Medical Image Analysis
Volume 12, Issue 5 , Pages 626-637 , October 2008

Inferring brain variability from diffeomorphic deformations of currents: An integrative approach

  • Stanley Durrleman

      Affiliations

    • Asclepios Team Project, INRIA Sophia Antipolis Méditerranée, 2004 route des Lucioles, 06902 Sophia Antipolis Cedex, France
    • Centre de Mathématique et Leurs Applications, ENS Cachan, 61 avenue du président Wilson, 94235 Cachan Cedex, France
    • Corresponding Author InformationCorresponding author. Address: Asclepios Team Project, INRIA Sophia Antipolis Méditerranée, 2004 route des Lucioles, 06902 Sophia Antipolis Cedex, France. Tel.: +33 4 92 38 75 61; fax: +33 4 92 38 76 69.
  • ,
  • Xavier Pennec

      Affiliations

    • Asclepios Team Project, INRIA Sophia Antipolis Méditerranée, 2004 route des Lucioles, 06902 Sophia Antipolis Cedex, France
  • ,
  • Alain Trouvé

      Affiliations

    • Centre de Mathématique et Leurs Applications, ENS Cachan, 61 avenue du président Wilson, 94235 Cachan Cedex, France
  • ,
  • Paul Thompson

      Affiliations

    • Laboratory of NeuroImaging, Department of Neurology, UCLA School of Medicine, 225E Neuroscience Research Building, Los Angeles, CA, USA
  • ,
  • Nicholas Ayache

      Affiliations

    • Asclepios Team Project, INRIA Sophia Antipolis Méditerranée, 2004 route des Lucioles, 06902 Sophia Antipolis Cedex, France

Received 31 January 2008 ,Revised 11 June 2008 ,Accepted 11 June 2008.

References 

  1. Aronszajn N. Theory of reproducing kernels. Transactions of the American Mathematical Society. 1950;(68):337–404
  2. Arsigny V, Fillard P, Pennec X, Ayache N. Log-Euclidean metrics for fast and simple calculus on diffusion tensors. Magnetic Resonance in Medicine. 2006;56(2):411–421
  3. Ashburner , et al. Identifying global anatomical differences: deformation-based morphometry. Human Brain Mapping. 1998;6(5–6):348–357
  4. Ashburner J, Friston K. Morphometry. In:  Frackowiak R,  Friston K,  Frith C,  Dolan R,  Friston K,  Price C,  Zeki S,  Ashburner J,  Penny W editor. Human Brain Function. second ed.. Academic Press; 2003;
  5. Auzias, G., Glaunès, J.-A., Cachia, A., Cathier, P., Bardinet, E., Colliot, O., Mangin, J.F., Trouvé, A., Baillet, S., 2008. Multi-scale diffeomorphic cortical registration under manifold sulcal constraints. In: Proceedings of the IEEE International Symposium on Biomedical Imaging, Macro to Nano, pp. 1127–1130.
  6. Avants BB, Epstein CL, Gee JC. Geodesic image normalization and temporal parameterization in the space of diffeomorphisms. In: Medical Imaging and Augmented Reality. Lecture Notes in Computer Science. vol. 4091:Springer; 2006;p. 9–16
  7. Bhattacharya R, Patrangenaru V. Large sample of theory of intrinsic and extrinsic sample means on manifolds. Annals of Statistics. 2003;31(1):1–29
  8. Cachier, P., Mangin, J.-F., Pennec, X., Rivière, D., Papadopoulos-Orfanos, D., Régis, J., Ayache, N., 2001. Multisubject non-rigid registration of brain mri using intensity and geometric features. In: Niessen, W., Viergever, M. (Eds.), Fourth International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI’01). Lecture Notes in Computer Science, vol. 2208, pp. 734–742.
  9. Cathier, P., Mangin, J.-F., 2006. Registration of cortical connectivity matrices. In: IEEE Computer Society Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA).
  10. Chui H, Rangarajan A. A new point matching algorithm for non-rigid registration. Computer Vision and Image Understanding. 2003;89(2–3):114–141
  11. Duchesnay E, Cachia A, Roche A, Rivière D, Cointepas Y, Papadopoulos-Orfanos D, et al. Classification from cortical folding patterns. IEEE Transactions on Medical Imaging. 2007;26(4):553–565
  12. Dupuis P, Grenander U, Miller M. Variational problems on flows of diffeomorphisms for image matching. Quarterly of Applied Mathematics. 1998;56(3):587–600
  13. Durrleman S, Pennec X, Trouvé A, Ayache N. Measuring brain variability via sulcal lines registration: a diffeomorphic approach. In:  Ayache N,  Ourselin S,  Maeder A editor. Proceedings of the Medical Image Computing and Computer Assisted Intervention (MICCAI). Lecture Notes in Computer Science. vol. 4791:Brisbane, Australia: Springer; 2007;p. 675–682
  14. Durrleman, S., Pennec, X., Trouvé, A., Ayache, N., in press. Sparse approximation of currents for statistics on curves and surfaces. In: Proceedings of the Medical Image Computing and Computer Assisted Intervention (MICCAI).
  15. Fillard P, Arsigny V, Pennec X, Hayashi K, Thompson P, Ayache N. Measuring brain variability by extrapolating sparse tensor fields measured on sulcal lines. NeuroImage. 2007;34(2):639–650
  16. Fillard, P., Pennec, X., Thompson, P., Ayache, N., 2007b. Evaluating brain anatomical correlations via canonical correlation analysis of sulcal lines. In: Proceedings of MICCAI’07 Workshop on Statistical Registration: Pair-wise and Group-wise Alignment and Atlas Formation, Brisbane, Australia.
  17. Fischl B, Liu A, Dale A. Automated manifold surgery: constructing geometrically accurate and topologically correct models of the human cerebral cortex. IEEE Transactions in Medical Imaging. 2001;20(1):70–80
  18. Fischl B, van der Kouwe A, Destrieux C, Halgren E, Ségonne F, Salat D, et al. Automatically parcellating the human cerebral cortex. Cerebral Cortex. 2004;14(1):11–22
  19. Glaunès, J., Joshi, S., 2006. Template estimation from unlabeled point set data and surfaces for computational anatomy. In: Pennec, X., Joshi, S. (Eds.), Proceedings of the International Workshop on the Mathematical Foundations of Computational Anatomy (MFCA-2006).
  20. Glaunès, J., 2005. Transport par difféomorphismes de points, de mesures et de courants pour la comparaison de formes et l’anatomie numérique. PhD Thesis, Université Paris 13. <http://cis.jhu.edu/joan/TheseGlaunes.pdf>.
  21. Gorczowski, K., Styner, M., Jeong, J.-Y., Marron, J.S., Piven, J., Hazlett, H.C., Pizer, S.M., Gerig, G., 2007. Statistical shape analysis of multi-object complexes. In: Computer Vision and Pattern Recognition CVPR. IEEE, pp. 1–8.
  22. Goualher GL, Argenti A, Duyme M, Baare W, Pol HH, Barillot C, et al. Statistical sulcal shape comparisons: application to the detection of genetic encoding of the central sulcus shape. NeuroImage. 2000;11(5):564–574
  23. Granger S, Pennec X. Multi-scale EM-ICP: a fast and robust approach for surface registration. In:  Heyden A,  Sparr G,  Nielsen M,  Johansen P editor. European Conference on Computer Vision (ECCV 2002). Lecture Notes in Computer Science. vol. 2353:Springer; 2002;p. 418–432
  24. Grenander U. General Pattern Theory: A Mathematical Theory of Regular Structures. Oxford University Press; 1994;
  25. Grenander U, Miller MI. Computational anatomy: an emerging discipline. Quarterly of Applied Mathematics. 1998;LVI(4):617–694
  26. Guéziec A, Ayache N. Smoothing and matching of 3-D space curves. The International Journal of Computer Vision. 1994;12(1):79–104
  27. Hamilton L, Narr K, Luders E, Szeszko P, Thompson P, Bilder R, et al. Asymmetries of cortical thickness: effects of handedness, sex, and schizophrenia. NeuroReport. 2007;18(14):1427–1431
  28. Hazlett H, Poe M, Gerig G, Smith R, Provenzale J, Ross A, et al. Magnetic resonance imaging and head circumference study of brain size in autism. The Archives of General Psychiatry. 2005;62:1366–1376
  29. Hellier P, Barillot C. Coupling dense and landmark-based approaches for non rigid registration. IEEE Transactions on Medical Imaging. 2003;22(2):217–227
  30. Joshi S, Miller M. Landmark matching via large deformation diffeomorphisms. IEEE Transaction on Image Processing. 2000;9(8):1357–1370
  31. Leow A, Yu C, Lee S, Huang S, Nicolson R, Hayashi K, et al. Brain structural mapping using a novel hybrid implicit/explicit framework based on the level-set method. NeuroImage. 2005;24(3):910–927
  32. Luders E, Narr K, Thompson P, Rex D, Jancke L, Toga A. Gender differences in cortical complexity. Nature Neuroscience. 2004;7(8):799–800
  33. Mangin J-F, Rivière D, Cachia A, Duchesnay E, Cointepas Y, Papadopoulos-Orfanos D, et al. Object-based morphometry of the cerebral cortex. IEEE Transactions on Medical Imaging. 2004;23(8):968–982
  34. Marsland S, Twining C. Constructing diffeomorphic representations for the groupwise analysis of non-rigid registrations of medical images. IEEE Transactions on Medical Imaging. 2004;23(8):1006–1020
  35. Miller MI, Trouvé A, Younes L. On the metrics and Euler–Lagrange equations of computational anatomy. Annual Review of Biomedical Engineering. 2002;4:375–405
  36. Miller M, Trouvé A, Younes L. Geodesic shooting for computational anatomy. Journal of Mathematical Imaging and Vision. 2006;24(2):209–228
  37. Narr K, Bilder R, Luders E, Thompson P, Woods R, Robinson D, et al. Asymmetries of cortical shape: effects of handedness, sex and schizophrenia. NeuroImage. 2007;34(3):939–948
  38. Oller J, Corcuera J. Intrinsic analysis of statistical estimation. Annals of Statistics. 1995;23(5):1562–1581
  39. Paus T, Collins D, Evans A, Leonard G, Pike B, Zijdenbos A. Maturation of white matter in the human brain: a review of magnetic resonance studies. Brain Research Bulletin. 2001;54(3):255–266
  40. Pennec, X., 1999. Probabilities and statistics on Riemannian manifolds: basic tools for geometric measurements. In: Cetin, A., Akarun, L., Ertuzun, A., Gurcan, M., Yardimci, Y. (Eds.), Proceedings of the Nonlinear Signal and Image Processing (NSIP’99). vol. 1. IEEE-EURASIP, pp. 194–198.
  41. Pennec X, Fillard P, Ayache N. A Riemannian framework for tensor computing. International Journal of Computer Vision. 2006;66(1):41–66a preliminary version appeared as INRIA Research Report 5255, July 2004
  42. Rivière D, Mangin J-F, Papadopoulos-Orfanos D, Martinez J-M, Frouin V, Régis J. Automatic recognition of cortical sulci of the human brain using a congregation of neural networks. Medical Image Analysis. 2002;6(2):77–92
  43. Saitoh S. Theory of Reproducing Kernels and Its Applications. Pitman Research Notes in Mathematics Series. vol. 189. Wiley; 1988;
  44. Shi Y, Thompson P, Dinov I, Osher S, Toga A. Direct cortical mapping via solving partial differential equations on implicit surfaces. Medical Image Analysis. 2007;11(3):207–223
  45. Thompson P, Toga A. A surface-based technique for warping 3-dimensional images of the brain. IEEE Transactions on Medical Imaging. 1996;15(4):1–16
  46. Thompson, P., Toga, A., 2003. Cortical diseases and cortical localization. Nature Encyclopedia of the Life Sciences, review article.
  47. Thompson P, Schwartz C, Lin R, Khan A, Toga A. 3D statistical analysis of sulcal variability in the human brain. Journal of Neuroscience. 1996;16(13):4261–4274
  48. Thompson P, Schwartz C, Toga A. High-resolution random mesh algorithms for creating a probabilistic 3d surface atlas of the human brain. NeuroImage. 1996;3(1):19–34
  49. Thompson P, Moussai J, Khan A, Zohoori S, Goldkorn A, Mega M, et al. Cortical variability and asymmetry in normal aging and alzheimer’s disease. Cerebral Cortex. 1998;8(6):492–509
  50. Thompson, P., Hayashi, K., de Zubicaray, G., Janke, A., Rose, S., Semple, J., Doddrell, D., Cannon, T., Toga, A., 2002. Detecting dynamic and genetic effects on brain structure using high-dimensional cortical pattern matching. In: Proceedings of the International Symposium on Biomedical Imaging (ISBI), pp. 473–476.
  51. Toga, A., Thompson, P., 2007. What is where and why it is important. NeuroImage Peer-Reviewed Invited Commentary on a paper by Devlin J, Poldrack R “In Praise of Tedious Anatomy”
  52. Tosun D, Prince J. Cortical surface alignment using geometry driven multispectral optical flow. In: Information Processing in Medical Imaging. Lecture Notes in Computer Science. vol. 3565:Springer; 2005;p. 480–492
  53. Trouvé A. Diffeomorphisms groups and pattern matching in image analysis. International Journal of Computer Vision. 1998;28:213–221
  54. Vaillant M, Davatzikos C. Hierarchical matching of cortical features for deformable brain image registration. In: Information Processing in Medical Imaging. Lecture Notes in Computer Science. vol. 1613:Springer; 1999;p. 182–195
  55. Vaillant M, Glaunès J. Surface matching via currents. In: Proceedings of Information Processing in Medical Imaging. Lecture Notes in Computer Science. vol. 3565:Springer; 2005;p. 381–392
  56. Vaillant M, Miller M, Younes L, Trouvé A. Statistics on diffeomorphisms via tangent space representations. NeuroImage. 2004;23:161–169
  57. Vaillant M, Qiu A, Glaunès J, Miller M. Diffeomorphic metric surface mapping in subregion of the superior temporal gyrus. NeuroImage. 2007;34(3):1149–1159
  58. Wang Y, Chiang M, Thompson P. Automated surface matching using mutual information applied to riemann surface structures. In: Medical Image Computing and Computer Assisted Interventions (MICCAI). Lecture Notes in Computer Science. vol. 3750:Springer; 2005;p. 666–674
  59. Zhang Z. Iterative point matching for registration of free-form curves and surfaces. International Journal of Computer Vision. 1994;13(2):119–152

PII: S1361-8415(08)00059-5

doi: 10.1016/j.media.2008.06.010

Medical Image Analysis
Volume 12, Issue 5 , Pages 626-637 , October 2008