Topo-Net: Retinal Image Analysis with Topological Deep Learning

The analysis of fundus images for the early screening of eye diseases is of great clinical importance. Traditional methods for such analysis are time-consuming and expensive as they require a trained clinician. Therefore, the need for a comprehensive and automated clinical decision support system to diagnose and grade retinal diseases has long been recognized. In the past decade, with the substantial developments in computer vision and deep learning, machine learning methods have become highly effective in this field to address this need. However, most of these algorithms face challenges like computational feasibility, reliability, and interpretability. In this paper, our contributions are two-fold. First, we introduce a very powerful feature extraction method for fundus images by employing the latest topological data analysis methods. Through our experiments, we observe that our topological feature vectors are highly effective in distinguishing normal and abnormal classes for the most common retinal diseases, i.e., Diabetic Retinopathy (DR), Glaucoma, and Age-related Macular Degeneration (AMD). Furthermore, these topological features are interpretable, computationally feasible, and can be seamlessly integrated into any forthcoming ML model in the domain. Secondly, we move forward in this direction, constructing a topological deep learning model by integrating our topological features with several deep learning models. Empirical analysis shows a notable enhancement in performance aided by the use of topological features. Remarkably, our model surpasses all existing models, demonstrating superior performance across several benchmark datasets pertaining to two of these three retinal diseases. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement This work was partially supported by the National Science Foundation under grants DMS-2202584 and DMS-2220613 and by Simons Foundation under grant # 579977. ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes The details of the IRB/oversight body that provided approval or exemption for the research described are given below: IChallenge-AMD dataset: https://refuge.grand-challenge.org/iChallenge-AMD/ ORIGA dataset: https://www.kaggle.com/datasets/arnavjain1/glaucoma-datasets APTOS: https://www.kaggle.com/datasets/mariaherrerot/aptos2019 I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable. Yes All data produced are available online at