Abstract
This paper describes a method based on metric structures for anatomical analysis on a large set of brain MR images. A geodesic distance between each pair was measured using large deformation diffeomorphic metric mapping (LDDMM). Manifold learning approaches were applied to seek a low-dimensional embedding in the high- dimensional shape space, in which inference between healthy control and disease groups can be done using standard classification algorithms. In particular, the proposed method was evaluated on ADNI, a dataset for Alzheimer’s disease study. Our work demonstrates that the high-dimensional anatomical shape space of the amygdala and hippocampi can be approximated by a relatively low dimension manifold.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Grenander, U., Miller, M.: Computational anatomy: An emerging discipline. Quarterly of Applied Mathematics 56(4), 617–694 (1998)
Beg, M., Miller, M., Trouvé, A., Younes, L.: Computing large deformation metric mappings via geodesic flows of diffeomorphisms. International Journal of Computer Vision 61(2), 139–157 (2005)
Mueller, S., Weiner, M., Thal, L., Petersen, R., Jack, C., Jagust, W., Trojanowski, J., Toga, A., Beckett, L.: The Alzheimers disease neuroimaging initiative. Neuroimaging Clinics of North America 15(4), 869 (2005)
Park, H.: Isomap induced manifold embedding and its application to Alzheimer’s disease and mild cognitive impairment. Neuroscience Letters (2012)
Gray, K.R., Aljabar, P., Heckemann, R.A., Hammers, A., Rueckert, D.: Random forest-based manifold learning for classification of imaging data in dementia. In: Suzuki, K., Wang, F., Shen, D., Yan, P. (eds.) MLMI 2011. LNCS, vol. 7009, pp. 159–166. Springer, Heidelberg (2011)
Gray, K., Aljabar, P., Heckemann, R., Hammers, A., Rueckert, D.: Random forest-based similarity measures for multi-modal classification of Alzheimer’s disease. NeuroImage (2012)
Wolz, R., Aljabar, P., Hajnal, J., Lötjönen, J., Rueckert, D.: Nonlinear dimensionality reduction combining mr imaging with non-imaging information. Medical Image Analysis (2011)
Yang, X., Goh, A., Qiu, A.: Approximations of the diffeomorphic metric and their applications in shape learning. In: Székely, G., Hahn, H.K. (eds.) IPMI 2011. LNCS, vol. 6801, pp. 257–270. Springer, Heidelberg (2011)
Gerber, S., Tasdizen, T., Fletcher, P., Joshi, S., Whitaker, R.: Manifold modeling for brain population analysis. Medical Image Analysis 14(5), 643 (2010)
Miller, M., Priebe, C., Qiu, A., Fischl, B., Kolasny, A., Brown, T., Park, Y., Ratnanather, J., Busa, E., Jovicich, J., et al.: Collaborative computational anatomy: an mri morphometry study of the human brain via diffeomorphic metric mapping. Human Brain Mapping 30(7), 2132–2141 (2008)
Qiu, A., Miller, M.I., et al.: Multi-structure network shape analysis via normal surface momentum maps. NeuroImage 42(4), 1430 (2008)
Fischl, B., Salat, D., Busa, E., Albert, M., Dieterich, M., Haselgrove, C., van der Kouwe, A., Killiany, R., Kennedy, D., Klaveness, S., et al.: Whole brain segmentation: automated labeling of neuroanatomical structures in the human brain. Neuron 33(3), 341–355 (2002)
Khan, A.R., Wang, L., Beg, M.F.: Freesurfer-initiated fully-automated subcortical brain segmentation in mri using large deformation diffeomorphic metric mapping. NeuroImage 41(3), 735 (2008)
Vaillant, M., Qiu, A., Glaunès, J., Miller, M.: Diffeomorphic metric surface mapping in subregion of the superior temporal gyrus. NeuroImage 34(3), 1149–1159 (2007)
Vaillant, M., Glaunès, J.: Surface matching via currents. In: Christensen, G.E., Sonka, M. (eds.) IPMI 2005. LNCS, vol. 3565, pp. 381–392. Springer, Heidelberg (2005)
Trosset, M.W., Priebe, C.E., Park, Y., Miller, M.I.: Semisupervised learning from dissimilarity data. Computational Statistics & Data Analysis 52(10), 4643–4657 (2008)
Tenenbaum, J., De Silva, V., Langford, J.: A global geometric framework for nonlinear dimensionality reduction. Science 290(5500), 2319–2323 (2000)
Belkin, M., Niyogi, P.: Laplacian eigenmaps and spectral techniques for embedding and clustering. In: Advances in Neural Information Processing Systems, vol. 14, pp. 585–591 (2001)
Chang, C.C., Lin, C.J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2, 27:1–27:27 (2011), Software available at http://www.csie.ntu.edu.tw/~cjlin/libsvm
Liaw, A., Wiener, M.: Classification and regression by randomforest. R News 2(3), 18–22 (2002)
Miller, M., Trouvé, A., Younes, L.: Geodesic shooting for computational anatomy. Journal of Mathematical Imaging and Vision 24(2), 209–228 (2006)
Vaillant, M., Miller, M.I., Younes, L., Trouvé, A., et al.: Statistics on diffeomorphisms via tangent space representations. NeuroImage 23(1), 161 (2004)
Wang, L., Beg, F., Ratnanather, T., Ceritoglu, C., Younes, L., Morris, J.C., Csernansky, J.G., Miller, M.I.: Large deformation diffeomorphism and momentum based hippocampal shape discrimination in dementia of the Alzheimer type. IEEE Transactions on Medical Imaging 26(4), 462–470 (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this paper
Cite this paper
Feng, J., Tang, X., Tang, M., Priebe, C., Miller, M. (2013). Metric Space Structures for Computational Anatomy. In: Wu, G., Zhang, D., Shen, D., Yan, P., Suzuki, K., Wang, F. (eds) Machine Learning in Medical Imaging. MLMI 2013. Lecture Notes in Computer Science, vol 8184. Springer, Cham. https://doi.org/10.1007/978-3-319-02267-3_16
Download citation
DOI: https://doi.org/10.1007/978-3-319-02267-3_16
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02266-6
Online ISBN: 978-3-319-02267-3
eBook Packages: Computer ScienceComputer Science (R0)