Abstract
Concepts from Information Theory have been used quite widely in Image Processing, Computer Vision and Medical Image Analysis for several decades now. Most widely used concepts are that of KL-divergence, minimum description length (MDL), etc. These concepts have been popularly employed for image registration, segmentation, classification etc. In this chapter we review several methods, mostly developed by our group at the Center for Vision, Graphics & Medical Imaging in the University of Florida, that glean concepts from Information Theory and apply them to achieve analysis of Diffusion-Weighted Magnetic Resonance (DW-MRI) data.
This relatively new MRI modality allows one to non-invasively infer axonal connectivity patterns in the central nervous system. The focus of this chapter is to review automated image analysis techniques that allow us to automatically segment the region of interest in the DWMRI image wherein one might want to track the axonal pathways and also methods to reconstruct complex local tissue geometries containing axonal fiber crossings. Implementation results illustrating the algorithm application to real DW-MRI data sets are depicted to demonstrate the effectiveness of the methods reviewed.
The research was in part funded by the grant NIH EB007082.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Stejskal, E.O., Tanner, J.E.: Spin diffusion measurements: spin echoes in the presence of a time-dependent field gradient. J. Chem. Phys. 42(1), 288–292 (1965)
Basser, P., Mattiello, J., Lebihan, D.: Estimation of the Effective Self-Diffusion Tensor from the NMR Spin Echo. J. Magn. Reson. B 103, 247–254 (1994)
Callaghan, P.T.: Principles of Nuclear Magnetic Resonance Microscopy. Clarendon Press, Oxford (1991)
Basser, P.J., Pajevic, S., Pierpaoli, C., Duda, J., Aldroubi, A.: In vivo fiber tractography using dt-mri data. Magnetic Resonance in Medicine 44(4), 625–632 (2000)
Wang, Z., Vemuri, B.C.: DTI segmentation using an information theoretic tensor dissimilarity measure. IEEE Transactions on Medical Imaging 24(10), 1267–1277 (2005)
Lenglet, C., Rousson, M., Deriche, R., Faugeras, O.: Statistics on the manifold of Multivariate Normal Distributions: Theory and Applications to Diffusion Tensor MRI processing. J. Math. Imaging Vis. 25, 423–444 (2006)
Pennec, X., Fillard, P., Ayache, N.: A Riemannian framework for tensor computing. International Journal of Computer Vision 65 (2005)
Pennec, X.: Probabilities and statistics on Riemannian manifolds: basic tools for geometric measurements. In: IEEE Workshop on Nonlinear Signal and Image Processing (1999)
Fletcher, P., Joshi, S.: Principal geodesic analysis on symmetric spaces: Statistics of diffusion tensors. In: Proc. of CVAMIA, pp. 87–98 (2004)
Barmpoutis, A., Vemuri, B., Shepherd, T., Forder, J.: Tensor splines for interpolation and approximation of DT-MRI with applications to segmentation of isolated rat hippocampi. IEEE Transactions on Medical Imaging 26(11), 1537–1546 (2007)
Arsigny, V., Fillard, P., Pennec, X., Ayache, N.: Fast and Simple Calculus on Tensors in the Log-Euclidean Framework. In: Duncan, J.S., Gerig, G. (eds.) MICCAI 2005. LNCS, vol. 3749, pp. 259–267. Springer, Heidelberg (2005)
Kindlmann, G., Estepar, R., Niethammer, M., Haker, S., Westin, C.F.: Geodesic-loxodromes for diffusion tensor interpolation and difference measurement. In: Ayache, N., Ourselin, S., Maeder, A. (eds.) MICCAI 2007, Part I. LNCS, vol. 4791, pp. 1–9. Springer, Heidelberg (2007)
Tuch, D.S., Reese, T.G., Wiegell, M.R., Wedeen, V.J.: Diffusion MRI of complex neural architecture. Neuron (40), 885–895 (2003)
Jian, B., Vemuri, B.C., Özarslan, E., Carney, P.R., Mareci, T.H.: A novel tensor distribution model for the diffusion-weighted MR signal. NeuroImage 37(1), 164–176 (2007)
Kumar, R., Barmpoutis, A., Vemuri, B.C., Carney, P.R., Mareci, T.H.: Multi-fiber reconstruction from DW-MRI using a continuous mixture of von mises-fisher distributions. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition CVPR Workshops 2008, pp. 1–8 (June 2008)
Barmpoutis, A., Kumar, R., Vemuri, B.C., Banerjee, A.: Beyond the Lambertian assumption: A generative model for apparent BRDF fields of faces using anti-symmetric tensor splines. In: IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2008, pp. 1–6 (June 2008)
Jian, B., Vemuri, B.C.: A unified computational framework for deconvolution to reconstruct multiple fibers from diffusion weighted MRI. TMI 26(11), 1464–1471 (2007)
Ozarslan, E., Mareci, T.H.: Generalized diffusion tensor imaging and analytical relationships between DTI and HARDI. MRM 50(5), 955–965 (2003)
Barmpoutis, A., Jian, B., Vemuri, B.C., Shepherd, T.M.: Symmetric positive 4th order tensors & their estimation from diffusion weighted MRI. In: Karssemeijer, N., Lelieveldt, B. (eds.) IPMI 2007. LNCS, vol. 4584, pp. 308–319. Springer, Heidelberg (2007)
Frank, L.R.: Characterization of anisotropy in high angular resolution diffusion-weighted MRI. Magn. Reson. Med. 47(6), 1083–1099 (2002)
Özarslan, E., Shepherd, T.M., Vemuri, B.C., Blackband, S.J., Mareci, T.H.: Resolution of complex tissue microarchitecture using the diffusion orientation transform (DOT). NeuroImage (2006)
Tuch, D.S.: Q-ball imaging. Magn. Reson. Med. 52(6), 1358–1372 (2004)
Descoteaux, M., Angelino, E., Fitzgibbons, S., Deriche, R.: Regularized, fast and robust analytical q-ball imaging. MRM 58(3), 497–510 (2007)
Wassermann, D., Descoteaux, M., Deriche, R.: Diffusion maps clustering for magnetic resonance q-ball imaging segmentation. Journal of Biomedical Imaging 8(3), 1–12 (2008)
Tournier, J.D., Calamante, F., Gadian, D.G., Connelly, A.: Direct estimation of the fiber orientation density function from DW-MRI data using spherical deconvolution. NeuroImage 23(3), 1176–1185 (2004)
Tournier, J.D., Calamante, F., Connelly, A.: Robust determination of the fibre orientation distribution in diffusion MRI: non-negativity constrained super-resolved spherical deconvolution
Tournier, J.D., Yeh, C.H., Calamante, F., Cho, K.H., Connelly, A., Lin, C.P.: Resolving crossing fibres using constrained spherical deconvolution: Validation using diffusion-weighted imaging phantom data. NeuroImage 42(2), 617–625 (2008)
Alexander, D.C.: Maximum entropy spherical deconvolution for diffusion MRI. Inf. Process Med. Imaging, 76–87 (2005)
Wedeen, V., Wang, R.P., Schmahmann, J.D., Benner, T., Tseng, W.Y., Dai, G., Pandya, D.N., Hagmann, P., D’Arceuil, H., de Crespigny, A.J.: Diffusion spectrum magnetic resonance imaging (dsi) tractography of crossing fibers. Neuroimage 41(4), 1267–1277 (2008)
Hasan, K.M., Gupta, R.K., Santos, R.M., Wolinsky, J.S., Narayana, P.A.: Diffusion tensor fractional anisotropy of the normal-appearing seven segments of the corpus callosum in healthy adults and relapsing-remitting multiple sclerosis patients. Journal of Magnetic Resonance Imaging 21(6), 735–743 (2005)
van Gelderen, P., de Vleeschouwer, M.H.M., DesPres, D., Pekar, J., van Zijl, P.C.M., Moonen, C.T.W.: Water diffusion and acute stroke. Magnetic Resonance in Medicine 31(2), 154–163 (1994)
Cover, T.M., Thomas, J.A.: Elements of Information Theory. John Wiley and Sons Inc., Chichester (2001)
Wang, Z., Vemuri, B., Chen, Y., Mareci, T.: A constrained variational principle for direct estimation and smoothing of the diffusion tensor field from DWI. In: Taylor, C.J., Noble, J.A. (eds.) IPMI 2003. LNCS, vol. 2732, pp. 660–671. Springer, Heidelberg (2003)
Wang, Z., Vemuri, B., Chen, Y., Mareci, T.: A Constrained Variational Principle for Direct Estimation and Smoothing of the Diffusion Tensor Field from complex DWI. TMI 23(8), 930–939 (2004)
Letac, G., Massam, H.: Quadratic and inverse regressions for Wishart distributions. Ann. Stat. 2(26), 573–595 (1998)
McGraw, T., Vemuri, B.C., Yezierski, R., Mareci, T.: Von Mises-Fisher mixture model of the diffusion ODF. In: ISBI, pp. 65–68 (2006)
McGraw, T., Vemuri, B.C., Yezierski, R., Mareci, T.: Segmentation of high angular resolution diffusion MRI modeled as a field of von Mises-Fisher mixtures. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol. 3953, pp. 463–475. Springer, Heidelberg (2006)
Bhalerao, A., Westin, C.F.
Jian, B., Vemuri, B.C.: Multi-fiber reconstruction from diffusion MRI using mixture of Wisharts and sparse deconvolution. In: Karssemeijer, N., Lelieveldt, B. (eds.) IPMI 2007. LNCS, vol. 4584, pp. 384–395. Springer, Heidelberg (2007)
Sen, P., Hürlimann, M., de Swiet, T.: Debye–Porod law of diffraction for diffusion in porous media. Phys. Rev. 51(1), 601–604 (1995)
Barmpoutis, A., Vemuri, B.C., Forder, J.R.: Fast displacement probability profile approximation from hardi using 4th-order tensors. In: Proceedings of ISBI 2008: IEEE International Symposium on Biomedical Imaging, May 14-17, 2008, pp. 911–914 (2008)
Barmpoutis, A., Vemuri, B.C., Howland, D., Forder, J.R.: Extracting tractosemas from a displacement probability field for tractography in DW-MRI. In: Metaxas, D., Axel, L., Fichtinger, G., Székely, G. (eds.) MICCAI 2008, Part I. LNCS, vol. 5241, pp. 9–16. Springer, Heidelberg (2008)
Deriche, R., Descoteaux, M.: Splitting tracking through crossing fibers: Multidirectional q-ball tracking. In: ISBI, pp. 756–759 (2007)
Söderman, O., Jönsson, B.: Restricted diffusion in cylindrical geometry. J. Magn. Reson. A (117), 94–97 (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Barmpoutis, A., Vemuri, B.C. (2009). Information Theoretic Methods for Diffusion-Weighted MRI Analysis. In: Nielsen, F. (eds) Emerging Trends in Visual Computing. ETVC 2008. Lecture Notes in Computer Science, vol 5416. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00826-9_15
Download citation
DOI: https://doi.org/10.1007/978-3-642-00826-9_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00825-2
Online ISBN: 978-3-642-00826-9
eBook Packages: Computer ScienceComputer Science (R0)