Skip to main content
SpringerLink
Log in

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

  • Chapter
Handbook of Biomedical Imaging

  • 2623 Accesses

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. T. Chan and L. Vese. Active contours without edges. IEEE Trans. on Image Processing, 10:266–277, 2001.

    Article  MATH  Google Scholar 

  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. 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.

    Article  Google Scholar 

  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. 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. M. Kass, A. Witkin, and D. Terzopoulos. Snakes: Active contour models. Int. J. of Comp. Vision, 1:321–331, 1988.

    Article  Google Scholar 

  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. 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. R. Malladi. Geometric Methods in Bio-Medical Image Processing. Springer, 2002.

    Google Scholar 

  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. D. Mumford and J. Shah. Optimal approximation by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math, 42:577–685, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  12. S. Osher and R. Fedkiw. Level Set Methods and Dynamic Implicit Surfaces. Springer, New York, 2003.

    MATH  Google Scholar 

  13. S. Osher and N. Paragios. Geometric Level Set Methods in Imaging, Vision, and Graphics. Springer, 2003.

    Google Scholar 

  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. N. Paragios, Y. Chen, and O. Faugeras. Handbook of Mathematical Models in Computer Vision. Springer, 2006.

    Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  17. P. Perona and J. Malik. Scale-space and edge detection using anisotropic diffusion. PAMI, 12(7):629–639, 1990.

    Article  Google Scholar 

  18. J. Sethian. Curvature and the evolution of fronts. Comm. In Math. Phys., 101:487–499, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  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.

    MATH  Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  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. 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. 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.

    Article  MATH  Google Scholar 

  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. 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. Q. Yang, B. Parvin, and M. Barcellos-Hoff. Localization of saliency through iterative voting. In ICPR (1), pages 63–66, 2004.

    Google Scholar 

  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. Y. Zhou, A. Kuijper, B. Heise, and L. He. Cell segmentation using the level set method. Technical Report 2007-17, RICAM, 2007. http://www.ricam.oeaw.ac.at/publications/reports/07/rep07-17.pdf.

Download references

Acknowledgements

The work was partially supported by the mYeasty pilot-project by the Austrian GEN_AU research program (www.gen-au.at). 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.

Author information

Authors and Affiliations

  1. Fraunhofer IGD, Institute for Computer Graphics Research, Department of Computer Science, TU Darmstadt, Darmstadt, Germany

    A. Kuijper

  2. Department of Knowledge-Based Mathematical Systems, Johannes Kepler University, Linz, Austria

    B. Heise

  3. Department of Virtual Design, Siemens AG, Munich, Germany

    Y. Zhou

  4. Luminescent Technologies Inc., Palo Alto, USA

    L. He

  5. SFB Biomembrane Research Center, Institute of Molecular Biosciences, Department Biochemistry, University of Graz, Graz, Austria

    H. Wolinski & S. Kohlwein

Authors
  1. A. Kuijper
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. Heise
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Y. Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. L. He
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. H. Wolinski
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. S. Kohlwein
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Kuijper .

Editor information

Editors and Affiliations

  1. Department of Applied Mathematics, École Centrale de Paris / INRIA Saclay, Île De France, Chatenay-Malabry, France

    Nikos Paragios

  2. Department of Biomedical Engineering, Diagnostic Radiology and Electrical Engineering, Yale University, New Haven, Connecticut, USA

    James Duncan

  3. INRIA Sophia Antipolis - Méditerranée, Sophia Antipolis Cedex, France

    Nicholas Ayache

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer Science+Business Media New York

About this chapter

Cite this chapter

Kuijper, A., Heise, B., Zhou, Y., He, L., Wolinski, H., Kohlwein, S. (2015). Segmentation of Clustered Cells in Microscopy Images by Geometric PDEs and Level Sets. In: Paragios, N., Duncan, J., Ayache, N. (eds) Handbook of Biomedical Imaging. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-09749-7_26

Download citation

  • DOI: https://doi.org/10.1007/978-0-387-09749-7_26

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-387-09748-0

  • Online ISBN: 978-0-387-09749-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation