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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
T. Chan and L. Vese. Active contours without edges. IEEE Trans. on Image Processing, 10:266–277, 2001.
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.
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.
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.
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.
M. Kass, A. Witkin, and D. Terzopoulos. Snakes: Active contour models. Int. J. of Comp. Vision, 1:321–331, 1988.
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.
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.
R. Malladi. Geometric Methods in Bio-Medical Image Processing. Springer, 2002.
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.
D. Mumford and J. Shah. Optimal approximation by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math, 42:577–685, 1989.
S. Osher and R. Fedkiw. Level Set Methods and Dynamic Implicit Surfaces. Springer, New York, 2003.
S. Osher and N. Paragios. Geometric Level Set Methods in Imaging, Vision, and Graphics. Springer, 2003.
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.
N. Paragios, Y. Chen, and O. Faugeras. Handbook of Mathematical Models in Computer Vision. Springer, 2006.
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.
P. Perona and J. Malik. Scale-space and edge detection using anisotropic diffusion. PAMI, 12(7):629–639, 1990.
J. Sethian. Curvature and the evolution of fronts. Comm. In Math. Phys., 101:487–499, 1985.
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.
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.
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.
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.
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.
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.
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.
Q. Yang, B. Parvin, and M. Barcellos-Hoff. Localization of saliency through iterative voting. In ICPR (1), pages 63–66, 2004.
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.
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.
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
Corresponding author
Editor information
Editors and Affiliations
Rights 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)