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Abstract

We propose a novel technique based on spherical splines for brain surface representation and analysis. This research is strongly inspired by the fact that, for brain surfaces, it is both necessary and natural to employ spheres as their natural domains. We develop an automatic and efficient algorithm, which transforms a brain surface to a single spherical spline whose maximal error deviation from the original data is less than the user-specified tolerance. Compared to the discrete mesh-based representation, our spherical spline offers a concise (low storage requirement) digital form with high continuity (C n − − 1 continuity for a degree n spherical spline). Furthermore, this representation enables the accurate evaluation of differential properties, such as curvature, principal direction, and geodesic, without the need for any numerical approximations. Thus, certain shape analysis procedures, such as segmentation, gyri and sulci tracing, and 3D shape matching, can be carried out both robustly and accurately. We conduct several experiments in order to demonstrate the efficacy of our approach for the quantitative measurement and analysis of brain surfaces.

Keywords

Principal Curvature Conformal Factor Brain Surface Conformal Representation Spherical Triangle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Avants, B.B., Gee, J.C.: The shape operator for differential analysis of images. In: IPMI, pp. 101–113 (2003)Google Scholar
  2. 2.
    Cachia, A., Mangin, J.-F., Rivière, D., Boddaert, N., Andrade, A., Kherif, F., Sonigo, P., Papadopoulos-Orfanos, D., Zilbovicius, M., Poline, J.-B., Bloch, I., Brunelle, F., Régis, J.: A mean curvature based primal sketch to study the cortical folding process from antenatal to adult brain. In: Niessen, W.J., Viergever, M.A. (eds.) MICCAI 2001. LNCS, vol. 2208, pp. 897–904. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  3. 3.
    Gu, X., Wang, Y., Chan, T.F., Thompson, P.M., Yau, S.T.: Genus zero surface conformal mapping and its application to brain surface mapping. In: IPMI, pp. 172–184 (2003)Google Scholar
  4. 4.
    Gu, X., Vemuri, B.C.: Matching 3d shapes using 2d conformal representations. In: Barillot, C., Haynor, D.R., Hellier, P. (eds.) MICCAI 2004. LNCS, vol. 3216, pp. 771–780. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  5. 5.
    Tao, X., Han, X., Rettmann, M.E., Prince, J.L., Davatzikos, C.: Statistical study on cortical sulci of human brains. In: IPMI, pp. 475–487 (2001)Google Scholar
  6. 6.
    Tao, X., Prince, J.L., Davatzikos, C.: An automated method for finding curves of sulcal fundi on human cortical surfaces. In: ISBI, pp. 1271–1274 (2004)Google Scholar
  7. 7.
    Thompson, P.M., Toga, A.W.: A surface-based technique for warping 3-dimensional images of the brain. IEEE Trans. Medical Images 15, 402–417 (1996)CrossRefGoogle Scholar
  8. 8.
    Thompson, P.M., Mega, M.S., Vidal, C., Rapoport, J.L., Toga, A.W.: Detecting disease-specific patterns of brain structure using cortical pattern matching and a population-based probabilistic brain atlas. In: IPMI, pp. 488–501 (2001)Google Scholar
  9. 9.
    Pfeifle, R., Seidel, H.P.: Spherical triangular b-splines with application to data fitting. Comput. Graph. Forum 14, 89–96 (1995)CrossRefGoogle Scholar
  10. 10.
    He, Y., Gu, X., Qin, H.: Fairing triangular B-splines of arbitrary topology. In: Proceedings of Pacific Graphics 2005 (2005) (to appear)Google Scholar
  11. 11.
    Seidel, H.P.: Polar forms and triangular B-spline surfaces. In: Du, D.Z., Hwang, F. (eds.) Euclidean Geometry and Computers, 2nd edn., pp. 235–286. World Scientific Publishing Co., Singapore (1994)Google Scholar
  12. 12.
    Gormaz, R.: B-spline knot-line elimination and Bézier continuity conditions. In: Curves and surfaces in geometric design, pp. 209–216. A.K. Peters, Wellesley (1994)Google Scholar
  13. 13.
    Meyer, M., Desbrun, M., Schröder, P., Barr, A.H.: Discrete differential-geometry operators for triangulated 2-manifolds. In: VisMath 2002 (2002)Google Scholar
  14. 14.
    Taubin, G.: Estimating the tensor of curvature of a surface from a polyhedral approximation. In: ICCV, pp. 902–907 (1995)Google Scholar
  15. 15.
    Goldfeather, J., Interrante, V.: A novel cubic-order algorithm for approximating principal direction vectors. ACM Trans. Graph. 23, 45–63 (2004)CrossRefGoogle Scholar
  16. 16.
    Rusinkiewicz, S.: Estimating curvatures and their derivatives on triangle meshes. In: 3DPVT, pp. 486–493 (2004)Google Scholar
  17. 17.
    Surazhsky, T., Magid, E., Soldea, O., Elber, G., Rivlin, E.: A comparison of gaussian and mean curvatures estimation methods on triangular meshes. In: ICRA, pp. 1021–1026 (2003)Google Scholar
  18. 18.
    Theisel, H., Rössl, C., Zayer, R., Seidel, H.P.: Normal based estimation of the curvature tensor for triangular meshes. In: Pacific Conference on Computer Graphics and Applications, pp. 288–297 (2004)Google Scholar
  19. 19.
    Belyaev, A.G., Pasko, A.A., Kunii, T.L.: Ridges and ravines on implicit surfaces. In: Computer Graphics International, pp. 530–535 (1998)Google Scholar
  20. 20.
    Ohtake, Y., Belyaev, A.G., Seidel, H.P.: Ridge-valley lines on meshes via implicit surface fitting. ACM Trans. Graph. 23, 609–612 (2004)CrossRefGoogle Scholar
  21. 21.
    Thompson, P.M., Toga, A.W.: A framework for computational anatomy. Computing and Visualization in Science 5, 1–12 (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Ying He
    • 1
  • Xin Li
    • 1
  • Xianfeng Gu
    • 1
  • Hong Qin
    • 1
  1. 1.Center for Visual Computing (CVC) and Department of Computer ScienceStony Brook UniversityStony BrookUSA

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