nach oben

International Journal of Computer Vision

Erschienen in:

01.03.2014

Anisotropy Preserving DTI Processing

verfasst von: Anne Collard, Silvère Bonnabel, Christophe Phillips, Rodolphe Sepulchre

Erschienen in: International Journal of Computer Vision | Ausgabe 1/2014

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

Statistical analysis of diffusion tensor imaging (DTI) data requires a computational framework that is both numerically tractable (to account for the high dimensional nature of the data) and geometric (to account for the nonlinear nature of diffusion tensors). Building upon earlier studies exploiting a Riemannian framework to address these challenges, the present paper proposes a novel metric and an accompanying computational framework for DTI data processing. The proposed approach grounds the signal processing operations in interpolating curves. Well-chosen interpolating curves are shown to provide a computational framework that is at the same time tractable and information relevant for DTI processing. In addition, and in contrast to earlier methods, it provides an interpolation method which preserves anisotropy, a central information carried by diffusion tensor data.

Vorheriger Artikel Probabilistic Joint Image Segmentation and Labeling by Figure-Ground Composition

Nächster Artikel A Klein-Bottle-Based Dictionary for Texture Representation

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Alexander, D., & Gee, J. (2000). Elastic matching of diffusion tensor images. Computer Vision and Image Understanding, 77(2), 233–250.CrossRef

Alexander, D. C. P., Basser, P., & Gee, J. (2001). Spatial transformations of diffusion tensor magnetic resonance images. IEEE Transactions on Medical Imaging, 20(11), 1131–1139.CrossRef

Ando, T., Li, C. K., & Mathias, R. (2004). Geometric means. Linear Algebra and its Applications, 385, 305–334.CrossRefMATHMathSciNet

Arsigny, V., Fillard, P., Pennec, X., & Ayache, N. (2006). Log-Euclidean metrics for fast and simple calculs on diffusion tensors. Magnetic Resonance in Medicine, 56, 411–421.

Arsigny, V., Fillard, P., Pennec, X., & Ayache, N. (2007). Geometric means in a novel vector space structure on symmetric positive-definite matrices. SIAM Journal on Matrix Analysis and Applications, 29(1), 328–347.CrossRefMATHMathSciNet

Awate, S., Zhang, H., Gee, J. (2007). Fuzzy nonparametric DTI segmentation for robust cingulum-tract extraction. MICCAI pp. 294–301.

Basser, P., & Pierpaoli, C. (1996). Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI. Journal of Magnetic Resonance, Series B, 111(3), 209–219.CrossRef

Basser, P., Mattiello, J., & Bihan, D. L. (1994). MR diffusion tensor spectroscopy and imaging. Biophysical Journal, 66(1), 259–267.CrossRef

Batchelor, P. G., Moakher, M., Atkinson, D., Calamante, F., & Connelly, A. (2005). A rigorous framework for diffusion tensor calculus. Magnetic Resonance in Medicine, 53(1), 221–225.CrossRef

Birkhoff, G. (1957). Extensions of Jentzsch’s theorem. Transactions of the American Mathematical Society, 85(1), 219–227.MATHMathSciNet

Bonnabel, S., & Sepulchre, R. (2009). Riemannian metric and geometric mean for positive semidefinite matrices of fixed rank. SIAM Journal on Matrix Analysis and Applications, 31(3), 1055–1070.CrossRefMathSciNet

Bonnabel, S., Collard, A., & Sepulchre, R. (2013). Rank-preserving geometric means of positive semi-definite matrices. Linear Algebra and its Applications, 438(8), 3202–3216.CrossRefMATHMathSciNet

Burbea, J., & Rao, C. (1982). Entropy differential metric, distance and divergence measures in probability spaces: A unified approach. Journal of Multivariate Analysis, 12(4), 575–596.CrossRefMATHMathSciNet

Castaño-Moraga, C., Lenglet, C., Deriche, R., Ruiz-Alzola, J. (2006). A fast and rigorous anisotropic smoothing method for DT-MRI. In Proceedings of the IEEE International Symposium on Biomedical Imaging: From Nano to Macro pp. 93–96.

Castro, F., Clatz, O., Dauguet, J., Archip, N., Thiran, J. P., Warfield, S. (2007). Evaluation of brain image nonrigid registration algorithms based on Log-Euclidean MR-DTI consistency measures. In Proceedings of the IEEE International Symposium on Biomedical Imaging: From Nano to Macro pp. 45–48.

Cetingül, H. E., Afsari, B., Wright, M. J., Thompson, P. M., Vidal, R. (2012). Group action induced averaging for HARDI processing. In Proceedings of the IEEE International Symposium on Biomedical Imaging pp. 1389–1392.

Chefd’hotel, C., Tschumperlé, D., Deriche, R., & Faugeras, O. (2004). Regularizing flows for constrained matrix-valued images. Journal of Mathematical Imaging and Vision, 20, 147–162.CrossRefMathSciNet

Cheng, J., Ghosh, A., Jiang, T., Deriche, R. (2009). A Riemannian framework for orientation distribution function computing, vol. 12. MICCAI pp. 911–918.

Chiang, M. C., Leow, A. D., Klunder, A. D., Dutton, R. A., Barysheva, M., Rose, S., et al. (2008). Fluid registration of diffusion tensor images using information theory. IEEE Transactions on Medical Imaging, 27(4), 442–456.CrossRef

Dai, Y., Trumpf, J., Li, H., Barnes, N., Hartley, R. (2010). Rotation averaging with application to camera-rig calibration. In: Computer vision—ACCV 2009 (pp. 335–346).

Dryden, I. L., Koloydenko, A., & Zhou, D. (2009). Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging. The Annals of Applied Statistics, 3(3), 1102–1123.CrossRefMATHMathSciNet

Fillard, P., Pennec, X., Arsigny, V., & Ayache, N. (2007). Clinical DT-MRI estimation, smoothing, and fiber tracking with log-Euclidean metrics. IEEE Transactions on Medical Imaging, 26(11), 1472–1482.CrossRef

Fletcher, P. T., & Joshi, S. (2007). Riemannian geometry for the statistical analysis of diffusion tensor data. Signal Processing, 87, 250–262.CrossRefMATH

Fletcher, P. T., Venkatasubramanian, S., & Joshi, S. (2009). The geometric median on Riemannian manifolds with application to robust atlas estimation. NeuroImage, 45(1 Suppl), S143–S152.CrossRef

Goh, A., Lenglet, C., Thompson, P. M., & Vidal, R. (2011). A nonparametric Riemannian framework for processing high angular resolution diffusion images and its applications to ODF-based morphometry. Neuroimage, 56(3), 1181–1201.CrossRef

Goodlett, C., Fletcher, P. T., Gilmore, J. H., & Gerig, G. (2009). Group analysis of DTI fiber tract statistics with application to neurodevelopment. NeuroImage, 45(1, Supplement 1), S133–S142.CrossRef

Gur, Y., Sochen, N. (2007). Fast invariant Riemannian DT-MRI regularization. In Proceedings of the International Conference on Computer Vision pp. 1–7.

Ingalhalikar, M., Yang, J., Davatzikos, C., & Verma, R. (2010). DTI-DROID: Diffusion tensor imaging-deformable registration using orientation and intensity descriptors. International Journal of Imaging Systems and Technology, 20(2), 99–107.CrossRef

Jensen, J. H., & Helpern, J. A. (2010). MRI quantification of non-Gaussian water diffusion by kurtosis analysis. NMR in Biomedicine, 23(7), 698–710.CrossRef

Karcher, H. (1977). Riemannian center of mass and mollifier smoothing. Communications on Pure and Applied Mathematics, 30(5), 509–541.CrossRefMATHMathSciNet

Kindlmann, G., San Jose Estepar, R., Niethammer, M., Haker, S., Westin, C. F. (2007). Geodesic-loxodromes for diffusion tensor interpolation and difference measurement. MICCAI pp. 1–9.

Lenglet, C., Rousson, M., Deriche, R., & Faugeras, O. (2006). Statistics on the manifold of multivariate normal distributions: Theory and application to diffusion tensor MRI processing. Journal of Mathematical Imaging and Vision, 25, 423–444.CrossRefMathSciNet

Lenglet, C., Campbell, J., Descoteaux, M., Haro, G., Savadjiev, P., Wassermann, D., et al. (2009). Mathematical methods for diffusion MRI processing. NeuroImage, 45(1, Supplement 1), S111–S122.CrossRef

Lepore, N., Brun, C., Chiang, M. C., Chou, Y. Y., Dutton, R., Hayashi, K., Lopez, O., Aizenstein, H., Toga, A., Becker, J., Thompson, P. (2006). Multivariate statistics of the Jacobian matrices in tensor based morphometry and their application to HIV/AIDS. MICCAI pp. 191–198.

Moakher, M. (2005). A differential geometric approach to the geometric mean of symmetric positive-definite matrices. SIAM Journal on Matrix Analysis and Applications, 26(3), 735–747.CrossRefMATHMathSciNet

Moakher, M., & Zéraï, M. (2011). The Riemannian geometry of the space of positive-definite matrices and its application to the regularization of positive-definite matrix-valued data. Journal of Mathematical Imaging and Vision, 40, 171–187.CrossRefMATHMathSciNet

Ncube, S., Srivastava, A. (2011). A novel Riemannian metric for analyzing HARDI data. In Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 7962 p. 7.

Nesterov, Y., Nemirovskii, A. S., Ye, Y. (1994). Interior-point polynomial algorithms in convex programming. SIAM, 13.

Parker, G. J. M., Haroon, H. A., & Wheeler-Kingshott, C. A. M. (2003). A framework for a streamline-based probabilistic index of connectivity (PICo) using a structural interpretation of MRI diffusion measurments. Journal of Magnetic Resonance Imaging, 18, 245–254.

Pennec, X., Fillard, P., & Ayache, N. (2006). A Riemannian framework for tensor computing. International Journal of Computer Vision, 66(1), 41–66.CrossRefMathSciNet

Perona, P., & Malik, J. (1990). Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(7), 629–639.CrossRef

Petz, D., & Temesi, R. (2005). Means of positive numbers and matrices. SIAM Journal on Matrix Analysis and Applications, 27(3), 712–720.CrossRefMATHMathSciNet

Sarlette, A., Sepulchre, R., Leonard, N. (2007). Cooperative attitude synchronization in satellite swarms: A consensus approach. In Proceedings of the 17th IFAC Symposium on Automatic Control in Aerospace.

Skovgaard, L. T. (1984). A Riemannian geometry of the multivariate normal model. Scandinavian Journal of Statistics, 11(4), 211–223.MATHMathSciNet

Smith, S. T. (2005). Covariance, subspace, and intrinsic Cramér-Rao bounds. IEEE Transactions on Signal Processing, 53, 1610–1630.CrossRefMathSciNet

Thévenaz, P., Blu, T., & Unser, M. (2000). Interpolation revisited [medical images application]. IEEE Transactions on Medical Imaging, 19(7), 739–758.CrossRef

Tschumperlé, D., & Deriche, R. (2001). Diffusion tensor regularization with constraints preservation. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1, 948.

Tuch, D. (2004). Q-ball imaging. Magnetic Resonance in Medicine, 52(6), 1358–1372.CrossRef

Weldeselassie, Y., Hamarneh, G. (2007). DT-MRI segmentation using graph cuts. SPIE, 6512.

Weldeselassie, Y., Hamarneh, G., Beg, F., Atkins, S. (2009). Novel decomposition of tensor distance into shape and orientation distances. MICCAI pp. 173–180.

Yeo, B., Vercautern, T., Fillard, P., Pennec, X., Gotland, P., Ayache, N., et al. (2008). DTI registration with exact finite-strain differential. In Proceedings of the IEEE International Symposium on Biomedical Imaging : From Nano to Macro.

Yeo, B., Vercauteren, T., Fillard, P., Peyrat, J. M., Pennec, X., Golland, P., et al. (2009). DT-REFinD: Diffusion Tensor registration with exact finite-strain differential. IEEE Transactions on Medical Imaging, 28(12), 1914–1928.CrossRef

Zhang, H., Yushkevich, P. A., Alexander, D., & Gee, J. (2006). Deformable registration of diffusion tensor MR images with explicit orientation optimization. Medical Image Analysis, 10(5), 764–785.CrossRef

Zhou, D. (2010). Statistical analysis of diffusion tensor imaging. PhD thesis, University of Nottingham.

Zhou, D., Dryden, I. L., Koloydenko, A., & Bai, L. (2013). Procrustes analysis for diffusion tensor image processing. International Journal of Computer Theory and Engineering, 5(1), 108–113.CrossRef

Titel: Anisotropy Preserving DTI Processing
verfasst von: Anne Collard
Silvère Bonnabel
Christophe Phillips
Rodolphe Sepulchre
Publikationsdatum: 01.03.2014
Verlag: Springer US
Erschienen in: International Journal of Computer Vision / Ausgabe 1/2014
Print ISSN: 0920-5691
Elektronische ISSN: 1573-1405
DOI: https://doi.org/10.1007/s11263-013-0674-4

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Weitere Artikel der Ausgabe 1/2014

Hough Pyramid Matching: Speeded-Up Geometry Re-ranking for Large Scale Image Retrieval

Probabilistic Joint Image Segmentation and Labeling by Figure-Ground Composition

Object Bank: An Object-Level Image Representation for High-Level Visual Recognition

A Klein-Bottle-Based Dictionary for Texture Representation