Stochastic Geometry for Automatic Assessment of Ki-67 Index in Breast Cancer Preparations

  • Marek KowalEmail author
  • Marcin Skobel
  • Józef Korbicz
  • Roman Monczak
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10814)


Proliferative activity of cells is one of the most critical factors in breast cancer diagnosis. It is used to evaluate tumor cell progression and to predict treatment responses in chemotherapy. Ki-67 is a nuclear biomarker commonly used to measure cellular proliferation rate. The ratio between the number of Ki-67 positive tumor nuclei and all tumor nuclei defines Ki-67 index. However, manual cell counting is tedious and time consuming because hundreds of nuclei must be labeled. To speed up the analysis process, nuclei can be segmented automatically and then classified based on staining color. Unfortunately, segmentation of individual nuclei is a big challenge because they often create complex clusters comprised of many touching and overlapping nuclei. To deal with complexities and ambiguities of cytological material we propose a generative model which approximates nuclei using ellipses. We assume that the process of generating a cytological sample has stochastic nature. Therefore it is possible to reconstruct this process using marked point process tuned according to observed cytological sample. To verify the potential of the proposed method, we applied it to determine Ki-67 index in breast cancer immunochemistry samples. The results of experiments have shown that Ki-67 indices determined by proposed approach correlate well with those computed manually.


Breast cancer Ki-67 index Nuclei segmentation Stochastic process Steepest ascent optimization Maximum a posteriori estimation 



The research was supported by National Science Centre, Poland (2015/17/B/ST7/03704).


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Marek Kowal
    • 1
    Email author
  • Marcin Skobel
    • 1
  • Józef Korbicz
    • 1
  • Roman Monczak
    • 2
  1. 1.Faculty of Computer, Electrical and Control Engineering, Institute of Control and Computation EngineeringUniversity of Zielona GóraZielona GóraPoland
  2. 2.Department of PathomorphologyUniversity Hospital in Zielona GóraZielona GóraPoland

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