Fractal Case Study for Mammary Cancer: Analysis of Interobserver Variability

  • Philipp Hermann
  • Sarah Piza
  • Sandra Ruderstorfer
  • Sabine Spreitzer
  • Milan StehlíkEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 136)


This paper discusses some features of the distribution of box-counting fractal dimension measured on a real data set from mammary cancer and masthopathy patients. During the study we found several reasons why mammary cancer and its following distribution cannot be easily represented by single box-counting dimension. The main problem is that without a histopathological examination of the tumor a simple algorithm based only on single box-counting dimension is difficult to be constructed. We have tried to understand the distribution underlying the real data, especially its departures from normality. Both normal and gamma distributions are related to the Tweedy distributions, which are given by multi-fractal dimension spectra present in histopathological images. Without having a histological examination of the data multifractality is unavoidable as can be seen from several analysis in this paper. We have seen a fair differentiation between cancer and masthopathy. Finally we studied the depths of the data based on the information divergence. Some practical conclusions are also given.


Depth Discrimination Mammary cancer Multifractality Skewness 



The research received partial support from the WTZ Project No. IN 11/2011 “Thermal modelling of cancer”. The corresponding author acknowledges Proyecto Interno 2015, REGUL. MAT 12.15.33, Modelaciòn del crecimientode tejidos con aplicaciones a la Investigaciòn del càncer. First author thanks to the support of ANR project Desire FWF I 833-N18. We also thank the editor and reviewers, whose insightful comments helped us to sharpen the paper considerably.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Philipp Hermann
    • 1
  • Sarah Piza
    • 1
  • Sandra Ruderstorfer
    • 1
  • Sabine Spreitzer
    • 1
  • Milan Stehlík
    • 1
    • 2
    Email author
  1. 1.Department of Applied StatisticsJohannes-Kepler-University LinzLinz a. D.Austria
  2. 2.Departamento de MatemáticaUniversidad Técnica Federico Santa MaríaValparaísoChile

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