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Title: Finite-volume level set method and its adaptive version in completing subjective contours (English)
Author: Krivá, Zuzana
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 43
Issue: 4
Year: 2007
Pages: 509-522
Summary lang: English
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Category: math
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Summary: 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. (English)
Keyword: image processing
Keyword: nonlinear partial differential equations
Keyword: numerical solution
Keyword: finite volume method
Keyword: adaptivity
Keyword: grid coarsening
MSC: 35A35
MSC: 35K20
MSC: 35K55
MSC: 65M06
MSC: 65M12
MSC: 68M10
idZBL: Zbl 1140.35323
idMR: MR2377929
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Date available: 2009-09-24T20:26:25Z
Last updated: 2012-06-06
Stable URL: http://hdl.handle.net/10338.dmlcz/135793
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Reference: [1] 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 MR 1700751
Reference: [2] 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 Zbl 1065.65105, MR 1961884
Reference: [3] Kanizsa G.: Organization in Vision.Hardcover 1979
Reference: [4] 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
Reference: [5] 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
Reference: [6] Krivá Z.: Adaptive Finite Volume Methods in Image Processing.Edícia vedeckých prác, STU Bratislava, Stavebná fakulta 2004
Reference: [7] 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 MR 2194701
Reference: [8] 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 MR 2214835
Reference: [9] 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
Reference: [10] 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
Reference: [11] 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 MR 0965860
Reference: [12] 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 Zbl 0966.68214, MR 1760935
Reference: [13] Sarti A., Citti G.: Subjective surfaces and Riemannian mean curvature flow graphs.Acta Math. Univ. Comenianae 70 (2001), 1, 85–104 MR 1865362
Reference: [14] Sarti A., Malladi, R., Sethian J. A.: Subjective surfaces: A geometric model for boundary completion.Internat. J. Computer Vision 46 (2002), 3, 201–221 Zbl 1012.68727
Reference: [15] Sethian J. A.: Numerical algorithm for propagating interfaces: Hamilton–Jacobi equations and conservation laws.J. Diff. Geom. 31 (1990), 131–161 MR 1030668
Reference: [16] 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 Zbl 0973.76003, MR 1700751
Reference: [17] Walkington N. J.: Algorithms for computing motion by mean curvature.In: SIAM J. Numer. Anal. 33 (1996), 6, 2215–2238 Zbl 0863.65061, MR 1427460
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