Analyzing Ocular Diseases Through Persistence Diagrams and Topological Data Analysis

Abstract

This study explores the topological characteristics of affected eyes through
the framework of Topological Data Analysis (TDA), with a focus on Betti
numbers derived from persistence diagrams. A dataset comprising retinal
images of both normal and disease affected eyes was analyzed using Ripser,
a tool for computing persistent homology in grayscale images. By extracting
Betti numbers (β0 and β1) from the persistence diagrams, we quantitatively
captured the topological features such as connected components and
loops present in each image. Comparative analysis revealed notable differences
in the distribution of Betti numbers between normal and disease eyes,
indicating measurable alterations in the topological structure of disease affected
eyes. These findings highlight the potential of TDA as a non-invasive
and quantitative method for distinguishing ocular health conditions based on
topological invariants.