| Title:
|
Numerical analysis of a semi-implicit DDFV scheme for the regularized curvature driven level set equation in 2D (English) |
| Author:
|
Handlovičová, Angela |
| Author:
|
Kotorová, Dana |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
49 |
| Issue:
|
6 |
| Year:
|
2013 |
| Pages:
|
829-854 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Stability and convergence of the linear semi-implicit discrete duality finite volume (DDFV) numerical scheme in 2D for the solution of the regularized curvature driven level set equation is proved. Numerical experiments concerning comparison with exact solution and image filtering problem using proposed scheme are included. (English) |
| Keyword:
|
mean curvature flow |
| Keyword:
|
level set equation |
| Keyword:
|
numerical solution |
| Keyword:
|
semi-implicit scheme |
| Keyword:
|
discrete duality finite volume method |
| Keyword:
|
stability |
| Keyword:
|
convergence |
| MSC:
|
35K55 |
| MSC:
|
35K65 |
| MSC:
|
65M08 |
| MSC:
|
65M12 |
| idZBL:
|
Zbl 1290.65083 |
| idMR:
|
MR3182643 |
| . |
| Date available:
|
2014-01-27T12:23:31Z |
| Last updated:
|
2015-03-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143573 |
| . |
| Reference:
|
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| Reference:
|
[2] Barles, G., Souganidis, P. E.: Convergence of approximation schemes for fully nonlineae second order equations..Asymptotic Anal. 4 (1991), 3, 271-283. Zbl 0729.65077 MR 1115933 |
| Reference:
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[3] Corsaro, S., Mikula, K., Sarti, A., Sgallari, F.: Semi-implicit covolume method in 3D image segmentation..SIAM J. Sci. Comput Vol. 28 (2006), 6, 2248-2265. Zbl 1126.65088 Zbl 1126.65088, MR 2272260, 10.1137/060651203 |
| Reference:
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[4] Evans, L. C., Spruck, J.: Motion of level sets by mean curvature I..J. Differential Geometry 33 (1991), 635-681. Zbl 0726.53029 Zbl 0726.53029, MR 1100206 |
| Reference:
|
[5] Eymard, R., Gallouët, T., Herbi, R.: The finite volume method..In: Handbook of Numerical Analysis, Ph. Ciarlet J.L. Lions eds 2000, pp. 715-1022. Zbl 0981.65095 MR 1804748 |
| Reference:
|
[6] Eymard, R., Handlovičová, A., Mikula, K.: Study of a finite volume scheme for the regularized mean curvature flow level set equation..IMA Journal of Numerical Analysis 31 (2011), 3, 813-846. Zbl 1241.65072 Zbl 1241.65072, MR 2832781, 10.1093/imanum/drq025 |
| Reference:
|
[7] Handlovičová, A., Mikula, K.: Stability and consistency of the semi-implicit co-volume scheme for regularized mean curvature flow equation in level set formulation..Appl. Math., Praha 53 (2008), 2, 105-129. Zbl 1199.35197 Zbl 1199.35197, MR 2399901, 10.1007/s10492-008-0015-z |
| Reference:
|
[8] Handlovičová, A., Kotorová, D.: Stability of the semi-implicit discrete duality finite volume scheme for the curvature driven level set equation in 2D..Accepted in Tatra mountains mathematical publications. |
| Reference:
|
[9] Handlovičová, A., Mikula, K., Sgallari, F.: Semi-implicit complementary volume scheme for solving level set like equations in image processing and curve evolution..Numer. Math.93 (2003), No. 4, 675-695. Zbl 1065.65105 Zbl 1065.65105, MR 1961884, 10.1007/s002110100374 |
| Reference:
|
[10] Handlovičová, A., Mikula, K., Sgallari, F.: Variational numerical methods for solving nonlinear diffusion equations arising in image processing..J. Visual Communication and Image Representation 13 (2002), 217-237. 10.1006/jvci.2001.0479 |
| Reference:
|
[11] Kotorová, D.: Discrete duality finite volume scheme for the curvature-driven level set equation in 3D..In: Advances in architectural, civil and environmental engineering: 22nd Annual PhD Student Conference. Bratislava 2012 |
| Reference:
|
[12] Kotorová, D.: Comparison of the 3D numerical scheme for solving curvature-driven level set equation based on discrete duality finite volumes..Accepted to proceedings of ODAM conference Olomouc 2013 |
| Reference:
|
[13] Mikula, K., Sarti, A., Sgallari, F.: Co-volume method for Riemannian mean curvature flow in subjective surfaces multiscale segmentation..Comput. Visual. Sci. 9 (2006), 1, 23-31. MR 2214835, 10.1007/s00791-006-0014-0 |
| Reference:
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[14] Oberman, A. M.: A convergent monotone difference scheme for motion of level sets by mean curvature..Numer. Math. 99 (2004), 2, 365-379. Zbl 1070.65082 Zbl 1070.65082, MR 2107436, 10.1007/s00211-004-0566-1 |
| Reference:
|
[15] Osher, S., Fedkiw, R.: Level set methods and dynamic implicit surfaces..Springer-Verlag 2003. Zbl 1026.76001 Zbl 1026.76001, MR 1939127 |
| Reference:
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[16] Sethian, J. A.: Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Material Science..Cambridge University Press, New York 1999. Zbl 0973.76003 MR 1700751 |
| Reference:
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[17] Walkington, N.: Algorithms for computing motion by mean curvature.SIAM J. Numer. Anal. 33 (1996), 6, 2215-2238. Zbl 0863.65061 Zbl 0863.65061, MR 1427460, 10.1137/S0036142994262068 |
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