The Robustness of Level Sets

Paul Bendich, Herbert Edelsbrunner, Dmitriy Morozov, Amit Patel.
Proceedings of the 18th Annnual European Symposium on Algorithms, Lecture Notes in Computer Science 6346, 1-10, 2010.
Update: The full version of this paper is Homology and Robustness of Level and Interlevel 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.
Torus robustness
Gunnar Carlsson, Vin de Silva, and Dmitriy Morozov. Zigzag persistent homology and real-valued functions. Proceedings of the Annual Symposium on Computational Geometry, pages 247–256, 2009.
Herbert Edelsbrunner, Dmitriy Morozov, and Amit Patel. Quantifying transversality by measuring the robustness of intersections. Manuscript, Deptartment of Computer Science, Duke University, Durham, North Carolina, 2009.