Shape Preservation Based on Gaussian Radial Basis Function Interpolation on Human Corpus Callosum

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10126)


The Corpus Callosum (CC) has been a structure of much interest in neuroimaging studies of normal brain development, schizophrenia, autism, bipolar and unipolar disorder. In this paper, we present a technique which allows us to develop a shape preservation methodology in the deformation of CC for further global and regional shape analyzes between two sample corpora callosa. Source and target CC are superpositioned individually from eleven anchor points. Source CC is deformed in order to get superpositioned onto the target CC from these anchor points and superposition operation leads other anatomical landmarks to get placed automatically in all of the regions of source CC for further deformation analysis. Region construction via quadratic Bézier curves, deformation by using Gaussian RBF and quantifying the amount of deformation via generalized Procrustes analysis are used to infer the proper parameters used in minimum deformation. Amount of deformation can be analyzed both regionally and globally.


Shape preserving interpolation Radial Basis Functions Space deformation 


  1. 1.
    Ben-Chen, M., Weber, O., Gotsman, C.: Variational harmonic maps for space deformation. ACM Trans. Graph. (TOG) 28, 34 (2009)CrossRefGoogle Scholar
  2. 2.
    Botsch, M., Kobbelt, L.: Real-time shape editing using radial basis functions. In: Computer Graphics Forum, vol. 24, pp. 611–621. Wiley Online Library (2005)Google Scholar
  3. 3.
    Botsch, M., Pauly, M., Wicke, M., Gross, M.: Adaptive space deformations based on rigid cells. In: Computer Graphics Forum, vol. 26, pp. 339–347. Wiley Online Library (2007)Google Scholar
  4. 4.
    Igarashi, T., Moscovich, T., Hughes, J.F.: As-rigid-as-possible shape manipulation. ACM Trans. Graph. (TOG) 24, 1134–1141 (2005)CrossRefGoogle Scholar
  5. 5.
    Joshi, P., Meyer, M., DeRose, T., Green, B., Sanocki, T.: Harmonic coordinates for character articulation. ACM Trans. Graph. (TOG) 26, 71 (2007)CrossRefGoogle Scholar
  6. 6.
    Levi, Z., Levin, D.: Shape deformation via interior RBF. IEEE Trans. Vis. Comput. Graph. 20(7), 1062–1075 (2014)CrossRefGoogle Scholar
  7. 7.
    Lewis, J.P., Cordner, M., Fong, N.: Pose space deformation: a unified approach to shape interpolation and skeleton-driven deformation. In: Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques, pp. 165–172. ACM Press/Addison-Wesley Publishing Co. (2000)Google Scholar
  8. 8.
    Lipman, Y., Kopf, J., Cohen-Or, D., Levin, D.: GPU-assisted positive mean value coordinates for mesh deformations. In: Symposium on Geometry Processing (2007)Google Scholar
  9. 9.
    Lipman, Y., Levin, D., Cohen-Or, D.: Green coordinates. ACM Trans. Graph. (TOG) 27, 78 (2008)CrossRefGoogle Scholar
  10. 10.
    MacCracken, R., Joy, K.I.: Free-form deformations with lattices of arbitrary topology. In: Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques, pp. 181–188. ACM (1996)Google Scholar
  11. 11.
    Schaefer, S., McPhail, T., Warren, J.: Image deformation using moving least squares. ACM Trans. Graph. (TOG) 25, 533–540 (2006)CrossRefGoogle Scholar
  12. 12.
    Sederberg, T.W., Parry, S.R.: Free-form deformation of solid geometric models. ACM SIGGRAPH Comput. Graph. 20(4), 151–160 (1986)CrossRefGoogle Scholar
  13. 13.
    Sumner, R.W., Schmid, J., Pauly, M.: Embedded deformation for shape manipulation. ACM Trans. Graph. (TOG) 26, 80 (2007)CrossRefGoogle Scholar
  14. 14.
    Weber, O., Ben-Chen, M., Gotsman, C.: Complex barycentric coordinates with applications to planar shape deformation. In: Computer Graphics Forum, vol. 28, pp. 587–597. Wiley Online Library (2009)Google Scholar
  15. 15.
    Witelson, S.F.: Hand and sex differences in the isthmus and genu of the human corpus callosum. Brain 112(3), 799–835 (1989)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Informatics Institute, METUAnkaraTurkey

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