# Finite-volume level set method and its adaptive version in completing subjective contours

Kybernetika (2007)

- Volume: 43, Issue: 4, page 509-522
- ISSN: 0023-5954

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topKrivá, Zuzana. "Finite-volume level set method and its adaptive version in completing subjective contours." Kybernetika 43.4 (2007): 509-522. <http://eudml.org/doc/33876>.

@article{Krivá2007,

abstract = {In this paper we deal with a problem of segmentation (including missing boundary completion) and subjective contour creation. For the corresponding models we apply the semi-implicit finite volume numerical schemes leading to methods which are robust, efficient and stable without any restriction to a time step. The finite volume discretization enables to use the spatial adaptivity and thus improve significantly the computational time. The computational results related to image segmentation with partly missing boundaries and subjective contour extraction are presented.},

author = {Krivá, Zuzana},

journal = {Kybernetika},

keywords = {image processing; nonlinear partial differential equations; numerical solution; finite volume method; adaptivity; grid coarsening; image processing; segmentation; subjective contour creation; spatial adaptivity},

language = {eng},

number = {4},

pages = {509-522},

publisher = {Institute of Information Theory and Automation AS CR},

title = {Finite-volume level set method and its adaptive version in completing subjective contours},

url = {http://eudml.org/doc/33876},

volume = {43},

year = {2007},

}

TY - JOUR

AU - Krivá, Zuzana

TI - Finite-volume level set method and its adaptive version in completing subjective contours

JO - Kybernetika

PY - 2007

PB - Institute of Information Theory and Automation AS CR

VL - 43

IS - 4

SP - 509

EP - 522

AB - In this paper we deal with a problem of segmentation (including missing boundary completion) and subjective contour creation. For the corresponding models we apply the semi-implicit finite volume numerical schemes leading to methods which are robust, efficient and stable without any restriction to a time step. The finite volume discretization enables to use the spatial adaptivity and thus improve significantly the computational time. The computational results related to image segmentation with partly missing boundaries and subjective contour extraction are presented.

LA - eng

KW - image processing; nonlinear partial differential equations; numerical solution; finite volume method; adaptivity; grid coarsening; image processing; segmentation; subjective contour creation; spatial adaptivity

UR - http://eudml.org/doc/33876

ER -

## References

top- Evans L. C., Spruck J., Motion of level sets by curvature I, In: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Material Science. Cambridge University Press, Cambridge 1999 MR1700751
- 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), 675–695 Zbl1065.65105MR1961884
- Kanizsa G., Organization in Vision, Hardcover 1979
- Krivá Z., Mikula K., An adaptive finite volume scheme for solving nonlinear diffusion equations in image processing, J. Visual Communication and Image Representation 13 (2002), 22–35
- Krivá Z., Mikula K., An adaptive finite volume scheme in processing of color images, In: Proc. ALGORITMY 2000, Conference on Scientific Computing, Podbanské 2000, pp. 174–188
- Krivá Z., Adaptive Finite Volume Methods in Image Processing, Edícia vedeckých prác, STU Bratislava, Stavebná fakulta 2004
- Krivá Z., Segmentation combining approaches based on mean curvature, In: Mathematical Modelling and Analysis 2005, Proc. 10th International Conference MMA2005&CMAM2, Trakai 2005, pp. 433–441 MR2194701
- Mikula K., Sarti,, A, Sgallari F., Co-volume method for Riemennian mean curvature flow in subjective surface multiscale segmentation, Comput. Visual Sci. 9 (2006), 1, 23–31 MR2214835
- Mikula K., Sarti, A., Sgallari F., Co-volume level set method in subjective surface based medical image segmentation, In: Handbook of Biomedical Image Analysis, Kluwer Academic/Plenum Publishers, Dordrecht 2005, pp. 583–626
- Mikula K., Sarti A., Parallel co-volume subjective surface method for 3D medical image segmentation, In: Deformable Model (J. Suri, ed.), Springer–Verlag, Berlin 2006, to appear
- Osher S., Sethian J. A., Front propagating with curvature dependent speed: algorithms based on the Hamilton–Jacobi formulation, J. Comput. Phys. 79 (1988), 12–49 (1988) MR0965860
- Sarti A., Malladi, R., Sethian J. A., Subjective surfaces: A method for completing missing boundaries, Proc. Nat. Acad. Sci. U.S.A. 12 (2000), 97, pp. 6258–6263 Zbl0966.68214MR1760935
- Sarti A., Citti G., Subjective surfaces and Riemannian mean curvature flow graphs, Acta Math. Univ. Comenianae 70 (2001), 1, 85–104 MR1865362
- Sarti A., Malladi, R., Sethian J. A., Subjective surfaces: A geometric model for boundary completion, Internat. J. Computer Vision 46 (2002), 3, 201–221 Zbl1012.68727
- Sethian J. A., Numerical algorithm for propagating interfaces: Hamilton–Jacobi equations and conservation laws, J. Diff. Geom. 31 (1990), 131–161 (1990) MR1030668
- Sethian J. A., Level set methods and fast marching methods, In: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Material Science. Cambridge University Press, Cambridge 1999 Zbl0973.76003MR1700751
- Walkington N. J., Algorithms for computing motion by mean curvature, In: SIAM J. Numer. Anal. 33 (1996), 6, 2215–2238 (1996) Zbl0863.65061MR1427460

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