Finite volume schemes for the generalized subjective surface equation in image segmentation

Karol Mikula; Mariana Remešíková

Kybernetika (2009)

  • Volume: 45, Issue: 4, page 646-656
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Mikula, Karol, and Remešíková, Mariana. "Finite volume schemes for the generalized subjective surface equation in image segmentation." Kybernetika 45.4 (2009): 646-656. <http://eudml.org/doc/37720>.

@article{Mikula2009,
abstract = {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.},
author = {Mikula, Karol, Remešíková, Mariana},
journal = {Kybernetika},
keywords = {image segmentation; finite volume method; flux-based level set method; finite volume method; flux-based level set method; image segmentation},
language = {eng},
number = {4},
pages = {646-656},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Finite volume schemes for the generalized subjective surface equation in image segmentation},
url = {http://eudml.org/doc/37720},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Mikula, Karol
AU - Remešíková, Mariana
TI - Finite volume schemes for the generalized subjective surface equation in image segmentation
JO - Kybernetika
PY - 2009
PB - Institute of Information Theory and Automation AS CR
VL - 45
IS - 4
SP - 646
EP - 656
AB - 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.
LA - eng
KW - image segmentation; finite volume method; flux-based level set method; finite volume method; flux-based level set method; image segmentation
UR - http://eudml.org/doc/37720
ER -

References

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  3. Convergence analysis of finite volume scheme for nonlinear tensor anisotropic diffusion in image processing, SIAM J. Numer. Anal. 46 (2007), 1, 37–60. MR2377254
  4. A counting number of cells and cell segmentation using advection-diffusion equations, Kybernetika 43 (2007), 6, 817–829. MR2388396
  5. Flux-based level set method: A finite volume method for evolving interfaces, Appl. Numer. Math. 57 (2007), 4, 436–454. MR2310759
  6. Zebrafish early embryogenesis 3D image filtering by nonlinear partial differential equations, Medical Image Analysis (to appear). 
  7. 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. MR2451456
  8. Subjective surfaces and Riemannian mean curvature flow graphs, Acta Math. Univ. Comenian. 70 (2000), 85–103. MR1865362
  9. Subjective Surfaces: A Method for Completing Missing Boundaries, Proc. Nat. Acad. Sci. 12 (2000), 97, 6258–6263. MR1760935
  10. Subjective surfaces: A geometric nodel for boundary completion, Internat. J. Comput. Vision 46 (2002), 3, 201–221. 

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