Simplified Reeb Graph as Effective Shape Descriptor for the Striatum

  • Antonietta Pepe
  • Laura Brandolini
  • Marco Piastra
  • Juha Koikkalainen
  • Jarmo Hietala
  • Jussi Tohka
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7599)

Abstract

In this work, we present a novel image and mesh processing pipeline for the computation of simplified Reeb graphs for closed triangle meshes of the human striatum extracted from 3D-T1 weighted MR images. The method uses active contours for computing the mesh partition and the simplified Reeb graph. Experimental results showed that simplified Reeb graphs, as obtained by our pipeline, provide an intrinsic, effective, and stable descriptor of striatal shapes to be used as an automatic tool for inter-subject mesh registration, mesh decomposition, and striatal shapes comparison. Particularly, the nodes of simplified Reeb graphs proved to be robust landmarks to guide the mesh registration. The quality of the inter-subject mesh registration obtained by the use of simplified Reeb graphs slightly outperformed the one obtained by surface-based registration techniques. In addition, we show the stability of the resulting mesh decomposition, and we propose its use as an automatic alternative to the manual sub-segmentation of the striatum. Finally we show some preliminary results on the inter-group comparisons among neuroleptic-naive schizophrenic patients and matched controls.

Keywords

Simplified Reeb Graph Surface Registration Mesh Decomposition Striatum Schizophrenia MRI 

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References

  1. 1.
    Lauer, M., Senitz, D., Beckmann, H.: Increased volume of the nucleus accumbens in schizophrenia. J. Neural Transmission 108, 645–660 (2001)CrossRefGoogle Scholar
  2. 2.
    Brickman, A., Buchsbaum, M., Shihabuddin, L., Hazlett, E., Borod, J., Mohs, R.: Striatal size, glucose metabolic rate, and verbal learning in normal aging. Cognitive Brain Res. 17(1), 106–116 (2003)CrossRefGoogle Scholar
  3. 3.
    Grahn, J., Parkinson, J., Owen, A.: The cognitive functions of the caudate nucleus. Prog. Neurobiol. 86(3), 141–155 (2008)CrossRefGoogle Scholar
  4. 4.
    Koikkalainen, J., Hirvonen, J., Nyman, M., Lötjönen, J., Hietala, J., Ruotsalainen, U.: Shape variability of the human striatum - effects of age and gender. NeuroImage 34(1), 85–93 (2007)CrossRefGoogle Scholar
  5. 5.
    Seger, C.: How do the basal ganglia contribute to categorization? their roles in generalization, response selection, and learning via feedback. Neurosci. Biobehav.l R. 32(2), 265–278 (2008)CrossRefGoogle Scholar
  6. 6.
    McCreadie, R., Srinivasan, T., Padmavati, R., Thara, R.: Extrapyramidal symptoms in unmedicated schizophrenia. J. Psychiat. Res. 39(3), 261–266 (2005)CrossRefGoogle Scholar
  7. 7.
    Buchsbaum, M.S., Shihabuddin, L., Brickman, A., Miozzo, R., Prikryl, R., Shaw, R., Davis, K.: Caudate and putamen volumes in good and poor outcome patients with schizophrenia. Schizophr. Res. 64(1), 53–62 (2003)CrossRefGoogle Scholar
  8. 8.
    Volz, H., Gaser, C., Sauer, H.: Supporting evidence for the model of cognitive dysmetria in schizophrenia - a structural magnetic resonance imaging study using deformation-based morphometry. Schizophr. Res. 46(1), 45–56 (2000)CrossRefGoogle Scholar
  9. 9.
    Reuter, M., Wolter, F., Shenton, M., Niethammer, M.: Laplace - beltrami eigenvalues and topological features of eigenfunctions for statistical shape analysis. Comput. Aided Design 41(10), 739–755 (2009)CrossRefGoogle Scholar
  10. 10.
    Pepe, A., Zhao, L., Tohka, J., Koikkalainen, J., Hietala, J., Ruotsalainen, U.: Automatic statistical shape analysis of local cerebral asymmetry in 3d t1-weighted magnetic resonance images. In: Paulsen, R.R., Levine, J.A. (eds.) Proc. of MICCAI 2011 MedMesh Workshop, pp. 127–134 (2011)Google Scholar
  11. 11.
    Vetsa, Y.S.K., Styner, M., Pizer, S.M., Lieberman, J.A., Gerig, G.: Caudate Shape Discrimination in Schizophrenia Using Template-Free Non-parametric Tests. In: Ellis, R.E., Peters, T.M. (eds.) MICCAI 2003, Part II. LNCS, vol. 2879, pp. 661–669. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  12. 12.
    Hwang, J., Lyoo, I., Dager, S., Friedman, S., Oh, J., Lee, J.Y., Kim, S., Dunner, D., Renshaw, P.: Basal ganglia shape alterations in bipolar disorder. Am. J. Psychiatry 163(2), 276–285 (2006)CrossRefGoogle Scholar
  13. 13.
    Shapira, L., Shamir, A., Cohen-Or, D.: Consistent mesh partitioning and skeletonization using the shape diameter function. Visual Comput. 24, 249–259 (2008)CrossRefGoogle Scholar
  14. 14.
    Shi, Y., Lai, R., Krishna, S., Dinov, I., Toga, A.: Anisotropic laplace-beltrami eigenmaps: Bridging reeb graphs and skeletons. In: Proc. of CVPR 2008 Workshop, Anchorage, AK, USA, pp. 1–7. IEEE Computer Society Press (2008)Google Scholar
  15. 15.
    Reeb, G.: Sur les points singuliers d une forme de pfaff completement integrable ou d une fonction numerique. Comptes rendus de l’Academie des Sciences 222, 847–849 (1946)Google Scholar
  16. 16.
    Milnor, J.: Morse theory, vol. 51. Princeton Univ Pr. (1963)Google Scholar
  17. 17.
    Banchoff, T.: Critical points and curvature for embedded polyhedral surfaces. T. Am. Math. Mon. 77(5), 475–485 (1970)MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Biasotti, S., Giorgi, D., Spagnuolo, M., Falcidieno, B.: Reeb graphs for shape analysis and applications. Theor. Comput. Sci. 392, 5–22 (2008)MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Cole-McLaughlin, K., Edelsbrunner, H., Harer, J., Natarajan, V., Pascucci, V.: Loops in reeb graphs of 2-manifolds. In: Proc. of the 19th SoCG, SCG 2003, pp. 344–350. ACM, New York (2003)Google Scholar
  20. 20.
    Shinagawa, Y., Kunii, T., Kergosien, Y.: Surface coding based on morse theory. IEEE Comput. Graph. Appl. 11, 66–78 (1991)CrossRefGoogle Scholar
  21. 21.
    Shinagawa, Y., Kunii, T.: Constructing a reeb graph automatically from cross sections. IEEE CG&A 11, 44–51 (1991)Google Scholar
  22. 22.
    Lazarus, F., Verroust, A.: Level set diagrams of polyhedral objects. In: Proc. of the 5th Symposium on Solid Modeling, pp. 130–140. ACM (1999)Google Scholar
  23. 23.
    Tierny, J., Vandeborre, J., Daoudi, M.: 3d mesh skeleton extraction using topological and geometrical analyses. In: Proc. of the 14th Pacific Graphics 2006, Taipei, Taiwan, pp. 85–94 (2006)Google Scholar
  24. 24.
    Pascucci, V., Scorzelli, G., Bremer, P.-T., Mascarenhas, A.: Robust on-line computation of reeb graphs: simplicity and speed. ACM Trans. Graph. 26 (July 2007)Google Scholar
  25. 25.
    Doraiswamy, H., Natarajan, V.: Efficient algorithms for computing reeb graphs. Comp. Geom. 42(6-7), 606–616 (2009)MATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Berretti, S., Del Bimbo, A., Pala, P.: 3d mesh decomposition using reeb graphs. Image Vision Comput. 27(10), 1540–1554 (2009); Special Section: Computer Vision Methods for Ambient IntelligenceCrossRefGoogle Scholar
  27. 27.
    Patane, G., Spagnuolo, M., Falcidieno, B.: A minimal contouring approach to the computation of the reeb graph. IEEE TVCG 15, 583–595 (2009)Google Scholar
  28. 28.
    Brandolini, L., Piastra, M.: Computing the reeb graph for triangle meshes with active contours. In: Proc. of ICPRAM 2012, vol. 2, pp. 80–89. SciTePress (2012)Google Scholar
  29. 29.
    Fischl, B., Salat, D., Busa, E., Albert, M., Dieterich, M., Haselgrove, C., van der Kouwe, A., Killiany, R., Kennedy, D., Klaveness, S., Montillo, A., Makris, N., Rosen, B., Dale, A.: Whole brain segmentation: automated labeling of neuroanatomical structures in the human brain. Neuron. 33, 341–355 (2002)CrossRefGoogle Scholar
  30. 30.
    Ben Hamza, A., Krim, H.: Geodesic Object Representation and Recognition. In: Nyström, I., Sanniti di Baja, G., Svensson, S. (eds.) DGCI 2003. LNCS, vol. 2886, pp. 378–387. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  31. 31.
    Ni, X., Garland, M., Hart, J.: Fair morse functions for extracting the topological structure of a surface mesh. ACM Trans. Graph. 23, 613–622 (2004)CrossRefGoogle Scholar
  32. 32.
    Novotni, M., Klein, R.: Computing geodesic distances on triangular meshes. In: Proc. of WSCG 2002, pp. 341–347 (2002)Google Scholar
  33. 33.
    Dijkstra, E.: A note on two problems in connexion with graphs. Numer. Math. 1, 269–271 (1959)MATHCrossRefMathSciNetGoogle Scholar
  34. 34.
    Laakso, M., Tiihonen, J., Syvälahti, E., Vilkman, H., Laakso, A., Alakare, B., Räkköläinen, V., Salokangas, R., Koivisto, E., Hietala, J.: A morphometric mri study of the hippocampus in first-episode, neuroleptic-naïve schizophrenia. Schizophr. Res. 50(1-2), 3–7 (2001)CrossRefGoogle Scholar
  35. 35.
    Lötjönen, J., Reissman, P.-J., Magnin, I., Katila, T.: Model extraction from magnetic resonance volume data using the deformable pyramid. Med. Image Anal. 3(4), 387–406 (1999)CrossRefGoogle Scholar
  36. 36.
    Kendall, D.G.: A survey of the statistical theory of shape. Statist. Sci. 4(2), 87–99 (1989)MATHCrossRefMathSciNetGoogle Scholar
  37. 37.
    Arun, K., Huang, T., Blostein, S.: Least-squares fitting of two 3-d point sets. IEEE Trans. Pattern. Anal. Mach. Intell. 9(5), 698–700 (1987)CrossRefGoogle Scholar
  38. 38.
    Huttenlocher, D., Klanderman, G., Rucklidge, W.: Comparing images using the hausdorff distance. IEEE Trans. Pattern Anal. Mach. Intell. 15, 850–863 (1993)CrossRefGoogle Scholar
  39. 39.
    Arun, K., Huang, T., Blostein, S.: Closed-form solution of absolute orientation using unit quaternions. J. Opt. Soc. Am. A. 4(4), 629–642 (1987)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Antonietta Pepe
    • 1
  • Laura Brandolini
    • 2
  • Marco Piastra
    • 2
  • Juha Koikkalainen
    • 3
  • Jarmo Hietala
    • 4
    • 5
  • Jussi Tohka
    • 1
  1. 1.Tampere University of TechnologyTampereFinland
  2. 2.Universitá di PaviaPaviaItaly
  3. 3.VTT Technical Research Centre of FinlandTampereFinland
  4. 4.University of TurkuTurkuFinland
  5. 5.Turku PET CentreFinland

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