Slow and fast diffusion effects in image processing

Computing and Visualization in Science

Volumn 3, Issue 4, 2001, Pages 185-195

  Kačur, Jozef ^a   Mikula, Karol ^b  

^a Physics and Informatics   (Slovakia)

^b SLOVAK UNIVERSITY OF TECHNOLOGY   (Slovakia)

Author keywords

[No Author keywords available]

Indexed keywords

INITIAL VALUE PROBLEMS; NONLINEAR EQUATIONS;

ANISOTROPIC DIFFUSION; CONVERGENCE RESULTS; INITIAL-BOUNDARY VALUE PROBLEMS; INTENSITY FUNCTIONS; MULTI SCALE ANALYSIS; NUMERICAL EXPERIMENTS; NUMERICAL TECHNIQUES; STRONGLY NONLINEAR;

IMAGE PROCESSING;

EID: 0008715823     PISSN: 14329360     EISSN: 14330369     Source Type: Journal    
DOI: 10.1007/s007910000047     Document Type: Article

References (31)

1. Alt, H.W., Luckhaus, S.: Quasilinear elliptic-parabolic differential equations. Math. Zeitschrift 183, 311-341 (1983)
2. Alvarez, L., Guichard, F., Lions, P.L., Morel, J.M.: Axioms and Fundamental Equations of Image Processing. Arch. Rat. Mech. Anal. 123, 200-257 (1993)
3. Alvarez, L., Morel, J.M.: Formalization and computational aspects of image analysis. Acta Numerica. 1-59 (1994)
4. Bänsch, E., Mikula, K.: A coarsening finite element strategy in image selective smoothing. Computing and Visualization in Science 1, 53-61 (1997)
5. Bänsch, E., Mikula, E.K.: Adaptivity in 3D image processing. Preprint 99-14, Zentrum für Technomathematik, Universität Bremen 1999
6. Berger, A.E., Brezis, H., Rogers, J.C.W.: A numerical method for solving the problem ut - f(u)= 0 R.A.I.R.O. Anal. Numer. 13, 297-312 (1979)
7. Catté, F. Lions, P.L., Morel, J.M., Coll, T.: Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal. 29, 182-193 (1992)
8. Gajewski, H., Gröger, K., Zacharias, K.: Nichtlineare Operatorgleichnungen und Operatordifferentialgleichungen. Berlin: Academia-Verlag 1974
9. Handlovicová, A.: Solution of Stefan problem by fully discrete linear schemes. Acta Math. Univ. Comenianae LXVII 2, 351-372 (1998)
10. Jäger,W., Kacur, J.: Solution of porous medium type systems by linear approximation schemes. Num. Math. 60, 407-427 (1991)
11. Jäger, W., Kacur, J.: Approximation of degenerate elliptic-parabolic problems by nondegenerate elliptic and parabolic problems. Preprint, University of Heidelberg 1991
12. Jäger, W., Kacur, J.: Solution of doubly nonlinear and degenerate parabolic problems by relaxation schemes. Mathematical Modelling and Numerical Analysis 29, 605-627 (1995)
13. Kacur, J.: Solution of some free boundary problems by relaxation schemes. SIAM J. Numer. Anal. 36, No. 1, 290-316 (1999)
14. Kacur, J.: Solution to strongly nonlinear parabolic problems by a linear approximation scheme. IMA J. Numer. Anal. 19, 119-145 (1999)
15. Kacur, J., Handlovicová, A., Kacurová, M.: Solution of nonlinear diffusion problems by linear approximation schemes. SIAM J. Num. Anal. 30, 1703-1722 (1993)
16. Kacur, J., Mikula, K.: Solution of nonlinear diffusion appearing in image smoothing and edge detection. Applied Numerical Mathematics 17, 47-59 (1995)
17. Kacur, J., Mikula, K.: Slow and fast diffusion effects in image processing - approximation schemes and numerical experiments. Preprint 96-26 IWR University of Heidelberg 1996
18. Kacur, J., Mikula, K.: Slowed anisotropic diffusion. Scale Space Theory in Computer Vision (ed. by B.M.t.H. Romeny et al.) Lecture Notes in Computer Science 1252, 357-360 (Springer 1997)
19. Krasnoselskij, M., Rutickij, J.: Convex functions and Orlicz Spaces. Moscow: GITTL 1958
20. Kufner, A., John, O., Fucik, S.: Function Spaces. Prague: Academia 1977
21. Lions, P.L.: Axiomatic derivation of image processing models. Mathematical Models Methods in Applied Sciences 4, 467-475 (1994)
22. Magenes, E., Nochetto, R.H., Verdi, C.: Energy error estimates for a linear scheme to approximate nonlinear parabolic problems. Math. Mod. Num. Anal. 21, 655-678 (1987)
23. Mikula, K.: Solution of nonlinear curvature driven evolution of plane convex curves. Applied Numerical Mathematics 23, 347-360 (1997)
24. Mikula, K., Kacur, J.: Evolution of convex plane curves describing anisotropic motions of phase interfaces. SIAM J. Sci. Comput. 17, 1302-1327 (1996)
25. Mikula, K., Ramarosy, N.: Semi-implicit finite volume scheme for solving nonlinear diffusion equations in image processing. to appear in Num. Math.
26. Necas, J.: Les methodes directes en theorie des equations elliptiques. Prague: Academia 1967
27. Nochetto, R.H., Verdi, C.: Approximation of degenerate parabolic problems using numerical integration. SIAM J. Numer. Anal. 25, 784- 814 (1988)
28. Patankar, S.: Numerical heat transfer and fluid flow. New York: Hemisphere Publ. Corp. 1980
29. Perona, P., Malik, J.: Scale space and edge detection using anisotropic diffusion. in Proc. IEEE Computer Society Workshop on Computer Vision 1987
30. Romeny, B.M.t.H. (ed.): Geometry driven diffusion in computer vision. Dodrecht: Kluwer Academic Publishers 1994
31. Slodicka, M.: Solution of nonlinear parabolic problems by linearization. in Proc. ISNA'92, Prague 1994