Sasse, Ramona: Mutual information based parameter extraction for spreading cell colonies. 2021
Inhalt
- Zusammenfassung
- Abstract
- Acknowledgments
- Contents
- Introduction
- Application background in the pharmaceutical field
- Preliminary image processing & feature images
- Introduction to the image data set
- Initial colony segmentation and moving fronts
- Feature images for colony analysis
- Mathematical modeling for spreading cell colonies
- A PDE model for colony spreading
- Concentric circles for colony spreading
- Review of model fitting approaches
- Mutual information based model fitting
- Mutual information - a brief introduction
- Optimization problem for cell colony spreading
- The Radon-Nikodym theorem - a small excursion
- Introduction to the MI optimization problem
- Measure-theoretical setting
- Histogram definition and partial derivatives
- Discretized histograms, discrete MI and its gradient
- Discretizations for numerical approach
- Feature images on a discrete pixel grid
- Classification images on a discrete pixel grid
- Uniform convergence of classification images
- Convergence of histogram density functions
- Convergence of probability density functions
- Analysis of MI-based optimization
- Prerequisites for existence and convergence proofs
- Existence of minimizers
- Convergence of minimizers
- Numerics of MI-based optimization
- Conclusion & Outlook
- List of Symbols
- List of Figures
- List of Tables
- Bibliography
- Curriculum Vitae