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.
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References
Lauer, M., Senitz, D., Beckmann, H.: Increased volume of the nucleus accumbens in schizophrenia. J. Neural Transmission 108, 645–660 (2001)
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)
Grahn, J., Parkinson, J., Owen, A.: The cognitive functions of the caudate nucleus. Prog. Neurobiol. 86(3), 141–155 (2008)
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)
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)
McCreadie, R., Srinivasan, T., Padmavati, R., Thara, R.: Extrapyramidal symptoms in unmedicated schizophrenia. J. Psychiat. Res. 39(3), 261–266 (2005)
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)
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)
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)
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)
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)
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)
Shapira, L., Shamir, A., Cohen-Or, D.: Consistent mesh partitioning and skeletonization using the shape diameter function. Visual Comput. 24, 249–259 (2008)
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)
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)
Milnor, J.: Morse theory, vol. 51. Princeton Univ Pr. (1963)
Banchoff, T.: Critical points and curvature for embedded polyhedral surfaces. T. Am. Math. Mon. 77(5), 475–485 (1970)
Biasotti, S., Giorgi, D., Spagnuolo, M., Falcidieno, B.: Reeb graphs for shape analysis and applications. Theor. Comput. Sci. 392, 5–22 (2008)
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)
Shinagawa, Y., Kunii, T., Kergosien, Y.: Surface coding based on morse theory. IEEE Comput. Graph. Appl. 11, 66–78 (1991)
Shinagawa, Y., Kunii, T.: Constructing a reeb graph automatically from cross sections. IEEE CG&A 11, 44–51 (1991)
Lazarus, F., Verroust, A.: Level set diagrams of polyhedral objects. In: Proc. of the 5th Symposium on Solid Modeling, pp. 130–140. ACM (1999)
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)
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)
Doraiswamy, H., Natarajan, V.: Efficient algorithms for computing reeb graphs. Comp. Geom. 42(6-7), 606–616 (2009)
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
Patane, G., Spagnuolo, M., Falcidieno, B.: A minimal contouring approach to the computation of the reeb graph. IEEE TVCG 15, 583–595 (2009)
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)
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)
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)
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)
Novotni, M., Klein, R.: Computing geodesic distances on triangular meshes. In: Proc. of WSCG 2002, pp. 341–347 (2002)
Dijkstra, E.: A note on two problems in connexion with graphs. Numer. Math. 1, 269–271 (1959)
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)
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)
Kendall, D.G.: A survey of the statistical theory of shape. Statist. Sci. 4(2), 87–99 (1989)
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)
Huttenlocher, D., Klanderman, G., Rucklidge, W.: Comparing images using the hausdorff distance. IEEE Trans. Pattern Anal. Mach. Intell. 15, 850–863 (1993)
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)
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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
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DOI: https://doi.org/10.1007/978-3-642-33463-4_14
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