The robustness of level sets

Abstract

We define the robustness of a level set homology class of a function f : double-struck X → ℝ as the magnitude of a perturbation necessary to kill the class. Casting this notion into a group theoretic framework, we compute the robustness for each class, using a connection to extended persistent homology. The special case double-struck X = ℝ3 has ramifications in medical imaging and scientific visualization. © 2010 Springer-Verlag.