Skip to main content
SpringerLink
Log in

Diffeomorphic Spectral Matching of Cortical Surfaces

  • Conference paper
Information Processing in Medical Imaging (IPMI 2013)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 7917))

Included in the following conference series:

Abstract

Accurate matching of cortical surfaces is necessary in many neuroscience applications. In this context diffeomorphisms are often sought, because they facilitate further statistical analysis and atlas building. Present methods for computing diffeomorphisms are based on optimizing flows or on inflating surfaces to a common template, but they are often computationally expensive. It typically takes several hours on a conventional desktop computer to match a single pair of cortical surfaces having a few hundred thousand vertices. We propose a very fast alternative based on an application of spectral graph theory on a novel association graph. Our symmetric approach can generate a diffeomorphic correspondence map within a few minutes on high-resolution meshes while avoiding the sign and multiplicity ambiguities of conventional spectral matching methods. The eigenfunctions are shared between surfaces and provide a smooth parameterization of surfaces. These properties are exploited to compute differentials on highly folded cortical surfaces. Diffeomorphisms can thus be verified and invalid surface folding detected. Our method is demonstrated to attain a vertex accuracy that is at least as good as that of FreeSurfer and Spherical Demons but in only a fraction of their processing time. As a practical experiment, we construct an unbiased atlas of cortical surfaces with a speed several orders of magnitude faster than current methods.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Talairach, J., Szikla, G., Tournoux, P., Prosalentis, A., Bordas-Ferrier, M., Covello, L., Iacob, M., Mempel, E.: Atlas stereotaxique du telencephale. Masson (1967)

    Google Scholar 

  2. Amunts, K., Malikovic, A., Mohlberg, H., Schormann, T., Zilles, K.: Brodmann’s areas 17 and 18 brought into stereotaxic space-where and how variable? NeuroImage (2000)

    Google Scholar 

  3. Drury, H., Van Essen, D., Joshi, S., Miller, M.: Analysis and comparison of areal partitioning schemes using 2-D fluid deformations. NeuroImage 3 (1996)

    Google Scholar 

  4. Van Essen, D., Drury, H.: Structural and functional analyses of human cerebral cortex using a surface-based atlas. Neuroscience 17(18) (1997)

    Google Scholar 

  5. Thompson, P., Toga, A.W.: A surface-based technique for warping three-dimensional images of the brain. TMI 15(4) (1996)

    Google Scholar 

  6. Fischl, B., Sereno, M.I., Tootell, R.B., Dale, A.M.: High-resolution intersubject averaging and a coordinate system for cortical surface. Human Brain Mapping 8 (1999)

    Google Scholar 

  7. Fischl, B., Rajendran, N., Busa, E., Augustinack, J., Hinds, O., Yeo, T., Mohlberg, H., Amunts, K., Zilles, K.: Cortical folding patterns and predicting cytoarchitecture. Cereb. Cortex 18(8) (2007)

    Google Scholar 

  8. Yeo, T., Sabuncu, M., Vercauteren, T., Ayache, N., Fischl, B., Golland, P.: Spherical demons: fast diffeomorphic landmark-free surface registration. TMI 29(3) (2010)

    Google Scholar 

  9. Beg, F., Miller, M., Trouvé, A., Younes, L.: Computing large deformation metric mappings via geodesic flows of diffeomorphisms. IJCV 61 (2005)

    Google Scholar 

  10. Vaillant, M., Glaunès, J.: Surface matching via currents. In: Christensen, G.E., Sonka, M. (eds.) IPMI 2005. LNCS, vol. 3565, pp. 381–392. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  11. Durrleman, S., Pennec, X., Trouvé, A., Ayache, N.: Statistical models of sets of curves and surfaces based on currents. MedIA 13(5) (2009)

    Google Scholar 

  12. Segonne, F., Pacheco, J., Fischl, B.: Geometrically accurate Topology-Correction of cortical surfaces using nonseparating loops. TMI 26(4) (2007)

    Google Scholar 

  13. Chung, F.: Spectral Graph Theory. AMS (1997)

    Google Scholar 

  14. Lombaert, H., Grady, L., Polimeni, J.R., Cheriet, F.: Fast brain matching with spectral correspondence. In: Székely, G., Hahn, H.K. (eds.) IPMI 2011. LNCS, vol. 6801, pp. 660–673. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  15. Lombaert, H., Grady, L., Polimeni, J.R., Cheriet, F.: FOCUSR: Feature Oriented Correspondence using Spectral Regularization - A Method for Accurate Surface Matching. TPAMI (2012)

    Google Scholar 

  16. Reuter, M.: Hierarchical shape segmentation and registration via topological features of Laplace-Beltrami eigenfunctions. IJCV (2009)

    Google Scholar 

  17. Niethammer, M., Reuter, M., Wolter, F.-E., Bouix, S., Peinecke, N., Koo, M.-S., Shenton, M.E.: Global Medical Shape Analysis Using the Laplace-Beltrami Spectrum. In: Ayache, N., Ourselin, S., Maeder, A. (eds.) MICCAI 2007, Part I. LNCS, vol. 4791, pp. 850–857. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  18. Mateus, D., Horaud, R., Knossow, D., Cuzzolin, F., Boyer, E.: Articulated shape matching using Laplacian eigenfunctions and unsupervised registration. In: CVPR (2008)

    Google Scholar 

  19. Jain, V., Zhang, H.: Robust 3D shape correspondence in the spectral domain. In: CSMA (2006)

    Google Scholar 

  20. Grady, L., Polimeni, J.R.: Discrete Calculus: Applied Analysis on Graphs for Computational Science. Springer (2010)

    Google Scholar 

  21. Courant, R., Hilbert, D.: Methods of Mathematical Physics. Wiley (1989)

    Google Scholar 

  22. Tlusty, T.: A relation between the multiplicity of the second eigenvalue of a graph Laplacian, Courant’s nodal line theorem and the substantial dimension of tight polyhedral surfaces. Linear Algebra 16 (2010)

    Google Scholar 

  23. Colin de Verdiere, Y.: Multiplicités des valeurs propres. Laplaciens discrets et laplaciens continus. Rendiconti di Matematica 13(7) (1993)

    Google Scholar 

  24. Belkin, M., Niyogi, P.: Convergence of Laplacian eigenmaps. In: NIPS (2006)

    Google Scholar 

  25. Nielsen, M., Andresen, P.R.: Feature displacement interpolation. In: ICIP (1998)

    Google Scholar 

  26. Studholme, C., Cardenas, V.: A template free approach to volumetric spatial normalization of brain anatomy. Pattern Recogn. Lett. 25(10) (2004)

    Google Scholar 

  27. Zöllei, L., Learned-Miller, E., Grimson, W., Wells, W.: Efficient population registration of 3D data. In: Liu, Y., Jiang, T.-Z., Zhang, C. (eds.) CVBIA 2005. LNCS, vol. 3765, pp. 291–301. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  28. Guimond, A., Meunier, J., Thirion, J.P.: Average brain models: A convergence study. CVIU 77(2) (2000)

    Google Scholar 

  29. Christensen, G., Johnson, H.: Invertibility and transitivity analysis for nonrigid image registration. J. Elec. Im. 12(1) (2003)

    Google Scholar 

  30. Fischl, B., van der Kouwe, A., Destrieux, C., Halgren, E., Segonne, F., Salat, D.H., Busa, E., Seidman, L.J., Goldstein, J., Kennedy, D., Caviness, V., Makris, N., Rosen, B., Dale, A.M.: Automatically parcellating the human cerebral cortex. Cereb. Cortex 14(1) (2004)

    Google Scholar 

  31. Gold, S., Rangarajan, A.: A graduated assignment algorithm for graph matching. TPAMI 18(4) (1996)

    Google Scholar 

  32. Zheng, Y., Doermann, D.: Robust point matching for nonrigid shapes by preserving local neighborhood structures. TPAMI 28(4) (2006)

    Google Scholar 

  33. Ovsjanikov, M., Mérigot, Q., Mémoli, F., Guibas, L.: One point isometric matching with the heat kernel. Computer Graphics Forum 29(5) (2010)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre for Intelligent Machines, McGill University, Montreal, Canada

    Herve Lombaert, Jon Sporring & Kaleem Siddiqi

  2. eScience Center, Computer Science, University of Copenhagen, Denmark

    Jon Sporring

Authors
  1. Herve Lombaert
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jon Sporring
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kaleem Siddiqi
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Radiology, University of Pennsylvania, 3600 Market Street, 19104, Philadelphia, PA, USA

    James C. Gee  & Kilian M. Pohl  & 

  2. Department of Bioengineering, University of Utah, 72 S Central Campus Drive, 84112, Salt Lake City, UT, USA

    Sarang Joshi

  3. Department of Radiology, Harvard Medical School and Brigham and Women’s Hospital, 75 Francis Street, 02115, Boston, MA, USA

    William M. Wells

  4. A.A. Martinos Center for Biomedical Imaging, Harvard Medical School and Massachussetts General Hospital, 149 Thirteenth Street, 02129, Chalrestown, MA, USA

    Lilla Zöllei

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lombaert, H., Sporring, J., Siddiqi, K. (2013). Diffeomorphic Spectral Matching of Cortical Surfaces. In: Gee, J.C., Joshi, S., Pohl, K.M., Wells, W.M., Zöllei, L. (eds) Information Processing in Medical Imaging. IPMI 2013. Lecture Notes in Computer Science, vol 7917. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38868-2_32

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-38868-2_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38867-5

  • Online ISBN: 978-3-642-38868-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation