Topological Fidelity and Image Thresholding: A Persistent Homology Approach

We develop a method based on persistent homology to analyze topological structure in noisy digital images. The method returns threshold(s) for image segmentation to represent inherent topological structure as well as estimates of topological quantities in the form of Betti numbers. Two motivating data sets are scans of binary alloys and firn, the intermediate stage between snow and ice.