Abstract
The human brain may be considered as a genus-0 shape, topologically equivalent to a sphere. Various methods have been used in the past to transform the brain surface to that of a sphere using harmonic energy minimization methods used for cortical surface matching. However, very few methods have studied volumetric parameterization of the brain using a spherical embedding. Volumetric parameterization is typically used for complicated geometric problems like shape matching, morphing and isogeometric analysis. Using conformal mapping techniques, we can establish a bijective mapping between the brain and the topologically equivalent sphere. Our hypothesis is that shape analysis problems are simplified when the shape is defined in an intrinsic coordinate system. Our goal is to establish such a coordinate system for the brain. The efficacy of the method is demonstrated with a white matter clustering problem. Initial results show promise for future investigation in these parameterization technique and its application to other problems related to computational anatomy like registration and segmentation.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Floater, M.S., Hormann, K.: Surface parameterization: a tutorial and survey. In: Dodgson, N., Floater, M.S., Sabin, M. (eds.) Advances in Multiresolution for Geometric Modelling, vol. 1(1), pp. 157–186. Springer, Heidelberg (2005)
Gupta, V., Voruganti, H.K., Dasgupta, B.: Domain mapping for volumetric parameterization using harmonic functions. Comput. Aided Des. Appl. 11(4), 426–435 (2014)
Gu, X., Wang, Y., Chan, T.F., Thompson, P.M., Yau, S.-T.: Genus zero surface conformal mapping and its application to brain surface mapping. IEEE Trans. Med. Imaging 23(8), 949–958 (2004)
Wang, Y., Gu, X., Chan, T.F., Thompson, P.M., Yau, S.-T.: Brain surface conformal parameterization with algebraic functions. In: Larsen, R., Nielsen, M., Sporring, J. (eds.) MICCAI 2006. LNCS, vol. 4191, pp. 946–954. Springer, Heidelberg (2006). doi:10.1007/11866763_116
Wang, Y., Shi, J., Yin, X., Gu, X., Chan, T.F., Yau, S.-T., Toga, A.W., Thompson, P.M.: Brain surface conformal parameterization with the Ricci flow. IEEE Trans. Med. Imaging 31(2), 251–264 (2012)
Mémoli, F., Sapiro, G., Osher, S.: Solving variational problems and partial differential equations mapping into general target manifolds. J. Comput. Phys. 195(1), 263–292 (2004)
Gutman, B.A., Madsen, S.K., Toga, A.W., Thompson, P.M.: A family of fast spherical registration algorithms for cortical shapes. In: Shen, L., Liu, T., Yap, P.-T., Huang, H., Shen, D., Westin, C.-F. (eds.) MBIA 2013. LNCS, vol. 8159, pp. 246–257. Springer, Heidelberg (2013). doi:10.1007/978-3-319-02126-3_24
Shi, Y., Lai, R., Toga, A.W.: Conformal mapping via metric optimization with application for cortical label fusion. In: Gee, J.C., Joshi, S., Pohl, K.M., Wells, W.M., Zöllei, L. (eds.) IPMI 2013. LNCS, vol. 7917, pp. 244–255. Springer, Heidelberg (2013). doi:10.1007/978-3-642-38868-2_21
Lombaert, H., Arcaro, M., Ayache, N.: Brain transfer: spectral analysis of cortical surfaces and functional maps. In: Ourselin, S., Alexander, D.C., Westin, C.-F., Cardoso, M.J. (eds.) IPMI 2015. LNCS, vol. 9123, pp. 474–487. Springer, Heidelberg (2015). doi:10.1007/978-3-319-19992-4_37
Wang, Y., Gu, X., Chan, T.F., Thompson, P.M., Yau, S.T.: Volumetric harmonic brain mapping. In: IEEE International Symposium on Biomedical Imaging: Nano to Macro, pp. 1275–1278. IEEE (2004)
O’Donnell, L., Kubicki, M., Shenton, M.E., Dreusicke, M.H., Grimson, W.E.L., Westin, C.F.: A method for clustering white matter fiber tracts. Am. J. Neuroradiol. 27(5), 1032–1036 (2006)
Corouge, I., Gouttard, S., Gerig, G.: Towards a shape model of white matter fiber bundles using diffusion tensor MRI. In: IEEE International Symposium on Biomedical Imaging: Nano to Macro. pp. 344–347. IEEE (2004)
Liu, M., Vemuri, B.C., Deriche, R.: Unsupervised automatic white matter fiber clustering using a Gaussian mixture model. In: 2012 9th IEEE International Symposium on Biomedical Imaging (ISBI), pp. 522–525. IEEE (2012)
Guevara, P., Poupon, C., Rivière, D., Cointepas, Y., Descoteaux, M., Thirion, B., Mangin, J.F.: Robust clustering of massive tractography datasets. NeuroImage 54(3), 1975–1993 (2011)
Cook, P., Bai, Y., Nedjati-Gilani, S., Seunarine, K., Hall, M., Parker, G., Alexander, D.: Camino: open-source diffusion-MRI reconstruction and processing. In: 14th Scientific Meeting of the International Society for Magnetic Resonance in Medicine, Seattle, WA, USA, vol. 2759 (2006)
Parker, G.J.M., Alexander, D.C.: Probabilistic Monte Carlo based mapping of cerebral connections utilising whole-brain crossing fibre information. In: Taylor, C., Noble, J.A. (eds.) IPMI 2003. LNCS, vol. 2732, pp. 684–695. Springer, Heidelberg (2003). doi:10.1007/978-3-540-45087-0_57
Oishi, K., Faria, A., Jiang, H., Li, X., Akhter, K., Zhang, J., Hsu, J.T., Miller, M.I., van Zijl, P.C., Albert, M., Lyketsos, C.G., Woods, R., Toga, A.W., Pike, G.B., Rosa-Neto, P., Evans, A., Mazziotta, J., Mori, S.: Atlas-based whole brain white matter analysis using large deformation diffeomorphic metric mapping: application to normal elderly and Alzheimer’s disease participants. NeuroImage 46(2), 486–499 (2009)
Zhang, Y., Zhang, J., Oishi, K., Faria, A.V., Jiang, H., Li, X., Akhter, K., Rosa-Neto, P., Pike, G.B., Evans, A., et al.: Atlas-guided tract reconstruction for automated and comprehensive examination of the white matter anatomy. NeuroImage 52(4), 1289–1301 (2010)
Avants, B.B., Epstein, C.L., Grossman, M., Gee, J.C.: Symmetric diffeomorphic image registration with cross-correlation: evaluating automated labeling of elderly and neurodegenerative brain. Med. Image Anal. 12(1), 26–41 (2008)
O’Donnell, L.J., Westin, C.F.: Automatic tractography segmentation using a high-dimensional white matter atlas. IEEE Trans. Med. Imaging 26(11), 1562–1575 (2007)
Jin, Y., Shi, Y., Zhan, L., Gutman, B.A., de Zubicaray, G.I., McMahon, K.L., Wright, M.J., Toga, A.W., Thompson, P.M.: Automatic clustering of white matter fibers in brain diffusion MRI with an application to genetics. NeuroImage 100, 75–90 (2014)
Filippone, M., Camastra, F., Masulli, F., Rovetta, S.: A survey of kernel and spectral methods for clustering. Pattern Recogn. 41(1), 176–190 (2008)
Von Luxburg, U.: A tutorial on spectral clustering. Stat. Comput. 17(4), 395–416 (2007)
Acknowledgements
This study was supported in part by a Consortium grant (U54 EB020403) from the NIH Institutes contributing to the Big Data to Knowledge (BD2K) Initiative, including the NIBIB. The authors are also thankful to Dr. Ratnesh Kumar from Teradeep Inc., Sunnyvale (California) for valuable insights and suggestions.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this paper
Cite this paper
Gupta, V., Prasad, G., Thompson, P. (2016). A Volumetric Conformal Mapping Approach for Clustering White Matter Fibers in the Brain. In: Reuter, M., Wachinger, C., Lombaert, H. (eds) Spectral and Shape Analysis in Medical Imaging. SeSAMI 2016. Lecture Notes in Computer Science(), vol 10126. Springer, Cham. https://doi.org/10.1007/978-3-319-51237-2_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-51237-2_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-51236-5
Online ISBN: 978-3-319-51237-2
eBook Packages: Computer ScienceComputer Science (R0)