Abstract
One of the approaches in diffusion tensor imaging is to consider a Riemannian metric given by the inverse diffusion tensor . Such a metric is used for white matter tractography and connectivity analysis. We propose a modified metric tensor given by the adjugate rather than the inverse diffusion tensor. Tractography experiments on real brain diffusion data show improvement in the vicinity of isotropic diffusion regions compared to results for inverse (sharpened) diffusion tensors.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Astola, L., Florack, L., ter Haar Romeny, B.M.: Measures for pathway analysis in brain white matter using diffusion tensor images. In: Karssemeijer, N., Lelieveldt, B.P.F. (eds.) Proceedings of the IPMI 2007, Kerkrade. Lecture Notes in Computer Science, vol. 4584, pp. 642–649. Springer (2007)
Astola, L., Fuster, A., Florack, L.: A Riemannian scalar measure for diffusion tensor images. Pattern Recognit. 44(9), 1885–1891 (2011)
Basser, P.J., Mattiello, J., Le Bihan, D.: Estimation of the effective self-diffusion tensor from the NMR spin echo. J. Magn. Reson. 103, 247–254 (1994)
de Lara, M.C.: Geometric and symmetry properties of a nondegenerate diffusion process. Ann. Probab. 23(4), 1557–1604 (1995). doi:10.1214/aop/1176987794. http://projecteuclid.org/euclid.aop/1176987794
Descoteaux, M., Deriche, R., Lenglet, C.: Diffusion tensor sharpening improves white matter tractography. In: SPIE Image Processing: Medical Imaging, San Diego, pp. 1084–1087 (2007)
Fletcher, P.T., Joshi, S.: Riemannian geometry for the statistical analysis of diffusion tensor data. Signal Process. 87(2), 250–262 (2007)
Fletcher, P.T., Tao, R., Jeong, K.W., Whitaker, R.T.: A volumetric approach to quantifying region-to-region white matter connectivity in diffusion tensor MRI. In: Karssemeijer, N., Lelieveldt, B.P.F. (eds.) Proceedings of the IPMI 2007, Kerkrade. Lecture Notes in Computer Science, vol. 4584, pp. 346–358. Springer (2007)
Hao, X., Whitaker, R.T., Fletcher, P.T.: Adaptive Riemannian metrics for improved geodesic tracking of white matter. In: Székely, G., Hahn, H.K. (eds.) Proceedings of the IPMI 2011, Kloster Irsee. Lecture Notes in Computer Science, vol. 6801, pp. 13–24. Springer, Berlin (2011)
Jbabdi, S., Bellec, P., Toro, R., Daunizeau, J., Pélégrini-Issac, M., Benali, H.: Accurate anisotropic fast marching for diffusion-based geodesic tractography. Int. J. Biomed. Imaging 2008, 1–12 (2008). doi:10.1155/2008/320195. http://www.hindawi.com/journals/ijbi/2008/320195/
Lazar, M., Weinstein, D.M., Tsuruda, J.S., Hasan, K.M., Arfanakis, K., Meyerand, M.E., Badie, B., Rowley, H.A., Haughton, V., Field, A., Alexander, A.L.: White matter tractography using diffusion tensor deflection. Hum. Brain Mapp. 18(4), 306–321 (2003). doi:10.1002/hbm.10102. http://dx.doi.org/10.1002/hbm.10102
Lenglet, C., Deriche, R., Faugeras, O.: Inferring white matter geometry from diffusion tensor MRI: application to connectivity mapping. In: Pajdla, T., Matas, J. (eds.) Proceedings of the 8th European Conference on Computer Vision, Prague, May 2004. Lecture Notes in Computer Science, vol. 3021–3024, pp. 127–140. Springer, Berlin (2004)
Melonakos, J., Pichon, E., Angenent, S., Tannenbaum, A.: Finsler active contours. IEEE Trans. Pattern Anal. Mach. Intell. 30(3), 412–423 (2008)
O’Donnell, L., Haker, S., Westin, C.F.: New approaches to estimation of white matter connectivity in diffusion tensor MRI: elliptic PDEs and geodesics in a tensor-warped space. In: Proceedings of Medical Imaging, Computing and Computer Assisted Intervention, Tokyo. Lecture Notes in Computer Science, vol. 2488, pp. 459–466. Springer (2002)
Pennec, X., Fillard, P., Ayache, N.: A Riemannian framework for tensor computing. Int. J. Comput. Vis. 66(1), 41–66 (2006)
Pieper, S., Halle, M., Kikinis, R.: 3D Slicer. In: IEEE International Symposium on Biomedical Imaging ISBI 2004, Arlington, pp. 632–635 (2004)
Prados, E., Soatto, S., Lenglet, C., Pons, J.P., Wotawa, N., Deriche, R., Faugeras, O.: Control theory and fast marching techniques for brain connectivity mapping. In: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, New York, June 2006, vol. 1, pp. 1076–1083. IEEE Computer Society (2006)
Tournier, J.D., Calamante, F., Gadian, D.G., Connelly, A.: Diffusion-weighted magnetic resonance imaging fibre tracking using a front evolution algorithm. NeuroImage 20(1), 276–288 (2003). doi:10.1016/S1053-8119(03)00236-2. http://www.sciencedirect.com/science/article/pii/S1053811903002362
Acknowledgements
Tom Dela Haije gratefully acknowledges The Netherlands Organisation for Scientific Research (NWO) for financial support. Andrea Fuster would like to thank Lauren O’Donnell for feedback on brain white matter anatomy and Ana Achúcarro.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Fuster, A., Tristan-Vega, A., Haije, T.D., Westin, CF., Florack, L. (2014). A Novel Riemannian Metric for Geodesic Tractography in DTI. In: Schultz, T., Nedjati-Gilani, G., Venkataraman, A., O'Donnell, L., Panagiotaki, E. (eds) Computational Diffusion MRI and Brain Connectivity. Mathematics and Visualization. Springer, Cham. https://doi.org/10.1007/978-3-319-02475-2_9
Download citation
DOI: https://doi.org/10.1007/978-3-319-02475-2_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02474-5
Online ISBN: 978-3-319-02475-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)