Homology and robustness of level and interlevel sets
Paul Bendich, Herbert Edelsbrunner, Dmitriy Morozov, Amit Patel · Homology Homotopy and Applications · 2013
Given a continuous function f : X → R on a topological space, we consider the preimages of intervals and their homology groups and show how to read the ranks of these groups from the extended persistence diagram of f .In addition, we quantify the robustness of the homology classes under perturbations of f using well groups, and we show how to read the ranks of these groups from the same extended persistence diagram.The special case X = R 3 has ramifications in the fields of medical imaging and scientific visualization.