Template Estimation for Large Database: A Diffeomorphic Iterative Centroid Method Using Currents

  • Claire Cury
  • Joan A. Glaunès
  • Olivier Colliot
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8085)

Abstract

Computing a template in the Large Deformation Diffeomorphic Metric Mapping framework is a key step for the shape analysis of anatomical structures, but can lead to very computationally expensive algorithms in the case of large databases. We present an iterative method which quickly provides a centroid of the population in shape space. This centroid can be used as a rough template estimate or as initialization for template estimation methods.

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References

  1. 1.
    Grenander, U., Miller, M.I.: Computational anatomy: An emerging discipline. Quarterly of Applied Mathematics 56(4), 617–694 (1998)MathSciNetMATHGoogle Scholar
  2. 2.
    Christensen, G.E., Rabbitt, R.D., Miller, M.I.: Deformable templates using large deformation kinematics. IEEE Transactions on Image Processing 5(10), 1435–1447 (1996)CrossRefGoogle Scholar
  3. 3.
    Beg, M.F., Miller, M.I., Trouvé, A., Younes, L.: Computing large deformation metric mappings via geodesic flows of diffeomorphisms. International Journal of Computer Vision 61(2), 139–157 (2005)CrossRefGoogle Scholar
  4. 4.
    Ma, J., Miller, M.I., Trouvé, A., Younes, L.: Bayesian template estimation in computational anatomy. NeuroImage 42(1), 252–261 (2008)CrossRefGoogle Scholar
  5. 5.
    Glaunès, J., Joshi, S.: Template estimation from unlabeled point set data and surfaces for computational anatomy. In: Pennec, X., Joshi, S. (eds.) Proc. of the International Workshop on the Mathematical Foundations of Computational Anatomy (MFCA 2006), pp. 29–39 (October 1, 2006)Google Scholar
  6. 6.
    Durrleman, S., Pennec, X., Trouvé, A., Ayache, N., et al.: A forward model to build unbiased atlases from curves and surfaces. In: 2nd Medical Image Computing and Computer Assisted Intervention. Workshop on Mathematical Foundations of Computational Anatomy, pp. 68–79 (2008)Google Scholar
  7. 7.
    Durrleman, S., Prastawa, M., Korenberg, J.R., Joshi, S., Trouvé, A., Gerig, G.: Topology preserving atlas construction from shape data without correspondence using sparse parameters. In: Ayache, N., Delingette, H., Golland, P., Mori, K. (eds.) MICCAI 2012, Part III. LNCS, vol. 7512, pp. 223–230. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  8. 8.
    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)CrossRefGoogle Scholar
  9. 9.
    Glaunes, J.: Transport par difféomorphismes de points, de mesures et de courants pour la comparaison de formes et l’anatomie numérique. PhD thesis, Université Paris 13 (2005)Google Scholar
  10. 10.
    Yang, X., Goh, A., Qiu, A.: Approximations of the diffeomorphic metric and their applications in shape learning. In: Székely, G., Hahn, H.K. (eds.) IPMI 2011. LNCS, vol. 6801, pp. 257–270. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  11. 11.
    Tenenbaum, J., Silva, V., Langford, J.: A global geometric framework for nonlinear dimensionality reduction. Science 290(5500), 2319–2323 (2000)CrossRefGoogle Scholar
  12. 12.
    Arnaudon, M., Nielsen, F.: On approximating the riemannian 1-center. Computational Geometry 46(1), 93–104 (2013)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Chupin, M., Hammers, A., Liu, R.S.N., Colliot, O., Burdett, J., Bardinet, E., Duncan, J.S., Garnero, L., Lemieux, L.: Automatic segmentation of the hippocampus and the amygdala driven by hybrid constraints: Method and validation. NeuroImage 46(3), 749–761 (2009)CrossRefGoogle Scholar
  14. 14.
    Durrleman, S., Pennec, X., Trouvé, A., Ayache, N.: Statistical models of sets of curves and surfaces based on currents. Medical Image Analysis 13(5), 793–808 (2009)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Claire Cury
    • 1
    • 2
    • 3
    • 4
  • Joan A. Glaunès
    • 5
  • Olivier Colliot
    • 1
    • 2
    • 3
    • 4
  1. 1.Centre de Recherche de l’Institut du Cerveau et de la Moëlle épinièreUniversité Pierre et Marie Curie-Paris 6ParisFrance
  2. 2.UMR-S975, CNRS, UMR 7225InsermParisFrance
  3. 3.ICM – Institut du Cerveau et de la Moëlle épinièreParisFrance
  4. 4.Aramis Project-TeamInria Paris-RocquencourtParisFrance
  5. 5.MAP5Université Paris DescartesSorbonne Paris CitéFrance

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