A Landmark-Based Brain Conformal Parametrization with Automatic Landmark Tracking Technique

  • Lok Ming Lui
  • Yalin Wang
  • Tony F. Chan
  • Paul M. Thompson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4191)


In this paper, we present algorithms to automatically detect and match landmark curves on cortical surfaces to get an optimized brain conformal parametrization. First, we propose an automatic landmark curve tracing method based on the principal directions of the local Weingarten matrix. Our algorithm obtains a hypothesized landmark curves using the Chan-Vese segmentation method, which solves a Partial Differential Equation (PDE) on a manifold with global conformal parameterization. Based on the global conformal parametrization of a cortical surface, our method adjusts the landmark curves iteratively on the spherical or rectangular parameter domain of the cortical surface along its principal direction field, using umbilic points of the surface as anchors. The landmark curves can then be mapped back onto the cortical surface. Experimental results show that the landmark curves detected by our algorithm closely resemble these manually labeled curves. Next, we applied these automatically labeled landmark curves to generate an optimized conformal parametrization of the cortical surface, in the sense that homologous features across subjects are caused to lie at the same parameter locations in a conformal grid. Experimental results show that our method can effectively help in automatically matching cortical surfaces across subjects.


Riemann Surface Principal Direction Anchor Point Cortical Surface Conformal Factor 
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  1. 1.
    Vese, L., Chan, T.: International Journal of Computer Vision 50, 271–293 (2002)Google Scholar
  2. 2.
    Tao, X., Prince, J., Davatzikos, C.: IEEE TMI 21, 513–524 (2002)Google Scholar
  3. 3.
    Lohmann, G., Kruggel, F., von Cramon, D.: IPMI 1230, 368–374 (1997)Google Scholar
  4. 4.
    Zeng, X., Staib, L., Schultz, R., Win, L., Duncan, J.: In: Taylor, C., Colchester, A. (eds.) MICCAI 1999. LNCS, vol. 1679, Springer, Heidelberg (1999)Google Scholar
  5. 5.
    Gu, X., Wang, Y., Yau, S.T.: IEEE TMI 23, 949–958 (2004)Google Scholar
  6. 6.
    Glaunès, J., Vaillant, M., Miller, M.J.: Maths. Imaging and Vision 20, 179–200 (2004)Google Scholar
  7. 7.
    Leow, A., Yu, C., Lee, S., Huang, S., Protas, H., Nicolson, R., Hayashi, K., Toga, A., Thompson, P.: NeuroImage 24, 910–927 (2005)Google Scholar
  8. 8.
    Thompson, P., Woods, R., Mega, M., Toga, A.: Human Brain Mapping 9, 81–92 (2000)Google Scholar
  9. 9.
    Schoen, R., Yau, S.: International Press (1997)Google Scholar
  10. 10.
    Cipolla, R., Giblin, P.J.: Cambridge University Press (2000)Google Scholar
  11. 11.
    Gu, X., Yau, S.: ACM Symp on Geom. Processing 2003 (2003)Google Scholar
  12. 12.
    Wang, Y., Gu, X., Hayashi, K.M., Chan, T.F., Thompson, P.M., Yau, S.T.: In: Duncan, J.S., Gerig, G. (eds.) MICCAI 2005. LNCS, vol. 3750, pp. 26–29. Springer, Heidelberg (2005)Google Scholar
  13. 13.
    Rusinkiewicz, S.: Symp. on 3D Data Processing, Vis., and Trans. (2004)Google Scholar
  14. 14.
    Lui, L., Wang, Y., Chan, T.F.: VLSM, ICCV (2005)Google Scholar
  15. 15.
    Drury, H., Essen, D.V., Corbetta, M., Snyder, A.: Academic Press (1999)Google Scholar
  16. 16.
    Fischl, B., Sereno, M., Tootell, R., Dale, A.: Human Brain Mapping 8, 272–284 (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Lok Ming Lui
    • 1
  • Yalin Wang
    • 1
    • 2
  • Tony F. Chan
    • 1
  • Paul M. Thompson
    • 2
  1. 1.Department of MathematicsUCLA 
  2. 2.Laboratory of Neuroimaging, Department of NeurologyUCLA 

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