Abstract
We present a Bayesian probabilistic model to estimate the atlas of the brain white matter characterized by orientation distribution functions (ODFs) derived from HARDI. We employ the framework of large deformation diffeomorphic metric mapping and assume that the HARDI atlas is generated from a known hyperatlas through a flow of diffeomorphisms. We represent the shape prior of the HARDI atlas and the diffeomorphic transformation of individual observations relative to the atlas using centered Gaussian random fields (GRF). We then assume that the observed ODFs are generated by an exponential map of random tangent vectors at the deformed atlas ODF and model the likelihood of the ODFs using a GRF of their tangent vectors in the ODF Riemannian manifold. We solve for the maximum a posteriori using the Expectation-Maximization (EM) algorithm. We illustrate the HARDI atlas constructed based on a cohort of 40 normal adults and empirically demonstrate the convergence of this EM atlas generation algorithm and effects of the hyperatlas on the estimated HARDI atlas.
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References
Aganj, I., et al.: Reconstruction of the orientation distribution function in single- and multiple-shell q-ball imaging within constant solid angle. MRM 64, 554–566 (2010)
Allassonniére, S., et al.: Towards a coherent statistical framework for dense deformable template estimation. Journal of the Royal Statistical Society Series B 69(1), 3–29 (2007)
Avants, B., Gee, J.C.: Geodesic estimation for large deformation anatomical shape and intensity averaging. NeuroImage 23, 139–150 (2004)
Bloy, L., Ingalhalikar, M., Eavani, H., Schultz, R.T., Roberts, T.P., Verma, R.: White matter atlas generation using HARDI based automated parcellation. NeuroImage (2011)
Bouix, S., Rathi, Y., Sabuncu, M.: Building an average population HARDI atlas. In: Information MICCAI 2010 Workshop on Computational Diffusion MRI (2010)
Cheng, J., Ghosh, A., Jiang, T., Deriche, R.: A riemannian framework for orientation distribution function computing. In: Yang, G.-Z., Hawkes, D., Rueckert, D., Noble, A., Taylor, C. (eds.) MICCAI 2009, Part I. LNCS, vol. 5761, pp. 911–918. Springer, Heidelberg (2009)
Du, J., Goh, A., Qiu, A.: Diffeomorphic metric mapping of HARDI based on Riemannian structure of orientation distribution functions. IEEE TMI (2012)
Dupuis, P., Grenander, U., Miller, M.I.: Variational problems on flows of diffeomorphisms for image matching. Quart. App. Math. 56, 587–600 (1998)
Goh, A., et al.: A nonparametric Riemannian framework for processing HARDI and its applications to ODF-based morphometry. NeuroImage (2011)
Grenander, U., Miller, M.I.: Computational anatomy: An emerging discipline. Quart. App. Math. 56(4), 617–694 (1998)
Joshi, S.C., Davis, B., Jomier, M., Gerig, G.: Unbiased diffeomorphic atlas construction for computational anatomy. NeuroImage 23, 151–160 (2004)
Ma, J., Miller, M.I., Trouvé, A., Younes, L.: Bayesian template estimation in computational anatomy. NeuroImage 42, 252–261 (2008)
Miller, M.I., Trouvé, A., Younes, L.: Geodesic shooting for computational anatomy. J. Mathematical Imaging and Vision 24, 209–228 (2006)
Srivastava, A., Jermyn, I., Joshi, S.H.: Riemannian analysis of probability density functions with applications in vision. In: IEEE CVPR (2007)
Trouvé, A.: Diffeomorphism groups and pattern matching in image analysis. Int. J. of Comp. Vis. 28(3), 213–221 (1998)
Tuch, D.S.: High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity. MRM 48, 577–582 (2002)
Yeh, F.C., Tseng, W.Y.I.: NTU-90: A high angular resolution brain atlas constructed by q-space diffeomorphic reconstruction. NeuroImage 58(1), 91–99 (2011)
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Du, J., Goh, A., Qiu, A. (2013). Bayesian Atlas Estimation from High Angular Resolution Diffusion Imaging (HARDI). In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2013. Lecture Notes in Computer Science, vol 8085. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40020-9_15
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DOI: https://doi.org/10.1007/978-3-642-40020-9_15
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