Journal of Mathematical Imaging and Vision

, Volume 33, Issue 2, pp 239–252 | Cite as

High Angular Resolution Diffusion MRI Segmentation Using Region-Based Statistical Surface Evolution

  • Maxime Descoteaux
  • Rachid Deriche


In this article we develop a new method to segment high angular resolution diffusion imaging (HARDI) data. We first estimate the orientation distribution function (ODF) using a fast and robust spherical harmonic (SH) method. Then, we use a region-based statistical surface evolution on this image of ODFs to efficiently find coherent white matter fiber bundles. We show that our method is appropriate to propagate through regions of fiber crossings and we show that our results outperform state-of-the-art diffusion tensor (DT) imaging segmentation methods, inherently limited by the DT model. Results obtained on synthetic data, on a biological phantom, on real datasets and on all 13 subjects of a public NMR database show that our method is reproducible, automatic and brings a strong added value to diffusion MRI segmentation.


Diffusion tensor imaging (DTI) High angular resolution diffusion imaging (HARDI) Q-ball imaging (QBI) Orientation distribution function (ODF) Region-based segmentation Level set framework 


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  1. 1.
    Alexander, D., Barker, G., Arridge, S.: Detection and modeling of non-Gaussian apparent diffusion coefficient profiles in human brain data. Magn. Reson. Med. 48(2), 331–340 (2002) CrossRefGoogle Scholar
  2. 2.
    Alexander, D.C.: Maximum entropy spherical deconvolution for diffusion mri. In: Image Processing in Medical Imaging, pp. 76–87 (2005) Google Scholar
  3. 3.
    Anderson, A.: Measurements of fiber orientation distributions using high angular resolution diffusion imaging. Magn. Reson. Med. 54, 1194–1206 (2005) CrossRefGoogle Scholar
  4. 4.
    Andrews, G., Askey, R., Roy, R.: Special Functions. Cambridge University Press, Cambridge (1999) zbMATHGoogle Scholar
  5. 5.
    Anwander, A., Tittgemeyer, M., von Cramon, D.Y., Friederici, A.D., Knosche, T.R.: Connectivity-based parcellation of broca’s area. Cereb. Cortex 17(4), 816–825 (2007) CrossRefGoogle Scholar
  6. 6.
    Basser, P., Pierpaoli, C.: Microstructural and physiological features of tissues elucidated by quantitative diffusion tensor mri. J. Magn. Reson. 111(3), 209–219 (1996) CrossRefGoogle Scholar
  7. 7.
    Callaghan, P.T.: Principles of Nuclear Magnetic Resonance Microscopy. Oxford University Press, Oxford (1991) Google Scholar
  8. 8.
    Campbell, J., Siddiqi, K., Rymar, V., Sadikot, A., Pike, G.: Flow-based fiber tracking with diffusion tensor q-ball data: validation and comparison to principal diffusion direction techniques. NeuroImage 27(4), 725–736 (2005) CrossRefGoogle Scholar
  9. 9.
    Chan, T., Vese, L.: Active contours without edges. IEEE Trans. Image Process. 10(2), 266–277 (2001) zbMATHCrossRefGoogle Scholar
  10. 10.
    Cremers, D., Rousson, M., Deriche, R.: Review of statistical approaches to level set segmentation: integrating color, texture, motion and shape. Int. J. Comput. Vis. 72(2), 195–215 (2007) CrossRefGoogle Scholar
  11. 11.
    Dervieux, A., Thomasset, F.: A finite element method for the simulation of Rayleigh-Taylor instability. In: Lecture Notes in Mathematics, vol. 771, pp. 145–159. Springer, Berlin (1979) Google Scholar
  12. 12.
    Dervieux, A., Thomasset, F.: Multifluid incompressible flows by a finite element method. In: Lecture Notes in Physics, vol. 11, pp. 158–163. Springer, Berlin (1981) Google Scholar
  13. 13.
    Descoteaux, M., Angelino, E., Fitzgibbons, S., Deriche, R.: A linear and regularized odf estimation algorithm to recover multiple fibers in q-ball imaging. Technical Report 5768, INRIA Sophia Antipolis, November 2005 Google Scholar
  14. 14.
    Descoteaux, M., Angelino, E., Fitzgibbons, S., Deriche, R.: Apparent diffusion coefficients from high angular resolution diffusion imaging: Estimation and applications. Magn. Reson. Med. 56, 395–410 (2006) CrossRefGoogle Scholar
  15. 15.
    Descoteaux, M., Angelino, E., Fitzgibbons, S., Deriche, R.: Regularized, fast, and robust analytical q-ball imaging. Magn. Reson. Med. 58(3), 497–510 (2007) CrossRefGoogle Scholar
  16. 16.
    Descoteaux, M., Angelino, E., Fitzgibbons, S., Deriche, R.: A fast and robust odf estimation algorithm in q-ball imaging. In: Third IEEE International Symposium on Biomedical Imaging: from Nano to Macro, Arlington, VA, USA, April 2006, pp. 81–84 (2006) Google Scholar
  17. 17.
    Feddern, C., Weickert, J., Burgeth, B.: Level-set methods for tensor-valued images. In: Proceedings of the Second IEEE Workshop on Geometric and Level Set Methods in Computer Vision, pp. 65–72 (2003) Google Scholar
  18. 18.
    Feddern, C., Weickert, J., Burgeth, B., Welk, M.: Curvature-driven PDE methods for matrix-valued images. Technical Report 104, Department of Mathematics, Saarland University, Saarbrücken, Germany, April 2004 Google Scholar
  19. 19.
    Hagmann, P., Jonasson, L., Deffieux, T., Meuli, R., Thiran, J.-P., Wedeen, V.J.: Fibertract segmentation in position orientation space from high angular resolution diffusion mri. NeuroImage 32, 665–675 (2006) CrossRefGoogle Scholar
  20. 20.
    Hess, C., Mukherjee, P., Han, E., Xu, D., Vigneron, D.: Q-ball reconstruction of multimodal fiber orientations using the spherical harmonic basis. Magn. Reson. Med. 56, 104–117 (2006) CrossRefGoogle Scholar
  21. 21.
    Jansons, K.M., Alexander, D.C.: Persistent angular structure: new insights foam diffusion magnetic resonance imaging data. Inverse Probl. 19, 1031–1046 (2003) zbMATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Jonasson, L.: Segmentation of diffusion weighted MRI using the level set framework. PhD thesis, Ecole Polytechnique federale de Lausanne (2006) Google Scholar
  23. 23.
    Jonasson, L., Bresson, X., Hagmann, P., Cuisenaire, O., Meuli, R., Thiran, J.-P.: White matter fiber tract segmentation in dt-mri using geometric flows. Med. Image Anal. 9, 223–236 (2005) CrossRefGoogle Scholar
  24. 24.
    Jonasson, L., Hagmann, P., Bresson, X., Thiran, J.-P., Wedeen, V.J.: Representing diffusion mri in 5D for segmentation of white matter tracts with a level set method. In: Information Processing in Medical Imaging. Lecture Notes in Computer Science, pp. 311–320. Springer, Berlin (2005) Google Scholar
  25. 25.
    Lenglet, C., Rousson, M., Deriche, R.: Dti segmentation by statistical surface evolution. IEEE Trans. Med. Imaging 25(6), 685–700 (2006) CrossRefMathSciNetGoogle Scholar
  26. 26.
    McGraw, T., Vemuri, B., Yezierski, R., Mareci, T.: Segmentation of high angular resolution diffusion mri modeled as a field of von mises-fisher mixtures. In European Conference on Computer Vision (ECCV), vol. 3953, pp. 463–475 (2006) Google Scholar
  27. 27.
    Osher, S., Sethian, J.: Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton–Jacobi formulations. J. Comput. Phys. 79(1), 12–49 (1988) zbMATHCrossRefMathSciNetGoogle Scholar
  28. 28.
    Ozarslan, E., Shepherd, T., Vemuri, B., Blackband, S., Mareci, T.: Resolution of complex tissue microarchitecture using the diffusion orientation transform (dot). NeuroImage 31(3), 1086–1103 (2006) CrossRefGoogle Scholar
  29. 29.
    Paragios, N., Deriche, R.: Geodesic active regions: a new paradigm to deal with frame partition problems in computer vision. J. Vis. Commun. Image Represent. 13(1–2), 249–268 (2002). Special Issue on Partial Differential Equations in Image Processing, Computer Vision and Computer Graphics CrossRefGoogle Scholar
  30. 30.
    Poupon, C., Poupon, F., Allirol, L., Mangin, J.-F.: A database dedicated to anatomo-functional study of human brain connectivity. In: Twelfth Annual Meeting of the Organization for Human Brain Mapping (HBM) (2006) Google Scholar
  31. 31.
    Rousson, M.: Cue integration and front evolution in image segmentation. PhD thesis, Universite de Nice, Sophia Antipolis (2004) Google Scholar
  32. 32.
    Rousson, M., Lenglet, C., Deriche, R.: Level set and region based surface propagation for diffusion tensor mri segmentation. In: Computer Vision Approaches to Medical Image Analysis (CVAMIA) and Mathematical Methods in Biomedical Image Analysis (MMBIA) Workshop, Prague, May 2004 Google Scholar
  33. 33.
    Tournier, J.-D., Calamante, F., Gadian, D., Connelly, A.: Direct estimation of the fiber orientation density function from diffusion-weighted mri data using spherical deconvolution. NeuroImage 23, 1176–1185 (2004) CrossRefGoogle Scholar
  34. 34.
    Tuch, D.: Q-ball imaging. Magn. Reson. Med. 52(6), 1358–1372 (2004) CrossRefGoogle Scholar
  35. 35.
    Tuch, D., Reese, T., Wiegell, M., Makris, N., Belliveau, J., Wedeen, V.: High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity. Magn. Reson. Med. 48(4), 577–582 (2002) CrossRefGoogle Scholar
  36. 36.
    Vese, L., Chan, T.: A multiphase level set framework for image segmentation using the Mumford and Shah model. Int. J. Comput. Vis. 50(3), 271–293 (2002) zbMATHCrossRefGoogle Scholar
  37. 37.
    Wang, Z., Vemuri, B.C.: Tensor field segmentation using region based active contour model. In: European Conference on Computer Vision (ECCV). Lecture Notes in Computer Science, pp. 304–315. Springer, Berlin (2004) Google Scholar
  38. 38.
    Wang, Z., Vemuri, B.C.: Dti segmentation using an information theoretic tensor dissimilarity measure. IEEE Trans. Med. Imaging 24(10), 1267–1277 (2005) CrossRefGoogle Scholar
  39. 39.
    Wedeen, V., Reese, T., Tuch, D., Wiegel, M., Dou, J.-G., Weiskoff, R., Chessler, D.: Mapping fiber orientation spectra in cerebral white matter with Fourier-transform diffusion mri. In: Proceedings of the International Society of Magnetic Resonance in Medicine, p. 82. International Society for Magnetic Resonance in Medicine (2000) Google Scholar
  40. 40.
    Wiegell, M.R., Tuch, D.S., Larsson, H.B., Wedeena, V.J.: Automatic segmentation of thalamic nuclei from diffusion tensor magnetic resonance imaging. NeuroImage 19, 391–401 (2003) CrossRefGoogle Scholar
  41. 41.
    Zhang, H., Yushkevich, P.A., Gee, J.C.: Registration of diffusion tensor images. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 842–847 (2004) Google Scholar
  42. 42.
    Zhao, H.-K., Chan, T., Merriman, B., Osher, S.: A variational level set approach to multiphase motion. J. Comput. Phys. 127(1), 179–195 (1996) zbMATHCrossRefMathSciNetGoogle Scholar
  43. 43.
    Zhukov, L., Museth, K., Breen, D., Whitakert, R., Barr, A.H.: Level set modeling and segmentation of dt-mri brain data. J. Electron. Imaging 12, 125–133 (2003) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Project Team OdysséeINRIA/ENPC/ENS, INRIA Sophia Antipolis—MéditerranéeSophia AntipolisFrance

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