Segmentation of Clustered Cells in Microscopy Images by Geometric PDEs and Level Sets

  • A. KuijperEmail author
  • B. Heise
  • Y. Zhou
  • L. He
  • H. Wolinski
  • S. Kohlwein


With the huge amount of cell images produced in bio-imaging, automatic methods for segmentation are needed in order to evaluate the content of the images with respect to types of cells and their sizes. Traditional PDE-based methods using level-sets can perform automatic segmentation, but do not perform well on images with clustered cells containing sub-structures. We present two modifications for popular methods and show the improved results.


Automatic Segmentation Differential Interference Contrast Active Contour Model Cell Segmentation Differential Interference Contrast Image 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The work was partially supported by the mYeasty pilot-project by the Austrian GEN_AU research program ( It was carried out when A. Kuijper, Y. Zhou, and L. He were with the Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz, Austria.


  1. 1.
    T. Chan and L. Vese. Active contours without edges. IEEE Trans. on Image Processing, 10:266–277, 2001.CrossRefzbMATHGoogle Scholar
  2. 2.
    T. Chan and L. Vese. Active contour and segmentation models using geometric pde’s for medical imaging. In R. Malladi, editor, Geometric Methods in Bio-Medical Image Processing, chapter 4, pages 63–76. Springer, 2002.Google Scholar
  3. 3.
    H. Chang, Q. Yang, and B. Parvin. Segmentation of heterogeneous blob objects through voting and level set formulation. Pattern Recognition Letters, 28(13):1781–1787, 2007.CrossRefGoogle Scholar
  4. 4.
    L. He and S. Osher. Solving the chan-vese model by a multiphase level set method algorithm based on the toplogical derivative. In 1st International Conference on Scale Space and Variational Methods in Computer Vision, pages 777–788, 2007.Google Scholar
  5. 5.
    B. Heise and B. Arminger. Some aspects about quantitative reconstruction for differential interference contrast (dic) microscopy. In PAMM 7(1): (Special Issue: Sixth International Congress on Industrial Applied Mathematics (ICIAM07) and GAMM Annual Meeting, Zürich 2007), pages 2150031–2150032, 2007.Google Scholar
  6. 6.
    M. Kass, A. Witkin, and D. Terzopoulos. Snakes: Active contour models. Int. J. of Comp. Vision, 1:321–331, 1988.CrossRefGoogle Scholar
  7. 7.
    A. Kuijper, Y. Zhou, and B. Heise. Clustered cell segmentation - based on iterative voting and the level set method. In 3rd International Conference on Computer Vision Theory and Applications (VISAPP, Funchal, Portugal, 22 - 25 January 2008), pages 307–314, 2008.Google Scholar
  8. 8.
    C. Li, C. Xu, C. Gui, and M. Fox. Level set evolution without re-initialization: A new variational formulation. In IEEE Computer Society Conference on Computer Vision and Pattern Recognition, volume 1, pages 430–436, 2005.Google Scholar
  9. 9.
    R. Malladi. Geometric Methods in Bio-Medical Image Processing. Springer, 2002.Google Scholar
  10. 10.
    R. Malladi and J. A. Sethian. Fast methods for shape extraction in medical and biomedical imaging. In R. Malladi, editor, Geometric Methods in Bio-Medical Image Processing, chapter 1, pages 1–18. Springer, 2002.Google Scholar
  11. 11.
    D. Mumford and J. Shah. Optimal approximation by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math, 42:577–685, 1989.CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    S. Osher and R. Fedkiw. Level Set Methods and Dynamic Implicit Surfaces. Springer, New York, 2003.zbMATHGoogle Scholar
  13. 13.
    S. Osher and N. Paragios. Geometric Level Set Methods in Imaging, Vision, and Graphics. Springer, 2003.Google Scholar
  14. 14.
    S. Osher and J. Sethian. Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics, 79:12–49, 1988.Google Scholar
  15. 15.
    N. Paragios, Y. Chen, and O. Faugeras. Handbook of Mathematical Models in Computer Vision. Springer, 2006.Google Scholar
  16. 16.
    B. Parvin, Q. Yang, J. Han, H. Chang, B. Rydberg, and M. Barcellos-Hoff. Iterative voting for inference of structural saliency and characterization of subcellular events. IEEE Trans Image Process., 16(3):615–623, 2007.CrossRefMathSciNetGoogle Scholar
  17. 17.
    P. Perona and J. Malik. Scale-space and edge detection using anisotropic diffusion. PAMI, 12(7):629–639, 1990.CrossRefGoogle Scholar
  18. 18.
    J. Sethian. Curvature and the evolution of fronts. Comm. In Math. Phys., 101:487–499, 1985.CrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
    J. Sethian. Level set methods and fast marching methods: Evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science. Cambridge University Press, Cambridge, UK, 1999.zbMATHGoogle Scholar
  20. 20.
    C. Solorzano, R. Malladi, S. Lelievre, and S. Lockett. Segmentation of nuclei and cells using membrane related protein markers. Journal of Microscopy, 201:404–415, 2001.CrossRefMathSciNetGoogle Scholar
  21. 21.
    C. Solorzano, R. Malladi, and S. Lockett. A geometric model for image analysis in cytology. In R. Malladi, editor, Geometric Methods in Bio-Medical Image Processing, chapter 2, pages 19–42. Springer, 2002.Google Scholar
  22. 22.
    M. Sussman and E. Fatemi. An efficient, interface preserving level set redistancing algorithms and its application to interfacial incompressible fluid flow. SIAM J.Sci. Comp., 20:1165–1191, 1999.Google Scholar
  23. 23.
    L. Vese and T. Chan. A multiphase level set framework for image segmentation using the Mumford and Shan Model. Int. J. of Comp. Vision, 50(3):271–293, 2002.CrossRefzbMATHGoogle Scholar
  24. 24.
    H. Wolinski and S. Kohlwein. Microscopic analysis of lipid droplet metabolism and dynamics in yeast. In Membrane Trafficking, volume 457 of Methods in Molecular Biology, chapter 11, pages 151–163. Springer, 2008.Google Scholar
  25. 25.
    Q. Yang and B. Parvin. Harmonic cut and regularized centroid transform for localization of subceullar structures. IEEE Transactions on Biomedical Engineering, 50(4):469–475, April 2003.Google Scholar
  26. 26.
    Q. Yang, B. Parvin, and M. Barcellos-Hoff. Localization of saliency through iterative voting. In ICPR (1), pages 63–66, 2004.Google Scholar
  27. 27.
    Y. Zhou, A. Kuijper, and L. He. Multiphase level set method and its application in cell segmentation. In 5th International Conference on Signal Processing, Pattern Recognition, and Applications (SPPRA 2008, Innsbruck, Austria, February 13 - 15, 2008), pages 134–139, 2008.Google Scholar
  28. 28.
    Y. Zhou, A. Kuijper, B. Heise, and L. He. Cell segmentation using the level set method. Technical Report 2007-17, RICAM, 2007.

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • A. Kuijper
    • 1
    Email author
  • B. Heise
    • 2
  • Y. Zhou
    • 3
  • L. He
    • 4
  • H. Wolinski
    • 5
  • S. Kohlwein
    • 5
  1. 1.Fraunhofer IGD, Institute for Computer Graphics Research, Department of Computer ScienceTU DarmstadtDarmstadtGermany
  2. 2.Department of Knowledge-Based Mathematical SystemsJohannes Kepler UniversityLinzAustria
  3. 3.Department of Virtual DesignSiemens AGMunichGermany
  4. 4.Luminescent Technologies Inc.Palo AltoUSA
  5. 5.SFB Biomembrane Research Center, Institute of Molecular Biosciences, Department BiochemistryUniversity of GrazGrazAustria

Personalised recommendations