Riemannian anisotropic diffusion for tensor valued images

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5305 LNCS, Issue PART 4, 2008, Pages 326-339

  Krajsek, Kai ^a   Menzel, Marion I ^a   Zwanger, Michael ^b   Scharr, Hanno ^a  

^a FORSCHUNGSZENTRUM JÜLICH   (Germany)

^b SIEMENS AG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER VISION; DIFFUSION; EIGENVALUES AND EIGENFUNCTIONS; GEOMETRY; MAGNETIC RESONANCE IMAGING; OPTICAL ANISOTROPY; TENSORS;

ANISOTROPIC DIFFUSION; ANISOTROPIC DIFFUSION EQUATIONS; DIFFUSION TENSOR MAGNETIC RESONANCE IMAGING; GEOMETRIC FORMULATION; GEOMETRIC STRUCTURE; IMAGE PROCESSING TECHNIQUE; NONLINEAR STRUCTURE; TENSOR VALUED IMAGES;

DIFFUSION TENSOR IMAGING;

EID: 56749150563     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-88693-8_24     Document Type: Conference Paper

References (35)

1. Berger, M.-O., Deriche, R., Herlin, I., Jaffré, J., Morel, J.-M. (eds.): Icaos 1996: Images and wavelets and PDEs. Lecture Notes in Control and Information Sciences, vol. 219 (1996)
2. Weickert, J.: Anisotropic diffusion in image processing. Teubner, Stuttgart (1998)
3. Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence 12 (1990)
4. Bigün, J., Granlund, G.H.: Optimal orientation detection of linear symmetry. In: ICCV, London, UK, pp. 433-438 (1987)
5. Tschumperlé, D., Deriche, R.: Diffusion tensor regularization with constraints preservation. In: Proc. IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR 2001), pp. 948-953 (2001)
6. Chefd'hotel, C., Tschumperlé, D., Deriche, R., Faugeras, O.: Regularizing flows for constrained matrix-valued images. J. Math. Imaging Vis. 20(1-2), 147-162 (2004)
7. Pennec, X., Fillard, P., Ayache, N.: A Riemannian framework for tensor computing. International Journal of Computer Vision 66(1), 41-66 (2006)
8. Castano-Moraga, C.A., Lenglet, C., Deriche, R., Ruiz-Alzola, J.: A Riemannian approach to anisotropic filtering of tensor fields. Signal Processing 87(2), 263-276 (2007)
9. Weickert, J., Hagen, H.: Visualization and Processing of Tensor Fields (Mathematics and Visualization). Springer, New York (2005)
10. Rao, C.: Information and accuracy attainable in estimation of statistical parameters. Bull. Calcutta Math. Soc. 37, 81-91 (1945)
11. Martin-Fernandez, M., San-Jose, R., Westin, C.F., Alberola-Lopez, C.: A novel GaussMarkov random field approach for regularization of diffusion tensor maps. In: Moreno-D?́az Jr., R., Pichler, F. (eds.) EUROCAST 2003. LNCS, vol. 2809, pp. 506-517. Springer, Heidelberg (2003)
12. Weickert, J., Brox, T.: Diffusion and regularization of vector- and matrix-valued images. In: Inverse Problems, Image Analysis, and Medical Imaging. Contemporary Mathematics, pp. 251-268 (2002)
13. Westin, C.-F., Knutsson, H.: Tensor field regularization using normalized convolution. In: Moreno-D?́az Jr., R., Pichler, F. (eds.) EUROCAST 2003. LNCS, vol. 2809, pp. 564-572. Springer, Heidelberg (2003)
14. Burgeth, B., Didas, S., Florack, L.,Weickert, J.: A generic approach to the filtering of matrix fields with singular PDEs. In: Sgallari, F., Murli, A., Paragios, N. (eds.) SSVM 2007. LNCS, vol. 4485, pp. 556-567. Springer, Heidelberg (2007)
15. Gur, Y., Sochen, N.A.: Denoising tensors via Lie group flows. In: Paragios, N., Faugeras, O., Chan, T., Schnörr, C. (eds.) VLSM 2005. LNCS, vol. 3752, pp. 13-24. Springer, Heidelberg (2005)
16. Moakher, M.: A differential geometric approach to the geometric mean of symmetric positive-definite matrices. SIAM J. Matrix Anal. Appl (2003)
17. Fletcher, P., Joshi, S.: Principle geodesic analysis on symmetric spaces: Statistics of diffusion tensors. In: Computer Vision and Mathematical Methods in Medical and Biomedical Image Analysis, ECCV 2004 Workshops CVAMIA and MMBIA, pp. 87-98 (2004)
18. Lenglet, C., Rousson, M., Deriche, R., Faugeras, O.D., Lehericy, S., Ugurbil, K.: A Riemannian approach to diffusion tensor images segmentation. In: Christensen, G.E., Sonka, M. (eds.) IPMI 2005. LNCS, vol. 3565, pp. 591-602. Springer, Heidelberg (2005)
19. Batchelor, P.G., Moakher, M., Atkinson, D., Calamante, F., Connelly, A.: A rigorous framework for diffusion tensor calculus. Magn. Reson. Med. 53(1), 221-225 (2005)
20. Fillard, P., Arsigny, V., Ayache, N., Pennec, X.: A Riemannian framework for the processing of tensor-valued images. In: Fogh Olsen, O., Florack, L.M.J., Kuijper, A. (eds.) DSSCV 2005. LNCS, vol. 3753, pp. 112-123. Springer, Heidelberg (2005)
21. Lenglet, C., Rousson, M., Deriche, R., Faugeras, O.: Statistics on the manifold of multivariate normal distributions: Theory and application to diffusion tensor MRI processing. J. Math. Imaging Vis. 25(3), 423-444 (2006)
22. Zéra?̈, M., Moakher, M.: Riemannian curvature-driven flows for tensor-valued data. In: Sgallari, F., Murli, A., Paragios, N. (eds.) SSVM 2007. LNCS, vol. 4485, pp. 592-602. Springer, Heidelberg (2007)
23. Helgason, S.: Differential Geometry, Lie groups and symmetric spaces. Academic Press, London (1978)
24. El-Fallah, A., Ford, G.: On mean curvature diffusion in nonlinear image filtering. Pattern Recognition Letters 19, 433-437 (1998)
25. Sochen, N., Kimmel, R., Malladi, R.: A geometrical framework for low level vision. IEEE Transaction on Image Processing, Special Issue on PDE based Image Processing 7(3), 310-318 (1998)
26. Begelfor, E., Werman, M.: Affine invariance revisited. In: CVPR '06: Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp. 2087-2094. IEEE Computer Society Press, Washington (2006)
27. Zhang, F., Hancock, E.: Tensor MRI regularization via graph diffusion. In: BMVC 2006, pp. 578-589 (2006)
28. Arsigny, V., Fillard, P., Pennec, X., Ayache, N.: Log-Euclidean metrics for fast and simple calculus on diffusion tensors. Magnetic Resonance in Medicine 56(2), 411-421 (2006)
29. Gur, Y., Sochen, N.A.: Fast invariant Riemannian DT-MRI regularization. In: Proc. of IEEE Computer SocietyWorkshop on Mathematical Methods in Biomedical Image Analysis (MMBIA), Rio de Janeiro, Brazil, pp. 1-7 (2007)
30. Mémoli, F., Sapiro, G., Osher, S.: Solving variational problems and partial differential equations mapping into general target manifolds. Journal of Computational Physics 195(1), 263-292 (2004)
31. Brox, T., Weickert, J., Burgeth, B., Mrázek, P.: Nonlinear structure tensors. Revised version of technical report no. 113. Saarland University, Saarbrücken, Germany (2004)
32. Nielsen, M., Johansen, P., Olsen, O.,Weickert, J. (eds.): Scale-Space 1999. LNCS, vol. 1682. Springer, Heidelberg (1999)
33. Maaß, H.: Siegel's Modular Forms and Dirichlet Series. Lecture notes in mathematics, vol. 216. Springer, Heidelberg (1971)
34. 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. 115-122. Springer, Heidelberg (2005)
35. Bihan, D.L., Mangin, J.F., Poupon, C., Clark, C.A., Pappata, S., Molko, N., Chabriat, H.: Diffusion tensor imaging: Concepts and applications. Journal of Magnetic Resonance Imaging 13(4), 534-546 (2001)