| Title:
|
Finite volume schemes for the generalized subjective surface equation in image segmentation (English) |
| Author:
|
Mikula, Karol |
| Author:
|
Remešíková, Mariana |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
45 |
| Issue:
|
4 |
| Year:
|
2009 |
| Pages:
|
646-656 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we describe an efficient method for 3D image segmentation. The method uses a PDE model – the so called generalized subjective surface equation which is an equation of advection-diffusion type. The main goal is to develop an efficient and stable numerical method for solving this problem. The numerical solution is based on semi-implicit time discretization and flux-based level set finite volume space discretization. The space discretization is discussed in details and we introduce three possible alternatives of the so called diamond cell finite volume scheme for this type of 3D nonlinear diffusion equation. We test the performance of the method and all its variants introduced in the paper by determining the experimental order of convergence. Finally we show a couple of practical applications of the method. (English) |
| Keyword:
|
image segmentation |
| Keyword:
|
finite volume method |
| Keyword:
|
flux-based level set method |
| MSC:
|
35A99 |
| MSC:
|
35K93 |
| MSC:
|
65D18 |
| MSC:
|
65M08 |
| MSC:
|
68U10 |
| MSC:
|
74S10 |
| idZBL:
|
Zbl 1209.68473 |
| idMR:
|
MR2588630 |
| . |
| Date available:
|
2010-06-02T19:02:19Z |
| Last updated:
|
2013-09-21 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140062 |
| . |
| Reference:
|
[1] S. Corsaro, K. Mikula, A. Sarti, and F. Sgallari: Semi-implicit co-volume method in 3D image segmentation.SIAM J. Sci. Comput. 28 (2006), 6, 2248–2265. MR 2272260 |
| Reference:
|
[2] Y. Coudiere, J. P. Vila, and P. Villedieu: Convergence rate of a finite volume scheme for a two-dimensional convection-diffusion problem.M2AN Math. Model. Numer. Anal. 33 (1999), 493–516. MR 1713235 |
| Reference:
|
[3] O. Drblíková and K. Mikula: Convergence analysis of finite volume scheme for nonlinear tensor anisotropic diffusion in image processing.SIAM J. Numer. Anal. 46 (2007), 1, 37–60. MR 2377254 |
| Reference:
|
[4] P. Frolkovič, K. Mikula, N. Peyriéras, and A. Sarti: A counting number of cells and cell segmentation using advection-diffusion equations.Kybernetika 43 (2007), 6, 817–829. MR 2388396 |
| Reference:
|
[5] P. Frolkovič and K. Mikula: Flux-based level set method: A finite volume method for evolving interfaces.Appl. Numer. Math. 57 (2007), 4, 436–454. MR 2310759 |
| Reference:
|
[6] Z. Krivá, K.Mikula, N. Peyriéras, B. Rizzi, and A. Sarti: Zebrafish early embryogenesis 3D image filtering by nonlinear partial differential equations.Medical Image Analysis (to appear). |
| Reference:
|
[7] K. Mikula, N. Peyriéras, M. Remešíková, and A. Sarti: 3D embryogenesis image segmentation by the generalized subjective surface method using the finite volume technique.In: Proc. FVCA5 – 5th International Symposium on Finite Volumes for Complex Applications, Hermes Publ., Paris 2008. MR 2451456 |
| Reference:
|
[8] A. Sarti and G. Citti: Subjective surfaces and Riemannian mean curvature flow graphs.Acta Math. Univ. Comenian. 70 (2000), 85–103. MR 1865362 |
| Reference:
|
[9] A. Sarti, R. Malladi, and J. A. Sethian: Subjective Surfaces: A Method for Completing Missing Boundaries.Proc. Nat. Acad. Sci. 12 (2000), 97, 6258–6263. MR 1760935 |
| Reference:
|
[10] A. Sarti, R. Malladi, and J. A. Sethian: Subjective surfaces: A geometric nodel for boundary completion.Internat. J. Comput. Vision 46 (2002), 3, 201–221. |
| . |
