and structural maps on the neocortex via orthonormal bases of the Laplace-Beltrami operator. IEEE Trans Med Imaging 25(10):1296–1306CrossRefGoogle Scholar
  28. 28.
    Shi Y, Lai R, Morra J, Dinov I, Thompson P, Toga A (2010) Robust surface reconstruction via Laplace-Beltrami eigen-projection and boundary deformation. IEEE Trans Med Imaging 29(12):2009–2022CrossRefGoogle Scholar
  29. 29.
    Lai R, Shi Y, Dinov I, Chan TF, Toga AW (2009) Laplace-Beltrami nodal counts: a new signature for 3D shape analysis. In: International symposium on biomedical imaging, pp 694–697Google Scholar
  30. 30.
    Reuter M, Wolter F, Peinecke N (2006) Laplace-Beltrami spectra as shape-DNA of surfaces and solids. Comput Aided Des 38:342–366CrossRefGoogle Scholar
  31. 31.
    Reeb G (1946) Sur les Points Singuliers d’une Forme de Pfaff Completement Integrable ou d’une Fonction Nemérique. Comptes Rendus Acad Sci 222:847–849Google Scholar
  32. 32.
    Jost J (2001) Riemannian geometry and geometric analysis, 3rd edn. Springer, New YorkGoogle Scholar
  33. 33.
    Shinagawa Y, Kunii TL (1991) Constructing a reeb graph automatically from cross sections. IEEE Comput Graph Appl 11(6):44–51CrossRefGoogle Scholar
  34. 34.
    Takahashi S, Ikeda T, Shinagawa Y, Kunii TL, Ueda M (1995) Algorithms for extracting correct critical points and constructing topological graphs from discrete geographical elevation data. Comput Graph Forum 14(3):181–192CrossRefGoogle Scholar
  35. 35.
    Biasotti S, Falcidieno B, Spagnuolo M (2000) Extended reeb graphs for surface understanding and description. In: International conference on discrete geometry for computer imagery, pp 185–197Google Scholar
  36. 36.
    Lazarus F, Verroust A (1999) Level set diagrams of polyhedral objects. In: ACM symposium on solid modeling and applications, pp 130–140Google Scholar
  37. 37.
    Hilaga M, Shinagawa Y, Kohmura T, Kunii TL (2001) Topology matching for fully automatic similarity estimation of 3D shapes. In: SIGGRAPH, pp 203–212Google Scholar
  38. 38.
    Mortara M, Patané G (2002) Affine-invariant skeleton of 3D shapes. In: Shape modeling Internationl, pp 245–252Google Scholar
  39. 39.
    Tierny J, Vandeborre JP, Daoudi M (2006) Invariant high level reeb graphs of 3D polygonal meshes. In: International symposium on 3D data processing, visualization, and transmission, pp 105–112Google Scholar
  40. 40.
    Rustamov RM (2007) Laplace-Beltrami eigenfunctions for deformation invariant shape representation. In: Eurographics symposium on geometry processing, pp 225–233Google Scholar
  41. 41.
    Ovsjanikov M, Sun J, Guibas LJ (2008) Global intrinsic symmetries of shapes. Eurograph Symp Geom Process 27:1341–1348Google Scholar
  42. 42.
    Shi Y, Lai R, Toga AW (2013) Cortical surface reconstruction via unified reeb analysis of geometric and topological outliers in magnetic resonance images. IEEE Trans Med Imaging 32(3):511–530CrossRefGoogle Scholar
  43. 43.
    Dale AM, Fischl B, Sereno MI (1999) Cortical surface-based analysis I: Segmentation and surface reconstruction. NeuroImage 9:179–194CrossRefGoogle Scholar
  44. 44.
    Lai R, Shi Y, Scheibel K, Fears S, Woods R, Toga A, Chan T (2010) Metric induced optimal embedding for intrinsic 3D shape analysis. In: International conference on computer vision pattern recognition, pp 2871–2878Google Scholar
  45. 45.
    Shi Y, Lai R, Toga AW (2013) Conformal mapping via metric optimization with application for cortical label fusion. IPMI (in press)Google Scholar
  46. 46.
    Gu X, Wang Y, Chan TF, Thompson PM, Yau ST (2004) Genus zero surface conformal mapping and its application to brain surface mapping. IEEE Trans Med Imaging 23(8):949–958CrossRefGoogle Scholar
  47. 47.
    Gold SM, O’Connor, MF, Gill R, Kern KC, Shi Y, Henry RG, Pelletier D, Mohr DC, Sicotte NL (2012) Detection of Altered hippocampal morphology in multiple sclerosis associated depression using automated surface mesh modeling. Hum Brain Mapp. doi: 10.1002/hbm.22154. [Epub ahead of print]
  48. 48.
    Hu MK (1962) Visual pattern recognition by moment invariants. IRE Trans Inf Theory 8(2):179–187CrossRefzbMATHGoogle Scholar
  49. 49.
    Lo CH, Don HS (1989) 3-D moment forms: their construction and application to object identification and positioning. IEEE Trans Pattern Anal Mach Intel 11(10):1053–1064CrossRefGoogle Scholar
  50. 50.
    Fischl B, Liu A, Dale AM (2001) Automated manifold surgery: constructing geometrically accurate and topologically correct models of the human cerebral cortex. IEEE Trans Med Imaging 20(1):70–80CrossRefGoogle Scholar
  51. 51.
    Székely G, Kelemen A, Brechbühler C, Gerig G (1996) Segmentation of 2-D and 3-D objects from MRI volume data using constrained elastic deformations of flexible Fourier contour and surface models. Med Image Anal 1(1):19–34Google Scholar
  52. 52.
    Healy DM, Rockmore DN, Kostelec PJ, Moore S (2003) FFTs for the 2-sphere-improvements and variations. J Fourier Anal Appl 9(4):341–385CrossRefzbMATHMathSciNetGoogle Scholar
  53. 53.
    Mallat SG (1989) A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans Pattern Anal Mach Intel 11(7):674–693CrossRefzbMATHGoogle Scholar
  54. 54.
    Lindeberg T (1993) Scale-space theory in computer vision. Kluwer Academic, HinghamGoogle Scholar
  55. 55.
    Yu P, Grant PE, Qi Y, Han X, Ségonne F, Pienaar R, Busa E, Pacheco J, Makris N, Buckner RL, Golland P, Fischl B (2007) Cortical surface shape analysis based on spherical wavelets. IEEE Trans Med Imaging 26(4):582–597CrossRefGoogle Scholar
  56. 56.
    Bernal-Rusiel JL, Atienza M, Cantero JL (2008) Detection of focal changes in human cortical thickness: spherical wavelets versus gaussian smoothing. NeuroImage 41(4):1278–1292CrossRefGoogle Scholar
  57. 57.
    Kim WH, Pachauri D, Hatt C, Chung MK, Johnson S, Singh V (2012) Wavelet based multi-scale shape features on arbitrary surfaces for cortical thickness discrimination. In: Bartlett P (ed) NIPS 2012. LNCS, vol 25, pp 1250–1258Google Scholar
  58. 58.
    Sadjadi FA, Hall EL (1980) Three-dimensional moment invariants. IEEE Trans Pattern Anal Mach Intel 2:127–136CrossRefzbMATHGoogle Scholar
  59. 59.
    Mangin JF, Poupon F, Duchesnay E, Riviére D, Cachia A, Collins DL, Evans AC, Régis J (2004) Brain morphometry using 3D moment invariants. Med Image Anal 8(3):187–196CrossRefGoogle Scholar
  60. 60.
    Ng B, Abugharbieh R, Huang X, McKeown MJ (2009) Spatial characterization of fMRI activation maps using invariant 3-D moment descriptors. IEEE Trans Med Imaging 28(2):261–268CrossRefGoogle Scholar
  61. 61.
    Yang F, Kruggel F (2009) A graph matching approach for labeling brain sulci using location, orientation, and shape. Neurocomputing 73(1):179–190CrossRefGoogle Scholar
  62. 62.
    Zacharaki EI, Hogea CS, Shen D, Biros G, Davatzikos C (2009) Non-diffeomorphic registration of brain tumor images by simulating tissue loss and tumor growth. NeuroImage 46(3):762–774CrossRefGoogle Scholar
  63. 63.
    Millán RD, Dempere-Marco L, Pozo JM, Cebral JR, Frangi AF (2007) Morphological characterization of intracranial aneurysms using 3-D moment invariants. IEEE Trans Med Imaging 26(9):1270–1282CrossRefGoogle Scholar
  64. 64.
    Prastawa M, Bullitt E, Ho S, Gerig G (2004) A brain tumor segmentation framework based on outlier detection. Med Image Anal 8(3):275–283CrossRefGoogle Scholar
  65. 65.
    Warfield SK, Kaus M, Jolesz FA, Kikinis R (2000) Adaptive, template moderated, spatially varying statistical classification. Med Image Anal 4(1):43–55CrossRefGoogle Scholar
  66. 66.
    Gerig G, Styner M, Jones D, Weinberger D, Lieberman J (2001) Shape analysis of brain ventricles using SPHARM. In: IEEE workshop mathematical methods in biomedical image, analysis, pp 171–178Google Scholar
  67. 67.
    Levitt JJ, Styner M, Niethammer M, Bouix S, Koo MS, Voglmaier MM, Dickey CC, Niznikiewicz MA, Kikinis R, McCarley RW, Shenton ME (2009) Shape abnormalities of caudate nucleus in schizotypal personality disorder. Schizophr Res 110(1):127–139CrossRefGoogle Scholar
  68. 68.
    Zhao Z, Taylor WD, Styner M, Steffens DC, Krishnan KR, MacFall JR (2008) Hippocampus shape analysis and late-life depression. PLoS One 3(3):e1837CrossRefGoogle Scholar
  69. 69.
    Van De Ville D, Seghier ML, Lazeyras FO, Blu T, Unser M (2007) WSPM: wavelet-based statistical parametric mapping. NeuroImage 37(4):1205–1217CrossRefGoogle Scholar
  70. 70.
    Canales-Rodríguez EJ, Radua J, Pomarol-Clotet E, Sarró S, Alemán-Gómez Y, Iturria-Medina Y, Salvador R (2013) Statistical analysis of brain tissue images in the wavelet domain: wavelet-based morphometry. NeuroImage 72(22):214–226CrossRefGoogle Scholar
  71. 71.
    Hackmack K, Paul F, Weygandt M, Allefeld C, Haynes JD (2012) Multi-scale classification of disease using structural MRI and wavelet transform. NeuroImage 62(1):48–58CrossRefGoogle Scholar
  72. 72.
    Nain D, Haker S, Bobick A, Tannenbaum A (2007) Multiscale 3-D shape representation and segmentation using spherical wavelets. IEEE Trans Med Imaging 26(4):598–618CrossRefGoogle Scholar
  73. 73.
    Hamarneh G, Abugharbieh R, McInerney T (2004) Medial profiles for modeling deformation and statistical analysis of shape and their use in medical image segmentation. Int J Shape Model 10:187–210.Google Scholar
  74. 74.
    Ward A, Hamarneh G (2008) GMAT: The groupwise medial axis transform for fuzzy skeletonization and intelligent pruning. Technical report, School of Computing Science, Simon Fraser University, BurnabyGoogle Scholar
  75. 75.
    Blum H (1967) A transformation for extracting new descriptors of shape. Models for the perception of speech and visual form. MIT Press, Cambridge, pp 362–380Google Scholar
  76. 76.
    Bai X, Latecki LJ, Liu WY (2007) Skeleton pruning by contour partitioning with discrete curve evolution. IEEE Trans Pattern Anal Mach Intel 29(3):449–462CrossRefGoogle Scholar
  77. 77.
    Ward A, Hamarneh G (2010) GMAT: the groupwise medial axis transform for fuzzy skeletonization and intelligent pruning. IEEE Trans Pattern Anal Mach Intel 32(6):1084–1096CrossRefGoogle Scholar
  78. 78.
    Pizer SM, Fletcher PT, Joshi S, Thall A, Chen JZ, Fridman Y, Fritsch DS, Gash AG, Glotzer JM, Jiroutek MR, Lu C, Muller KE, Tracton G, Yushkevich P, Chaney EL (2003) Deformable M-reps for 3D medical image segmentation. Int J Comput Vis 55(2):85–106CrossRefGoogle Scholar
  79. 79.
    Siddiqi K, Pizer SM (2008) Medial representations: mathematics, algorithms and applications. Springer, New YorkCrossRefGoogle Scholar
  80. 80.
    Fletcher T, Lu C, Pizer SM, Joshi S (2004) Principal geodesic analysis for the study of nonlinear statistics of shape. IEEE Trans Med Imaging 23(8):995–1005CrossRefGoogle Scholar
  81. 81.
    Yushkevich PA, Zhang H, Gee JC (2006) Continuous medial representation for anatomical structures. IEEE Trans Med Imaging 25(12):1547–1564CrossRefGoogle Scholar
  82. 82.
    Yushkevich PA (2009) Continuous medial representation of brain structures using the Biharmonic PDE. NeuroImage 45(1):s99–s110CrossRefMathSciNetGoogle Scholar
  83. 83.
    Yushkevich PA (2003) Statistical shape characterization using the medial representation. Ph.D. thesis, University of North Carolina, Chapel HillGoogle Scholar
  84. 84.
    Matheron G (1988) Examples of topological properties of skeletons. In: Serra J (ed) Image analysis and mathematical morphology part II: theoretical advances. Academic Press, London, pp 217–238Google Scholar
  85. 85.
    Naf M, Kubler O, Kikinis R, Shenton M, Szekely G (1996) Characterization and recognition of 3D organ shape in medical image analysis using skeletonization. In: Workshop on mathematical methods in biomedical image analysis, pp 139–150. IEEE Computer SocietyGoogle Scholar
  86. 86.
    Styner M (2001) Combined boundary-medial shape description of variable biological objects. Ph.D. thesis, University of North Carolina, Chapel HillGoogle Scholar
  87. 87.
    Katz R (2002) Form metrics for interactive rendering via figural models of perception. Ph.D. thesis, University of North Carolina, Chapel HillGoogle Scholar
  88. 88.
    Siddiqi K, Ahokoufandeh A, Dickinson S, Zucker S (1998) Shock graphs and shape matching. Int Conf Comput Vis 35:13–32Google Scholar
  89. 89.
    Siddiqi K, Bouix S, Tannenbaum A, Zucker SW (1999) The Hamilton-Jacobi skeleton. Comput Vis 2:828–834. IEEE PressGoogle Scholar
  90. 90.
    Fridman Y, Pizer SM, Aylward S, Bullitt E (2003) Segmenting 3D branching tubular structures using cores. In: Ellis RE, Peters TM (eds) MICCAI 2003. LNCS, vol 2879, pp 570–577. Springer, New YorkGoogle Scholar
  91. 91.
    Golland P, Grimson W, Kikinis R (1999) Statistical shape analysis using fixed topology skeletons: corpus callosum study. In: Kuba A, Attila J, Samal M (eds) LNCS, vol 1613, pp 382–388. Springer, New YorkGoogle Scholar
  92. 92.
    Fletcher T (2004) Statistical variability in nonlinear spaces: application to shape analysis and DT-MRI. Ph.D. thesis, University of North Carolina, Chapel HillGoogle Scholar
  93. 93.
    Styner M, Lieberman JA, Pantazis D, Gerig G (2004) Boundary and medial shape analysis of the hippocampus in schizophrenia. Med Image Anal 8(3):197–203CrossRefGoogle Scholar
  94. 94.
    McClure RK, Styner M, Maltbie E, Lieberman JA, Gouttard S, Gerig G, Shi X, Zhu H (2013) Localized differences in caudate and hippocampal shape are associated with schizophrenia but not antipsychotic type. Psychiatry Res 211(1):1–10CrossRefGoogle Scholar
  95. 95.
    Ishaq O, Hamarneh G, Tam R, Traboulsee A (2007) Longitudinal, regional and deformation-specific corpus callosum shape analysis for multiple sclerosis. In: IEEE international conference of engineering in medicine and biology society, pp 2110–2113Google Scholar
  96. 96.
    Vaillant M, Glaunes J (2005) Surface matching via currents. In: Christensen GE, Sonka M (eds) LNCS, vol 3565, pp 381–392. Springer, New YorkGoogle Scholar
  97. 97.
    Charon N, Trouvé A The varifold representation of non-oriented shapes for diffeomorphic registration. SIAM J Imaging Sci (to appear), eprint arXiv:1304.6108Google Scholar
  98. 98.
    Durrleman S (2010) Statistical models of currents for measuring the variability of anatomical curves, surfaces and their evolution. Ph.D. thesis, Nice Sophia-Antipolis University, FranceGoogle Scholar
  99. 99.
    Christensen GE, Rabbitt RD, Miller MI (1994) 3D brain mapping using a deformable neuroanatomy. Phys Med Biol 39(3):609–618CrossRefGoogle Scholar
  100. 100.
    Trouvé A (1998) Diffeomorphisms groups and pattern matching in image analysis. Int J Comput Vis 28(3):213–221CrossRefGoogle Scholar
  101. 101.
    Dupuis P, Grenander U, Miller MI (1998) Variational problems on flows of diffeomorphisms for image matching. Q Appl Math 56(3):587–600zbMATHMathSciNetGoogle Scholar
  102. 102.
    Vercauteren T, Pennec X, Perchant A, Ayache N (2009) Diffeomorphic demons: efficient non-parametric image registration. NeuroImage 45(1):S61–S72CrossRefGoogle Scholar
  103. 103.
    Durrleman S, Prastawa M, Korenberg JR, Joshi S, Trouvé A, Gerig G (2012) Topology preserving atlas construction from shape data without correspondence using sparse parameters. In: Ayache N, Delingette H, Golland P, Mori K (eds) MICCAI 2012. LNCS, vol 7512, pp 223–230Google Scholar
  104. 104.
    Miller MI, Trouvé A, Younes L (2002) On the metrics and euler-lagrange equations of computational anatomy. Ann Rev Biomed Eng 4:375–405CrossRefGoogle Scholar
  105. 105.
    Miller MI, Trouvé A, Younes L (2006) Geodesic shooting for computational anatomy. J Math Imaging Vis 24(2):209–228CrossRefGoogle Scholar
  106. 106.
    Durrleman S, Pennec X, Trouvé A, Thompson P, Ayache N (2008) Inferring brain variability from diffeomorphic deformations of currents: an integrative approach. Med Image Anal 12(5):626–637CrossRefGoogle Scholar
  107. 107.
    Medical Image Computing and Computer-Assisted Intervention—MICCAI (2013) In: Mori K, Ichiro S (eds) LNCS, vol 8149, pp 267–274Google Scholar
  108. 108.
    Auzias G, Colliot O, Glaunès JA, Perrot M, Mangin J-F, Trouvé A, Baillet S (2011) Diffeomorphic brain registration under exhaustive sulcal constraints. IEEE Trans Med Imaging 30(6):1214–1227Google Scholar
  109. 109.
    Qiu A, Younes L, Wang L, Ratnanather JT, Gillepsie SK, Kaplan G, Csernansky J, Miller MI (2007) Combining anatomical manifold information via diffeomorphic metric mappings for studying cortical thinning of the cingulated gyrus in schizophrenia. Neuroimage 37(3):821–833CrossRefGoogle Scholar
  110. 110.
    Durrleman S, Pennec X, Trouvé A, Braga J, Gerig G, Ayache A (2013) Toward a comprehensive framework for the spatiotemporal analysis of longitudinal shape data. Int J Comput Vis 103(1):22–59CrossRefzbMATHMathSciNetGoogle Scholar
  111. 111.
    Mansi T, Voigt I, Leonardi B, Pennec X, Durrleman S, Sermesant M, Delingette H, Taylor AM, Boudjemline Y, Pongiglione G, Ayache N (2011) A statistical model for quantification and prediction of cardiac remodelling: application to tetralogy of fallot. IEEE Trans Med Imaging 9(30):1605–1616CrossRefGoogle Scholar
  112. 112.
    Allassonnière S, Kuhn E (2010) Stochastic algorithm for parameter estimation for dense deformable template mixture model. ESAIM-PS 14:382–408CrossRefzbMATHGoogle Scholar
  113. 113.
    van der Kolk AG, Hendrikse J, Zwanenburg JJ, Visser F, Luijten PR (2013) Clinical applications of 7 T MRI in the brain. Eur. J. Radiol. 82(5):708–718CrossRefGoogle Scholar
  114. 114.
    Warfield SK, Zou KH, Wells WM (2004) Simultaneous truth and performance level estimation (STAPLE): an algorithm for the validation of image segmentation. IEEE Trans Med Imaging 23(7):903–921CrossRefGoogle Scholar
  115. 115.
    Fischl B, Salat DH, Busa E, Albert M, Dieterich M, Haselgrove C, van der Kouwe A, Killiany R, Kennedy D, Klaveness S, Montillo A, Makris N, Rosen B, Dale AM (2002) Whole brain segmentation: automated labeling of neuroanatomical structures in the human brain. Neuron 33(3):341–355CrossRefGoogle Scholar
  116. 116.
    Desikan RS, Ségonne F, Fischl B, Quinn BT, Dickerson BC, Blacker D, Buckner RL, Dale AM, Maguire RP, Hyman BT, Albert MS, Killiany RJ (2006) An automated labeling system for subdividing the human cerebral cortex on MRI scans into gyral based regions of interest. NeuroImage 31(3):968–980CrossRefGoogle Scholar
  117. 117.
    Top A, Hamarneh G, Abugharbieh R (2011) Active learning for interactive 3D image segmentation. In: Fichtinger G, Peters T (eds) MICCAI 2011. LNCS, vol 14, pp 603–610Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Bernard Ng
    • 1
    • 2
    Email author
  • Matthew Toews
    • 3
  • Stanley Durrleman
    • 4
    • 5
  • Yonggang Shi
    • 6
  1. 1.PARIETAL TeamINRIAGif-Sur-YvetteFrance
  2. 2.FIND LabStanford UniversityStanfordUSA
  3. 3.Surgical Planning Laboratory, Brigham and Women’s HospitalHarvard Medical SchoolBostonUSA
  4. 4.ARAMIS TeamINRIAParisFrance
  5. 5.Institut du Cerveau et de la Moëlle épinière (ICM)Hôpital de la Pitié SalpêtrièreParisFrance
  6. 6.Institute for Neuroimaging and Informatics, Keck School of MedicineUniversity of Southern CaliforniaLosAngelesUSA

Personalised recommendations