@inproceedings{3848, abstract = {We define the robustness of a level set homology class of a function f:XR 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.}, author = {Bendich, Paul and Edelsbrunner, Herbert and Morozov, Dmitriy and Patel, Amit}, location = {Liverpool, UK}, pages = {1 -- 10}, publisher = {Springer}, title = {{The robustness of level sets}}, doi = {10.1007/978-3-642-15775-2_1}, volume = {6346}, year = {2010}, }