The robustness of level sets

Authors:
Paul Bendich;Herbert Edelsbrunner;Dmitriy Morozov;Amit Patel
Affiliations:
Institute of Science and Technology Austria, Klosterneuburg, Austria and Dept. Comput. Sci., Duke Univ., Durham, North Carolina and Dept. Mathematics, Duke Univ., Durham, North Carolina;Institute of Science and Technology Austria, Klosterneuburg, Austria and Dept. Comput. Sci., Duke Univ., Durham, North Carolina and Dept. Mathematics, Duke Univ., Durham, North Carolina and Geomag ...;Depts. Comput. Sci. and Math., Stanford Univ., Stanford, California;Institute of Science and Technology Austria, Klosterneuburg, Austria and Dept. Comput. Sci., Duke Univ., Durham, North Carolina
Venue:
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Year:
2010

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Abstract

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.