nach oben

Erschienen in:

2012 | OriginalPaper | Buchkapitel

Edge-Enhancing Diffusion Filtering for Matrix Fields

verfasst von : Bernhard Burgeth, Luis Pizarro, Stephan Didas

Erschienen in: New Developments in the Visualization and Processing of Tensor Fields

Verlag: Springer Berlin Heidelberg

Einloggen

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

search-config

KI-gestützte Suche

Aus

Abstract

The elimination of noise and small details from an image while simultaneously preserving or enhancing the edge structures in an image is a ever-lasting task in image processing. Edge-enhancing anisotropic diffusion is known to tackle this problem successfully. The problem of noise removal and edge enhancement is also a major concern in diffusion tensor magnetic resonance imaging (DT-MRI). This medical image acquisition technique outputs a 3D matrix field of symmetric 3 ×3-matrices, and it helps to visualise, for example, the nerve fibres in brain tissue. As any physical measurement DT-MRI is subjected to errors causing faulty representations of the tissue structure corrupted by noise. In this paper we address that problem by proposing a edge-enhancing diffusion filtering methodology for matrix fields. The approach is based on a generic structure tensor concept for matrix fields that relies on the operator-algebraic properties of symmetric matrices, rather than their channel-wise treatment of earlier proposals. Numerical experiments with artificial and real DT-MRI data confirm the noise-removing and edge-enhancing qualities of the technique presented.

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 "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

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

Vorheriges Kapitel Adaptation of Tensor Voting to Image Structure Estimation

Nächstes Kapitel Fabric-Like Visualization of Tensor Field Data on Arbitrary Surfaces in Image Space

Basser, P.J., Pierpaoli, C.: Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI. J. Magn. Reson. 11, 209–219 (1996)

Bigun, J.: Vision with Direction. Springer, Berlin (2006)

Brox, T., Weickert, J., Burgeth, B., Mrázek, P.: Nonlinear structure tensors. Technical report 113, Department of Mathematics, Saarland University, Saarbrücken, October 2004

Burgeth, B., Bruhn, A., Didas, S., Weickert, J., Welk, M.: Morphology for matrix-data: ordering versus PDE-based approach. Image Vis. Comput. 25(4), 496–511 (2007)

Burgeth, B., Didas, S., Florack, L., Weickert, J.: A Generic Approach for Singular PDEs for and Variational Methods in Computer Vision. Lecture Notes in Computer Science, vol. 4485, pp. 556–567. Springer, Berlin (2007)

Burgeth, B., Didas, S., Florack, L., Weickert, J.: A generic approach to diffusion filtering of matrix-fields. Computing 81, 179–197 (2007)

Burgeth, B., Didas, S., Weickert, J.: A general structure tensor concept and coherenceenhancing diffusion filtering for matrix fields. In: Laidlaw, D., Weickert, J. (eds.) Visualization and Processing of Tensor Fields, pp. 305–323. Springer, Berlin (2009)

Burgeth, B., Pizarro, L., Didas, S., Weickert, J.: 3D-coherence-enhancing diffusion filtering for matrix fields. In: Florack, L., Duits, R., Jongbloed, G., van Lieshout, M.-C., Davies, L. (eds.) Locally Adaptive Filters in Signal and Image Processing, pp. 55–70. Springer (2011)

Chefd’Hotel, C., Tschumperlé, D., Deriche, R., Faugeras, O.: Constrained flows of matrixvalued functions: Application to diffusion tensor regularization. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) Computer Vision – ECCV 2002. Lecture Notes in Computer Science, vol. 2350, pp. 251–265. Springer, Berlin (2002)

10.

Förstner, W., Gülch, E.: A fast operator for detection and precise location of distinct points, corners and centres of circular features. In: Proceedings of ISPRS Intercommission Conference on Fast Processing of Photogrammetric Data, Interlaken, pp. 281–305 (1987)

11.

Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge University Press, Cambridge (1990)

12.

Mori, S., van Zijl, P.C.: Fiber tracking: principles and strategies – a technical review. NRM Biomed 15, 468–480 (2002)

13.

Nucifora, P.G., Verma, R., Lee, S.-K., Melhem, E.R.: Diffusion-tensor MR imaging and tractography: exploring brain microstructure and connectivity. Radiology 245, 367–384 (2007)

14.

Pajevic, S., Basser, P.J.: Parametric and non-parametric statistical analysis of DT-MRI data. J. Magn. Reson. 161(1), 1–14 (2003)

15.

Perona, P., Malik, J.: Scale space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12, 629–639 (1990)

16.

Schultz, T., Burgeth, B., Weickert, J.: Flexible segmentation and smoothing of DT-MRI fields through a customizable structure tensor. In: Bebis, G., Boyle, R., Parvin, B., Koracin, D., Remagnino, P., Nefian, A., Meenakshisundaram, G., Pascucci, V., Zara, J., Molineros, J., Theisel, H., Malzbender, T. (eds.) Advances in Visual Computing. Lecture Notes in Computer Science, vol. 4291, pp. 454–464. Springer, Berlin (2006)

17.

Tschumperlé, D., Deriche, R.: Regularization of orthonormal vector sets using coupled PDE’s. In: Proceedings of First IEEE Workshop on Variational and Level Set Methods in Computer Vision, Vancouver, pp. 3–10. IEEE Computer Society Press (2001)

18.

Weickert, J.: Theoretical foundations of anisotropic diffusion in image processing. Comput. Suppl. 11, 221–236 (1996)

19.

Weickert, J.: Anisotropic Diffusion in Image Processing. Teubner, Stuttgart (1998)

20.

Weickert, J.: Coherence-enhancing diffusion filtering. Int. J. Comput. Vis. 31(2/3), 111–127 (1999)

21.

Weickert, J.: Design of nonlinear diffusion filters. In: Jähne, B., Haußecker, H. (eds.) Computer Vision and Applications, pp. 439–458. Academic, San Diego (2000)

22.

Weickert, J., Brox, T.: Diffusion and regularization of vector- and matrix-valued images. In: Nashed, M.Z., Scherzer, O. (eds.) Inverse Problems, Image Analysis, and Medical Imaging. Contemporary Mathematics, vol. 313, pp. 251–268. AMS, Providence (2002)

Titel: Edge-Enhancing Diffusion Filtering for Matrix Fields
verfasst von: Bernhard Burgeth
Luis Pizarro
Stephan Didas
Verlag: Springer Berlin Heidelberg
Buch: New Developments in the Visualization and Processing of Tensor Fields
Print ISBN: 978-3-642-27342-1

Electronic ISBN: 978-3-642-27343-8

Copyright-Jahr: 2012
DOI: https://doi.org/10.1007/978-3-642-27343-8_3

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 "Technik"

Springer Professional "Wirtschaft"