Persistent Homology in Medical Image Processing: A Literature Review

Medical image analysis has experienced significant advances with the integration of machine learning, deep learning, and other mathematical and computational methodologies into the pipelines of data analysis. One methodology that has received less attention is Persistent Homology (PH), which comes from the growing field of Topological Data Analysis and has the ability to extract features from data at different scales and build multi-scale summaries. In this work, we present a systematic review of PH applied in medical images. To illustrate the potential of PH, we introduce the main concepts of PH and demonstrate with an example of histopathology. Fifteen articles where PH was applied to medical image analysis tasks such as segmentation and classification were selected and reviewed. It was observed that PH is very versatile, as it can be applied in many different contexts and to different data types, whilst also showing great potential in increasing model accuracy in both classification and segmentation. It was also observed that image segmentation predominantly uses basic level-set filtration to calculate PH, while classification takes various approaches using filtration on more complex structures built from data. This review highlights PH as an important tool that can further advance medical image analysis.