# ESTIMATION OF PARAMETERS IN A PLANAR SEGMENT PROCESS WITH A BIOLOGICAL APPLICATION

## Authors

• Viktor Benes Charles University, Faculty of Mathematics and Physics, Department of Probability and Mathematical Statistics
• Jakub Vecera Charles University, Faculty of Mathematics and Physics, Department of Probability and Mathematical Statistics
• Benjamin Eltzner Georg-August-University of Goettingen, Institute of Mathematical Stochastics
• Carina Wollnik Georg-August-University of Goettingen, Third Institute of Physics - Biophysics
• Florian Rehfeldt Georg-August-University of Goettingen, Third Institute of Physics - Biophysics
• Veronika Kralova Charles University, Faculty of Mathematics and Physics, Department of Probability and Mathematical Statistics
• Stephan Huckemann Georg-August-University of Goettingen, Institute of Mathematical Stochastics

## Keywords:

parameter estimation, random segment process, stem cell, stress fibre

## Abstract

The paper deals with modeling of segment systems in a bounded planar set (a cell) by means of random segment processes. Two models with a density with respect to the Poisson process are presented. In model I interactions are given by the number of intersections, model II includes the length distribution and takes into account distances from the centre of the cell. The estimation of parameters of the models is suggested based on Takacz-Fiksel method. The method is tested first using simulated data. Further the real data from fluorescence imaging of stress fibres in mesenchymal human stem cells are evaluated. We apply model II which is inhomogeneous. The degree-of-fit testing of the model using various characteristics yields quite satisfactory results.

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2017-03-31

## How to Cite

Benes, V., Vecera, J., Eltzner, B., Wollnik, C., Rehfeldt, F., Kralova, V., & Huckemann, S. (2017). ESTIMATION OF PARAMETERS IN A PLANAR SEGMENT PROCESS WITH A BIOLOGICAL APPLICATION. Image Analysis and Stereology, 36(1), 25–33. https://doi.org/10.5566/ias.1627

## Section

Original Research Paper