Optimal Transport Based Methods for Analyzing Co-localization and Statistical Dependence

by Thomas Giacomo Nies
Doctoral thesis
Date of Examination:2024-12-06
Date of issue:2025-07-31
Advisor:Prof. Dr. Axel Munk
Referee:Prof. Dr. Axel Munk
Referee:Prof. Dr. Bernhard Schmitzer
Persistent Address: http://dx.doi.org/10.53846/goediss-11421

 

 

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Abstract

English

This dissertation develops optimal transport-based methodologies to advance statistical dependency analysis and co-localization studies, with applications in biological imaging. First, we introduce transport dependency, a novel measure grounded in optimal transport theory, that quantifies statistical dependence between random variables in general Polish spaces. Due to its broad applicability, transport dependency allows for independence testing on complex data with diverse internal structures, enabling robust detection of dependencies across a wide range of data types. We then introduce a more specialized framework that combines point process theory with optimal transport to describe dependence and co-localization in dual-channel fluorescence microscopy images. Using a Bayesian approach, we demonstrate how prior information can be seamlessly integrated into the analysis through the cost function, enhancing model flexibility and accuracy. Simulations show that this model enables precise quantification of protein interactions, distinguishing between true statistical dependencies and random co-occurrences. Finally, we present MultiMatch, an advanced tool utilizing multi-marginal optimal unbalanced transport to analyze spatial arrangements in multi-color microscopy images. In particular, MultiMatch aims in detecting specific biological structures while addressing challenges posed by incomplete labeling. Validated on DNA origami nanoruler data, MultiMatch consistently outperforms geometry-agnostic methods and supports multi-channel co-localization through accessible, user-friendly visualization tools.
Keywords: Optimal Transport; Dependency; Co-localization; Fluorescence microscopy
 
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