Coherence-enhancing diffusion filtering

International Journal of Computer Vision

Volumn 31, Issue 2, 1999, Pages 111-127

  Weickert, Joachim ^a,b  

^a UNIVERSITY MEDICAL CENTER UTRECHT   (Netherlands)

^b UNIVERSITY OF MANNHEIM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

IMAGE ANALYSIS; IMAGE ENHANCEMENT; OPTICAL FILTERS; TENSORS;

ADDITIVE OPERATOR SPLITTING; NONLINEAR DIFFUSION;

COMPUTER VISION;

EID: 0032666007     PISSN: 09205691     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1008009714131     Document Type: Article

References (62)

1. Almansa, A. and Lindeberg, T. 1997. Enhancement of fingerprint images using shape-adapted scale-space operators, in J. Sporring, M. Nielsen, L. Florack and P. Johansen, Eds., Gaussian Scale-space Theory, Kluwer Academic Publishers, Dordrecht, pp. 3-19.
2. Alt, H.W. 1992. Lineare Funktionalanalysis, Springer, Berlin.
3. Alvarez, L., Guichard, F., Lions, P.L. and Morel, J.-M. 1993. Axioms and fundamental equations in image processing, Arch. Rational Mech. Anal., Vol. 123, pp. 199-257.
4. Alvarez, L., Lions, P.L. and Morel, J.-M. 1992. Image selective smoothing and edge detection by nonlinear diffusion. II, SIAM J. Numer. Anal., Vol. 29, pp. 845-866.
5. Babaud, J., Witkin, A.P., Baudin, M. and Duda, R.O. 1986 Uniqueness of the Gaussian kernel for scale space filtering, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 8, pp. 26-33.
6. Bacon, G.E., Bacon, P.J. and Griffiths, R.K. 1979 The orientation of apatite crystals in bone, J. Appl. Crystallography, Vol. 12, pp. 99-103.
7. Bigün, J. and Granlund, G.H. 1987. Optimal orientation detection of linear symmetry, Proc. First Int. Conf. on Computer Vision (ICCV '87), London, IEEE Computer Society Press, Washington, pp. 433-438.
8. van den Boomgaard, R. 1992. The morphological equivalent of the Gauss convolution, Nieuw Archief Voor Wiskunde, Vierde Serie, Deel 10, pp. 219-236.
9. Brezis, H. 1973. Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hubert, North Holland, Amsterdam.
10. Brezis, H. 1992. Analyse fonctionelle, Masson, Paris.
11. Buck, B. and Macaulay, V, Eds. 1991. Maximum entropy in action, Clarendon, Oxford.
12. Carmona, R. and Zhong, S. 1998. Adaptive smoothing respecting feature directions, IEEE Trans. Image Proc., Vol. 7, pp. 353-358.
13. Catté, F., Lions, P.-L, Morel, J.-M. and Coll, T. 1992. Image selective smoothing and edge detection by nonlinear diffusion, SIAM J. Numer. Anal., Vol. 29, pp. 182-193.
14. Cottet, G.-H. and El Ayyadi, M. 1996. Nonlinear PDE operators with memory terms for image processing, Proc. IEEE Int. Conf. Image Processing (ICIP-96), Lausanne, Vol. 1, pp. 481-483.
15. Cottet, G.-H. and Germain, L. 1993. Image processing through reaction combined with nonlinear diffusion, Math. Comp., Vol. 61, pp. 659-673.
16. Ford, G.E., Estes, R.R. and Chen, H. 1992. Scale-space analysis for image sampling and interpolation, Proc. IEEE Int. Conf. Acoustics, Speech and Signal Processing (ICASSP-92), San Francisco, Vol. 3, pp. 165-168.
17. Förstner, M.A. and Gülch, E. 1987. A fast operator for detection and precise location of distinct points, corners and centres of circular features, Proc. ISPRS Intercommission Conf. on Fast Processing of Photogrammetric Data (Interlaken), pp. 281-305.
18. Gerig, G., Kühler, O., Kikinis, R. and Jolesz, F.A. 1992. Nonlinear anisotropic filtering of MRI data, IEEE Trans. Medical Imaging, Vol. 11, pp. 221-232.
19. van Gogh, V. 1889. Selfportrait, Saint-Rémy, Paris, Museé d'Orsay.
20. van Gogh, V. 1890. Road with cypress and star, Auvers-sur-Oise, Otterlo, Rijksmuseum Kröller-Müller.
21. Granlund, G.H. and Knutsson, H. 1995. Signal processing for computer vision, Kluwer, Dordrecht.
22. Gonzalez, R.C. and Wintz, P. 1987. Digital image processing, Addison-Wesley, Reading.
23. ter Haar Romeny, B.M., Ed. 1994. Geometry-driven diffusion in computer vision, Kluwer, Dordrecht.
24. ter Haar Romeny, B.M., Niessen, W.J., Weickert, J., van Roermund, P., van Enk, W.J., Lopez, A. and Maas, R. 1996. Orientation detection of trabecular bone, in Progress in Biophysics and Molecular Biology, Proc. 12th Int. Biophysics Congress, Amsterdam, Vol. 65, Poster P-H5-43.
25. Hummel, R.A. 1986. Representations based on zero-crossings in scale space, Proc. IEEE Comp. Soc. Conf. Computer Vision and Pattern Recognition (CVPR '86), Miami Beach, IEEE Computer Society Press, Washington, pp. 204-209.
26. Iijima, T. 1962. Basic theory on normalization of pattern (in case of typical one-dimensional pattern), Bulletin of the Electrotechnical Laboratory, Vol. 26, pp. 368-388 (in Japanese).
27. Jähne, B. 1993. Spatio-temporal image processing, Lecture Notes in Comp. Science, Vol. 751, Springer, Berlin.
28. Kass, M. and Witkin, A. 1987. Analyzing oriented patterns, Computer Vision, Graphics, and Image Processing, Vol. 37, pp. 362-385.
29. Kawohl, B. and Kutev, N. 1997 Maximum and comparison principles for anisotropic diffusion, Preprint, Mathematical Institute, University of Cologne, 50923 Cologne, Germany.
30. Kimia, B.B., Tannenbaum, A. and Zucker, S.W. 1990. Towarda computational theory of shape: An overview, in O. Faugeras, Ed., Computer Vision - ECCV '90, Lecture Notes in Comp. Science, 427, Springer, Berlin, pp. 402-407.
31. Koenderink, J.J. 1984. The structure of images, Biol. Cybern., Vol. 50, pp. 363-370.
32. Krissian, K., Malandain, G. and Ayache, N. 1996. Directional anisotropic diffusion applied to segmentation of vessels in 3D images, in B. ter Haar Romeny, L. Florack, J. Koenderink and M. Viergever, Eds., Scale-space theory in computer vision, Lecture Notes in Comp. Science, 1252, Springer, Berlin, pp. 345-348.
33. Lindeberg, T. and Gårding, J. 1997. Shape-adapted smoothing in estimation of 3-D depth cues from affine distortions of local 2-D brightness structure, Image and Vision Computing, Vol. 15, pp. 415-434.
34. Marchuk, G.I. 1990. Splitting and alternating direction methods, in P.O. Ciarlet and J.-L. Lions, Eds., Handbook of numerical analysis. Vol. I, pp. 197-462.
35. Meyer, H. and Culman, M. 1867. Die Architektur der Spongiosa, Arch. Anat. Physiol., Vol. 47, pp. 615-628.
36. Niessen, W.J., López, A.M., van Enk, W.J., van Roermund, P.M., ter Haar Romeny, B.M. and Viergever, M.A. 1997. In vivo analysis of trabecular bone architecture, in J.S. Duncan and G. Gindi, Eds., Information processing in medical imaging, Lecture Notes in Comp. Science, 1230, Springer, Berlin, pp. 435-440.
37. Niessen, W.J., Vincken, K.L., Weickert, J. and Viergever, M.A. 1997a. Nonlinear multiscale representations for image segmentation, Computer Vision and Image Understanding, Vol. 66, pp. 233-245.
38. Niessen, W.J., Vincken, K.L., Weickert, J. and Viergever, M.A. 1998. Three-dimensional MR brain segmentation, Proc. Sixth Int. Conf. on Computer Vision (ICCV '98), Bombay, pp. 53-58.
39. Nitzberg, M. and Shiota, T. 1992. Nonlinear image filtering with edge and corner enhancement, IEEE Trans. Pattern Anal. Mach. Intell, Vol. 14, pp. 826-833.
40. Olver, P.J., Sapiro, G. and Tannenbaum, A. 1994. Classification and uniqueness of invariant geometric flows, C. R. Acad. Sci. Paris, t. 319, Série I, pp. 339-344.
41. Payot, E., Guillemaud, R., Trousset, Y. and Preteux, F. 1996. An adaptive and constrained model for 3D X-ray vascular reconstruction, in P. Orangeat and J.-L. Amans, Eds., Three-dimensional image reconstruction in radiation and nuclear medicine, Kluwer Academic Publishers, Dordrecht, pp. 47-57.
42. Perona, P. and Malik, J. 1990. Scale space and edge detection using anisotropic diffusion, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 12, pp. 629-639.
43. Rambaux, I. and Garçon, P. 1994. Nonlinear anisotropic diffusion filtering of 3D images, project work, Département Génie Mathématique, INSA de Rouen and Laboratory of Technomathematics, University of Kaiserslautern.
44. Rao, A.R. and Schunck, B.G. 1991. Computing oriented texture fields, CVGIP: Graphical Models and Image Processing, Vol. 53, pp. 157-185.
45. Rieger, J.H. 1995. Generic evolution of edges on families of diffused greyvalue surfaces, J. Math. Imag. Vision, Vol. 5, pp. 207-217.
46. Sapiro, G. and Tannenbaum, A. 1993. Affine invariant scale-space, Int. J. Comput. Vision, Vol. 11, pp. 25-44.
47. Schwarz, H.R. 1988. Numerische Mathematik, Teubner, Stuttgart.
48. Sporring, J. and Weickert, J. 1997. On generalized entropies and scale-space, in B. ter Haar Romeny, L. Florack, J. Koenderink and M. Viergever, Eds., Scale-space theory in computer vision, Lecture Notes in Comp. Science, 1252, Springer, Berlin, pp. 53-64.
49. Vincken, K.L., Koster, A.S.E, and Viergever, M.A. 1997. Probabilistic multiscale image segmentation, IEEE Trans. Pattern Anal. Mach. Intell, pp. 109-120.
50. Weickert, J. 1995. Multiscale texture enhancement, in V Hlaváč and R. Šára, Eds., Computer analysis of images and patterns, Lecture Notes in Comp. Science, 970, Springer, Berlin, pp. 230-237.
51. Weickert, J. 1996. Theoretical foundations of anisotropic diffusion in image processing, Computing, Suppl. 11, pp. 221-236.
52. Weickert, J. 1997. Coherence-enhancing diffusion of colour images, in A. Sanfeliu, J.J. Villanueva and J. Vitrià, Eds., Pattern Recognition and Image Analysis (VII NSPRIA), Barcelona, Vol. 1, pp. 239-244.
53. Extended version to appear in Image and Vision Computing, Vol. 17, pp. 199-210, 1999.
54. Weickert, J. 1997a. A review of nonlinear diffusion filtering, in B. ter Haar Romeny, L. Florack, J. Koenderink and M. Viergever, Eds., Scale-space theory in computer vision, Lecture Notes in Comp. Science, 1252, Springer, Berlin, pp. 3-28.
55. Weickert, J. 1998. Anisotropic diffusion in image processing, Teubner-Verlag, Stuttgart.
56. Weickert, J., Ishikawa, S. and A. Imiya. 1997. On the history of Gaussian scale-space axiomatics, in J. Sporring, M. Nielsen, L. Florack and P. Johansen, Eds., Gaussian scale-space theory, Kluwer Academic Publishers, Dordrecht, pp. 45-59.
57. Weickert, J., ter Haar Romeny, B.M., Lopez, A. and van Enk, W.J. 1997a. Orientation analysis by coherence-enhancing diffusion, Proc. Symp. Real World Computing (RWC '97), Tokyo, pp. 96-103.
58. Weickert, J., ter Haar Romeny, B.M. and Viergever, M.A. 1998. Efficient and reliable schemes for nonlinear diffusion filtering, IEEE Trans. Image Proc., Vol. 7, pp. 398-410.
59. Weickert, J., Zuiderveld, K.J., ter Haar Romeny, B.M. and Niessen, W.J. 1997b. Parallel implementations of AOS schemes: A fast way of nonlinear diffusion filtering, Proc. 1997 IEEE International Conference on Image Processing (ICIP-97), Santa Barbara, Vol 3., pp. 396-399.
60. Witkin, A.P. 1983. Scale-space filtering, Proc. Eighth Int. Joint Conf. on Artificial Intelligence (IJCAI '83), Karlsruhe, Vol. 2, pp. 1019-1022.
61. Wolff, J. 1870. Über die innere Architektur der Knochen, Virchows Arch., Vol. 50, pp. 389-453.
62. Yang, G.Z., Burger, P., Firmin, D.N., Underwood, S.R. 1996. Structure adaptive anisotropic filtering, Image and Vision Computing, Vol. 14, pp. 135-145.