The Robustness of Level Sets

We define the robustness of a level set homology class of a function f : 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 X = R3 has ramifications in medical imaging and scientific visualization. Keywords. Topological spaces, continuous functions, level sets, perturbations, homology, extended persistence, well groups, well diagrams, robustness.

• Type: Conference
• Year: 2010
• Where: ESA
• Authors: Paul Bendich, Herbert Edelsbrunner, Dmitriy Morozov, Amit K. Patel
• Keywords: Algorithms, ESA 2010, Extended Persistent Homology, Level Set Homology, Robustness