Topological Machine Learning in Medical Image Analysis

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December 2023

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Abstract

Medical image analysis is a critical component of modern healthcare, aiding in the detection, diagnosis, and treatment of various diseases. In recent years, the fusion of topological data analysis (TDA) and machine learning has brought about a transformative approach to understanding and leveraging the complex patterns inherent in medical images. This thesis explores the application of TDA, with a focus on persistent and cubical homology, as a powerful tool for extracting topological features from 2D and 3D medical images. By capturing the birth and death of these features through a filtration process and representing them as feature vectors, we enhance the interpretability and performance of machine learning models. Our journey begins with the transformation of color images into grayscale, RGB, and HSV channels, laying the foundation for versatility in our approach. The three-step process of persistent homology unfolds through filtration, persistence diagram generation, and vectorization, leading to feature vectors that outperform traditional image inputs in machine learning models. In our investigations, we utilized this methodology across various medical imaging contexts such as cancer histopathology, chest X-rays, retinal images, and MEDMNIST a collection of various medical image datasets. Our findings highlight the effectiveness of topological features in analyzing images, particularly in classifying and identifying abnormalities in these settings. Additionally, when we merged these topological aspects with deep learning characteristics, we observed an improved model efficiency. This presents a novel, comprehensive approach to medical image analysis. This research further demonstrates the potential of TDA in image analysis and classification, providing valuable insights into complex structural information not readily apparent through conventional techniques. In the realm of histopathological cancer detection, we introduce a groundbreaking Topo-ML model that adapts to multiple cancer types, offering remarkable computational efficiency. In the evaluation of chest X-ray images, our Topo-CXR model excels in terms of reliability and interpretability, outperforming deep learning models on benchmark datasets to detect Pneumonia and Tuberculosis. Additionally, our analysis of fundus images for retinal diseases presents a dual contribution, introducing effective feature extraction methods and topological deep learning models that surpass existing models. Beyond these specific applications, we conducted a comprehensive evaluation of TDA methods across various medical image datasets, demonstrating competitive performance with deep learning models in certain cases. These findings underscore the potential of topological features in boosting the capabilities of future machine learning models in diverse medical domains, ultimately advancing our understanding and utilization of digital images in healthcare.

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Topological data analysis (TDA), Machine learning, Mathematics, Medical image, Deep learning (Machine learning)

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