Abstract
We define the robustness of a level set homology class of a function \(f: {\mathbb X} \to {\mathbb R}\) 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 \({\mathbb X} = {\mathbb R}^3\) has ramifications in medical imaging and scientific visualization.
This research is partially supported by the Defense Advanced Research Projects Agency (DARPA), under grants HR0011-05-1-0057 and HR0011-09-0065, as well as the National Science Foundation (NSF), under grant DBI-0820624.
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Bendich, P., Edelsbrunner, H., Morozov, D., Patel, A. (2010). The Robustness of Level Sets. In: de Berg, M., Meyer, U. (eds) Algorithms – ESA 2010. ESA 2010. Lecture Notes in Computer Science, vol 6346. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15775-2_1
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