Recursive separable schemes for nonlinear diffusion filters

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

Volumn 1252, Issue , 1997, Pages 260-271

  Weickert, Joachim ^a,b  

^a UNIVERSITY MEDICAL CENTER UTRECHT   (Netherlands)

^b UNIVERSITY OF COPENHAGEN   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

BANDPASS FILTERS; COMPUTATIONAL COMPLEXITY; COMPUTER VISION; DIFFUSION; EFFICIENCY;

ABSOLUTE STABILITY; ADDITIVE OPERATOR SPLITTING; FAST RECURSIVE ALGORITHMS; NONLINEAR DIFFUSION; NONLINEAR DIFFUSION FILTERING; NONLINEAR DIFFUSION FILTERS; ROTATIONAL INVARIANCES; SEMI-IMPLICIT SCHEME;

ONE DIMENSIONAL;

EID: 77957060002     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-63167-4_20     Document Type: Conference Paper

References (22)

1. S.T. Acton, A.C. Bovik, M.M. Crawford, Anisotropic diffusion pyramids for image segmentation,Pioc. IEEE Int. Conf. Image Processing (ICIP-94, Austin, Nov. 13-16, 1994), Vol. 3, IEEE Computer Society Press, Los Alamitos, 478-482, 1994.
2. L. Alvarez, Images and PDE's, M.-O. Berger, R. Deriche, I. Herlin, J. Jaffre, J.-M. Morel (Eds.), ICAOS '96: Images, wavelets and PDEs, Lecture Notes in Control and Information Sciences, Vol. 219, Springer, London, 3-14, 1996.
3. L.D. Cai, Some notes on repeated averaging smoothing, J. Kittler (Ed.), Pattern recognition, Lecture Notes in Comp. Science, Vol. 301, Springer, Berlin, 597-605, 1988.
4. F. Catte, P.-L. Lions, J.-M. Morel, T. Coll, Image selective smoothing and edge detection by nonlinear diffusion, SIAM J. Numer. Anal., Vol. 29, 182-193, 1992.
5. R. Deriche, Fast algorithms for low-level vision, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 12, 78-87, 1990.
6. J. Frohlieh, J. Weickert, Image processing using a wavelet algorithm for nonlinear diffusion, Report No. 104, Laboratory of Technomathematics, University of Kaiserslautern, P.O. Box 3049, 67653 Kaiserslautern, Germany, 1994.
7. T. Gijbels, P. Six, L. Van Gool, F. Catthoor, H. De Man, A. Oosterlinck, A VLSI-architecture for parallel non-linear diffusion with applications in vision, Proc. IEEE Workshop on VLSI Signal Processing, Vol. 7, 398-707, 1994.
8. A.R. Gourlay, Implicit convolution, Image Vision Comput., Vol. 3, 15-23, 1985.
9. B.M. ter Haar Romeny (Ed.), Geometry-driven diffusion in computer vision, Kluwer, Dordrecht, 1994.
10. R.A. Hummel, Representations based on zero-crossings in scale space, Proc. IEEE Comp. Soc. Conf. Computer Vision and Pattern Recognition (CVPR '86, Miami Beach, June 22-26, 1986), IEEE Computer Society Press, Washington, 204-209, 1986.
11. T. Iijima, Basic theory of pattern normalization (for the case of a typical one-dimensional pattern), Bulletin of the Electrotechnical Laboratory, Vol. 26, 368-388, 1962 (in Japanese).
12. J. Kacur, K. Mikula, Solution of nonlinear diffusion appearing in image smoothing and edge detection, Appl. Num. Math., Vol. 17, 47-59, 1995.
13. T. Lindeberg, Scale-space theory in computer vision, Kluwer, Boston, 1994.
14. G.I. Marchuk, Splitting and alternating direction methods, P.G. Ciarlet, J.-L. Lions (Eds.), Handbook of numerical analysis, Vol. 1, 197-462, 1990.
15. M. Nielsen, L. Florack, R. Deriche, Regularization, scale-space, and edge detection filters, B. Baxton, R. Cipolla (Eds.), Computer vision - ECCV '96, Volume II, Lecture Notes in Comp. Science, Vol. 1065, Springer, Berlin, 70-81, 1996.
16. W.J. Niessen, K.L. Vincken, J.A. Weickert, M.A. Viergever, Nonlinear mul-tiscale representations for image segmentation, Computer Vision and Image Understanding, 1997, in press.
17. P. Perona, J. Malik, Scale space and edge detection using anisotropic diffusion, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 12, 629-639, 1990.
18. J. Weickert, Theoretical foundations of anisotropic diffusion in image processing, W. Kropatsch, R. Klette, F. Solina (Eds.), Theoretical foundations of computer vision, Computing Suppl. 11, Springer, Wien, 221-236, 1996.
19. J. Weickert, Nonlinear diffusion scale-spaces: From the continuous to the discrete setting, M.-O. Berger, R. Deriche, I. Herlin, J. Jaffre, J.-M. Morel (Eds.), ICAOS '96: Images, wavelets and PDEs, Lecture Notes in Control and Information Sciences, Vol. 219, Springer, London, 111-118, 1996.
20. J. Weickert, Anisotropic diffusion in image processing, Teubner Verlag, Stuttgart, 1997, to appear.
21. J. Weickert, B.M. ter Haar Romeny, M.A. Viergever, Efficient and reliable schemes for nonlinear diffusion filtering, IEEE Trans. Image Proc, 1998, to appear.
22. J. Weickert, S. Ishikawa, A. Imiya, On the history of Gaussian scale-space ax-iomatics, J. Sporring, M. Nielsen, L. Florack, P. Johansen (Eds.), Gaussian scale-space theory, Kluwer, Dordrecht, 1997, in press.