Variogram Based Estimator of Fractal Dimension for the Analysis of Cell Nuclei from the Papanicolaou Smears

  • Dorota Oszutowska–Mazurek
  • Przemysław Mazurek
  • Kinga Sycz
  • Grażyna Waker–Wójciuk
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 184)


The aim of cervical screening is detection of potentially pre–cancerous and cancerous changes in the endocervical canal of female reproductive system. There are many Fractal Dimension (FD) that are important for the computer assisted analysis of the texture of cell nuclei. The best method is the algorithm that process all pixels of the cell nuclei, not limited by the constraints. Variogram algorithm is proposed for cell nuclei classification (correct and atypical cell classes). Obtained results shows that variogram and cell nuclei size are important for the automatic classification of cell nuclei.


Fractal Dimension Cell Nucleus Cervical Screening Female Reproductive System Cervical Cytology 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Blackledge, J., Dubovitskiy, D.: An Optical Machine Vision System for Applications in Cytopathology. ISAST Transactions on Computers and Intelligent Systems 2(1), 95–109 (2010)Google Scholar
  2. 2.
    Chosia, M., Domagała, W.: Cytologia szyjki macicy. Fundacja Pro Pharmacia Futura (2010) (book in Polish)Google Scholar
  3. 3.
    Clarke, K.C.: Computation of the Fractal Dimension of Topographic Surfaces using the Triangular Prism Surface Area Method. Computer and Geosciences 12(5), 713–722 (1986)CrossRefGoogle Scholar
  4. 4.
    Dey, P.: Fractal geometry: Basic principles and applications in pathology. Anal. Quant. Cytol. Histol. 27(5), 284–290 (2005) PMID: 16447821Google Scholar
  5. 5.
    Hoda, R.S., Hoda, S.A.: Fundamentals of Pap Test Cytology. Humana Press (2007)Google Scholar
  6. 6.
    IARC, Cytopathology of the uterine cervix – digital atlas. International Agency for Research on Cancer,
  7. 7.
    Kaye, B.H.: A Random Walk Through Fractal Dimensions. VCH (1994)Google Scholar
  8. 8.
    Mandelbrot, B.B.: The Fractal Geometry of the Nature. W. H. Freeman and Company (1983)Google Scholar
  9. 9.
    McKenna, S.J.: Automated analysis of Papanicolaou smears. PhD Thesis, University of Dundee (1994)Google Scholar
  10. 10.
    Oszutowska–Mazurek, D., Mazurek, P.: Fractal–based generator for microscopic cell and cell nucleus contour synthesis. Metody Informatyki Stosowanej 27(2), 105–112 (2011)Google Scholar
  11. 11.
    Oszutowska–Mazurek, D., Waker–Wójciuk, G., Mazurek, P.: Fractal analysis limitations in digital analysis of Papanicolaou cytological images. Measurement Automation and Monitoring 58(1), 52–54 (2012)Google Scholar
  12. 12.
    Oszutowska-Mazurek, D., Mazurek, P., Sycz, K., Waker-Wójciuk, G.: Estimation of Fractal Dimension According to Optical Density of Cell Nuclei in Papanicolaou Smears. In: Piętka, E., Kawa, J. (eds.) ITIB 2012. LNCS, vol. 7339, pp. 456–463. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  13. 13.
    Peitgen, H.O., Jurgens, H., Saupe, D.: Fractal for the Classroms, Part 1: Introduction to Fractals and Chaos. Springer (1992)Google Scholar
  14. 14.
    Seuront, L.: Fractals and Multifractals in Ecology and Acquatic Science. CRC Press (2010)Google Scholar
  15. 15.
    Solomon, D., Nayar, R.: The Bethesda System for Reporting Cervical Cytology. Springer (2004)Google Scholar
  16. 16.
    Steven, I.: Linear Richardson Plots from Non–Fractal Data Sets. Dutch Mathematical Geology 25(6), 737–751 (1993), doi:10.1007/BF00893176Google Scholar
  17. 17.
    Sun, W., Xu, G., Gong, P., Liang, S.: Fractal analysis of remotely sensed images: A review of methods and applications. International Journal of Remote Sensing 27(22), 4963–4990 (2006), doi:10.1080/01431160600676695CrossRefGoogle Scholar
  18. 18.
    Zhou, G., Lam, N.: A comparison of fractal dimension estimators based on multiple surface generation algorithms. Computers & Geosciences 31, 1260–1269 (2005), doi:10.1016/j.cageo.2005.03.016CrossRefGoogle Scholar
  19. 19.
    Zieliński, K.W., Strzelecki, M.: Komputerowa analiza obrazu biomedycznego. Wstęp do morfometrii i patrologii ilościowej. Wydawnictwo Naukowe PWN (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Dorota Oszutowska–Mazurek
    • 1
  • Przemysław Mazurek
    • 2
  • Kinga Sycz
    • 3
  • Grażyna Waker–Wójciuk
    • 3
  1. 1.Department of PathomorphologyGryfice Hospital MedicamGryficePoland
  2. 2.Department of Signal Processing and Multimedia EngineeringWest–Pomeranian University of Technology, SzczecinSzczecinPoland
  3. 3.Department of PatomorphologyIndependent Public Voivodeship United HospitalSzczecinPoland

Personalised recommendations