Skip to main content

Simplified Reeb Graph as Effective Shape Descriptor for the Striatum

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNIP,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.

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

Buying options

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   49.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Lauer, M., Senitz, D., Beckmann, H.: Increased volume of the nucleus accumbens in schizophrenia. J. Neural Transmission 108, 645–660 (2001)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  3. Grahn, J., Parkinson, J., Owen, A.: The cognitive functions of the caudate nucleus. Prog. Neurobiol. 86(3), 141–155 (2008)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  6. McCreadie, R., Srinivasan, T., Padmavati, R., Thara, R.: Extrapyramidal symptoms in unmedicated schizophrenia. J. Psychiat. Res. 39(3), 261–266 (2005)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  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)

    Article  Google Scholar 

  13. Shapira, L., Shamir, A., Cohen-Or, D.: Consistent mesh partitioning and skeletonization using the shape diameter function. Visual Comput. 24, 249–259 (2008)

    Article  Google Scholar 

  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. 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. Milnor, J.: Morse theory, vol. 51. Princeton Univ Pr. (1963)

    Google Scholar 

  17. Banchoff, T.: Critical points and curvature for embedded polyhedral surfaces. T. Am. Math. Mon. 77(5), 475–485 (1970)

    Article  MATH  MathSciNet  Google Scholar 

  18. Biasotti, S., Giorgi, D., Spagnuolo, M., Falcidieno, B.: Reeb graphs for shape analysis and applications. Theor. Comput. Sci. 392, 5–22 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  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. Shinagawa, Y., Kunii, T., Kergosien, Y.: Surface coding based on morse theory. IEEE Comput. Graph. Appl. 11, 66–78 (1991)

    Article  Google Scholar 

  21. Shinagawa, Y., Kunii, T.: Constructing a reeb graph automatically from cross sections. IEEE CG&A 11, 44–51 (1991)

    Google Scholar 

  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. 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. 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. Doraiswamy, H., Natarajan, V.: Efficient algorithms for computing reeb graphs. Comp. Geom. 42(6-7), 606–616 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  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 Intelligence

    Article  Google Scholar 

  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. 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. 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)

    Article  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Article  Google Scholar 

  32. Novotni, M., Klein, R.: Computing geodesic distances on triangular meshes. In: Proc. of WSCG 2002, pp. 341–347 (2002)

    Google Scholar 

  33. Dijkstra, E.: A note on two problems in connexion with graphs. Numer. Math. 1, 269–271 (1959)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  36. Kendall, D.G.: A survey of the statistical theory of shape. Statist. Sci. 4(2), 87–99 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  38. Huttenlocher, D., Klanderman, G., Rucklidge, W.: Comparing images using the hausdorff distance. IEEE Trans. Pattern Anal. Mach. Intell. 15, 850–863 (1993)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Pepe, A., Brandolini, L., Piastra, M., Koikkalainen, J., Hietala, J., Tohka, J. (2012). Simplified Reeb Graph as Effective Shape Descriptor for the Striatum. In: Levine, J.A., Paulsen, R.R., Zhang, Y. (eds) Mesh Processing in Medical Image Analysis 2012. MeshMed 2012. Lecture Notes in Computer Science, vol 7599. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33463-4_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-33463-4_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33462-7

  • Online ISBN: 978-3-642-33463-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics