Analysing retinal images using (extended) persistent homology

Abstract

Biometrics are data used for the automatic verification and identification of individuals, two important routines commonly performed to enhance the level of security within a system. Therefore, improvements to the analysis of biometrics are crucial. Common examples of biometrics include fingerprints and facial features. In this thesis, we consider retinal fundus images, which are scans of a person's retina blood vessels at the back of the eyeballs. They have become a popular choice for these tasks due to their uniqueness and stability over time. Traditional methods mainly utilise specific biological features observed in the scans. These methods generally rely on highly accurate automated extractions of these traits, which are challenging to produce especially when abnormalities appear in diseased individuals. In this paper, we instead propose a novel approach, which is more tolerant of the errors from the feature extraction process, to analyse retina biometrics. In particular, we compute the \emph{(extended) persistent homology} of the blood vessel structure (viewed as a manifold with boundary embedded in $\R^2$) in a retinal image with respect to some filtration and produce a summary statistic called a \emph{persistence diagram}. This then allows us to perform further statistical tests. We test our method on a publicly available database using different filtrations choices to capture the vessels' shapes. Some of these choices achieve a high level of accuracy compared with tests done on the same database. Our method also takes significantly less time compared to other proposed methods. In the future, we can explore more filtrations and/or use combinations of results obtained from different filtrations to see if we can further increase accuracy. Show more