| Title:
|
Perona-Malik equation: properties of explicit finite volume scheme (English) |
| Author:
|
Handlovičová, Angela |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
43 |
| Issue:
|
4 |
| Year:
|
2007 |
| Pages:
|
523-532 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The Perona–Malik nonlinear parabolic problem, which is widely used in image processing, is investigated in this paper from the numerical point of view. An explicit finite volume numerical scheme for this problem is presented and consistency property is proved. (English) |
| Keyword:
|
Perona–Malik equation |
| Keyword:
|
finite volume method |
| Keyword:
|
consistency |
| Keyword:
|
stability monotonicity property |
| MSC:
|
35K20 |
| MSC:
|
35K55 |
| MSC:
|
65M12 |
| MSC:
|
65M60 |
| MSC:
|
68M10 |
| idZBL:
|
Zbl 1140.35321 |
| idMR:
|
MR2377930 |
| . |
| Date available:
|
2009-09-24T20:26:33Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135794 |
| . |
| Reference:
|
[1] Barles G., Souganidis P. E.: Convergence of approximation schemes for fully nonlinear second order equations.Asymptotic Analysis 4 (1991), 271–283 Zbl 0729.65077, MR 1115933 |
| Reference:
|
[2] Catté F. , Lions P. L., Morel J. M., Coll T.: Image selective smoothing and edge detection by nonlinear diffusion.SIAM J. Numer. Anal. 29 (1992), 182–193 Zbl 0746.65091, MR 1149092 |
| Reference:
|
[3] Eymard R., Gallouet, T., Herbin R.: The Finite Volume Method.In: Handbook of Numerical Analysis, Vol. VII, 2000 (Ph. Ciarlet and J. L. Lions, eds.), pp. 715–1022 Zbl 1173.76359, MR 1804748 |
| Reference:
|
[4] Handlovičová A., Krivá Z.: Properties of explicit finite volume scheme for Perona–Malik Equation.In: Proc. Prastan 04, Kočovce 2004, pp. 133–140 |
| Reference:
|
[5] Handlovičová A., Krivá Z.: Error estimates for finite volume scheme for Perona–Malik Equation.Acta Math. Univ. Comenianae LXXIV 1 (2005), 79–94 Zbl 1108.35083, MR 2154399 |
| Reference:
|
[6] Handlovičová A., Mikula K.: Convergence of the semi-implicit co-volume scheme for the curvature driven level set equation.To appear |
| Reference:
|
[7] Krivá Z.: Explicit finite volume scheme for the Perona–Malik equation.Computational Methods in Applied Math. 5 (2005), 2, 170–200 |
| Reference:
|
[8] Krivá Z., Mikula K.: An adaptive finie volume scheme for solving nonlinear diffusion equations in image processing.J. Visual. Comm. and Image Representation 13 (2002), 22–35 |
| Reference:
|
[9] Mikula K., Ramarosy N.: Semi-implicit finite volume scheme for solving nonlinear diffusion equations in image processing.Numer. Math. 89 (2001), 3, 561–590 Zbl 1013.65094, MR 1864431 |
| . |
