Counting number of cells and cell segmentation using advection-diffusion equations

Peter Frolkovič; Karol Mikula; Nadine Peyriéras; Alex Sarti

Kybernetika (2007)

  • Volume: 43, Issue: 6, page 817-829
  • ISSN: 0023-5954

Abstract

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We develop a method for counting number of cells and extraction of approximate cell centers in 2D and 3D images of early stages of the zebra-fish embryogenesis. The approximate cell centers give us the starting points for the subjective surface based cell segmentation. We move in the inner normal direction all level sets of nuclei and membranes images by a constant speed with slight regularization of this flow by the (mean) curvature. Such multi- scale evolutionary process is represented by a geometrical advection-diffusion equation which gives us at a certain scale the desired information on the number of cells. For solving the problems computationally we use flux-based finite volume level set method developed by Frolkovič and Mikula in [FM1] and semi-implicit co-volume subjective surface method given in [CMSSg, MSSgCVS, MSSgchapter]. Computational experiments on testing and real 2D and 3D embryogenesis images are presented and the results are discussed.

How to cite

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Frolkovič, Peter, et al. "Counting number of cells and cell segmentation using advection-diffusion equations." Kybernetika 43.6 (2007): 817-829. <http://eudml.org/doc/33899>.

@article{Frolkovič2007,
abstract = {We develop a method for counting number of cells and extraction of approximate cell centers in 2D and 3D images of early stages of the zebra-fish embryogenesis. The approximate cell centers give us the starting points for the subjective surface based cell segmentation. We move in the inner normal direction all level sets of nuclei and membranes images by a constant speed with slight regularization of this flow by the (mean) curvature. Such multi- scale evolutionary process is represented by a geometrical advection-diffusion equation which gives us at a certain scale the desired information on the number of cells. For solving the problems computationally we use flux-based finite volume level set method developed by Frolkovič and Mikula in [FM1] and semi-implicit co-volume subjective surface method given in [CMSSg, MSSgCVS, MSSgchapter]. Computational experiments on testing and real 2D and 3D embryogenesis images are presented and the results are discussed.},
author = {Frolkovič, Peter, Mikula, Karol, Peyriéras, Nadine, Sarti, Alex},
journal = {Kybernetika},
keywords = {image processing; partial differential equations; nonlinear advection-diffusion equations; flux-based level set method; subjective surface method; embryogenesis; zebra-fish embryogenesis; flux-based finite volume level set method},
language = {eng},
number = {6},
pages = {817-829},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Counting number of cells and cell segmentation using advection-diffusion equations},
url = {http://eudml.org/doc/33899},
volume = {43},
year = {2007},
}

TY - JOUR
AU - Frolkovič, Peter
AU - Mikula, Karol
AU - Peyriéras, Nadine
AU - Sarti, Alex
TI - Counting number of cells and cell segmentation using advection-diffusion equations
JO - Kybernetika
PY - 2007
PB - Institute of Information Theory and Automation AS CR
VL - 43
IS - 6
SP - 817
EP - 829
AB - We develop a method for counting number of cells and extraction of approximate cell centers in 2D and 3D images of early stages of the zebra-fish embryogenesis. The approximate cell centers give us the starting points for the subjective surface based cell segmentation. We move in the inner normal direction all level sets of nuclei and membranes images by a constant speed with slight regularization of this flow by the (mean) curvature. Such multi- scale evolutionary process is represented by a geometrical advection-diffusion equation which gives us at a certain scale the desired information on the number of cells. For solving the problems computationally we use flux-based finite volume level set method developed by Frolkovič and Mikula in [FM1] and semi-implicit co-volume subjective surface method given in [CMSSg, MSSgCVS, MSSgchapter]. Computational experiments on testing and real 2D and 3D embryogenesis images are presented and the results are discussed.
LA - eng
KW - image processing; partial differential equations; nonlinear advection-diffusion equations; flux-based level set method; subjective surface method; embryogenesis; zebra-fish embryogenesis; flux-based finite volume level set method
UR - http://eudml.org/doc/33899
ER -

References

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  1. Evans L. C., Spruck J., Motion of level sets by mean curvature I, J. Differential Geom. 33 (1991), 635–681 (1991) Zbl0726.53029MR1100206
  2. Handlovičová A., Mikula, K., Sgallari F., 10.1007/s002110100374, Numer. Math. 93 (2003), 675–695 Zbl1065.65105MR1961884DOI10.1007/s002110100374
  3. Mikula K., Sarti, A., Sgallari F., 10.1007/s00791-006-0014-0, Comput. Visual. Sci. 9 (2006), 23–31 MR2214835DOI10.1007/s00791-006-0014-0
  4. Mikula K., Sarti, A., Sgallari F., Semi-implicit co-volume level set method in medical image segmentation, In: Handbook of Biomedical Image Analysis: Segmentation and Registration Models (J. Suri et al., eds.), Springer, New York, 2005, pp. 583–626 
  5. Osher S., Sethian J., 10.1016/0021-9991(88)90002-2, J. Comput. Phys. 79 (1988), 12–49 (1988) MR0965860DOI10.1016/0021-9991(88)90002-2
  6. Sarti A., Malladi, R., Sethian J. A., 10.1073/pnas.110135797, Proc. Nat. Acad. Sci. U. S. A. 12 (2000), 97, 6258–6263 Zbl0966.68214MR1760935DOI10.1073/pnas.110135797
  7. Sarti A., Citti G., Subjective surfaces and Riemannian mean curvature flow of graphs, Acta Math. Univ. Comenian. 79 (2001), 1, 85–104 Zbl0995.65100MR1865362

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