Diabetic retinopathy is a complication of diabetes that produces changes in the blood vessel structure in the retina, which can cause severe vision problems and even blindness. In this paper, we demonstrate that by identifying topological features in very high resolution retinal images, we can construct a classifier that discriminates between healthy patients and those with diabetic retinopathy using summary statistics of these features. Topological data analysis identifies the features as connected components and holes in the images and describes the extent to which they persist across the image. These features are encoded in persistence diagrams, summaries of which can be used to discrimate between diabetic and healthy patients. The method has the potential to be an effective automated screening tool, with high sensitivity and specificity.
We investigate the performance of uncertainty quantification methods, namely deep ensembles and bootstrap resampling, for deep neural network (DNN) predictions of transition metal K-edge X-ray absorption near-edge structure (XANES) spectra....
Persistent homology is used to track the appearance and disappearance of features as we move through a nested sequence of topological spaces. Equating the nested sequence to a filtration and the appearance and disappearance of features to events, we show that simple event history methods can be used for the analysis of topological data. We propose a version of the well known Nelson-Aalen cumulative hazard estimator for the comparison of topological features of random fields and for testing parametric assumptions. We suggest a Cox proportional hazards approach for the analysis of embedded metric trees. The Nelson-Aalen method is illustrated on globally distributed climate data and on neutral hydrogen distribution in the Milky Way. The Cox method is use to compare vascular patterns in fundus images of the eyes of healthy and diabetic retinopathy patients.
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