{"oa_version":"None","author":[{"first_name":"Paul","last_name":"Bendich","full_name":"Bendich, Paul","id":"43F6EC54-F248-11E8-B48F-1D18A9856A87"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","orcid":"0000-0002-9823-6833"},{"full_name":"Morozov, Dmitriy","first_name":"Dmitriy","last_name":"Morozov"},{"full_name":"Patel, Amit","id":"34A254A0-F248-11E8-B48F-1D18A9856A87","first_name":"Amit","last_name":"Patel"}],"abstract":[{"text":"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.","lang":"eng"}],"alternative_title":["LNCS"],"conference":{"end_date":"2010-09-08","start_date":"2010-09-06","name":"ESA: European Symposium on Algorithms","location":"Liverpool, UK"},"corr_author":"1","volume":6346,"_id":"3848","type":"conference","intvolume":"      6346","citation":{"chicago":"Bendich, Paul, Herbert Edelsbrunner, Dmitriy Morozov, and Amit Patel. “The Robustness of Level Sets,” 6346:1–10. Springer, 2010. <a href=\"https://doi.org/10.1007/978-3-642-15775-2_1\">https://doi.org/10.1007/978-3-642-15775-2_1</a>.","apa":"Bendich, P., Edelsbrunner, H., Morozov, D., &#38; Patel, A. (2010). The robustness of level sets (Vol. 6346, pp. 1–10). Presented at the ESA: European Symposium on Algorithms, Liverpool, UK: Springer. <a href=\"https://doi.org/10.1007/978-3-642-15775-2_1\">https://doi.org/10.1007/978-3-642-15775-2_1</a>","mla":"Bendich, Paul, et al. <i>The Robustness of Level Sets</i>. Vol. 6346, Springer, 2010, pp. 1–10, doi:<a href=\"https://doi.org/10.1007/978-3-642-15775-2_1\">10.1007/978-3-642-15775-2_1</a>.","short":"P. Bendich, H. Edelsbrunner, D. Morozov, A. Patel, in:, Springer, 2010, pp. 1–10.","ieee":"P. Bendich, H. Edelsbrunner, D. Morozov, and A. Patel, “The robustness of level sets,” presented at the ESA: European Symposium on Algorithms, Liverpool, UK, 2010, vol. 6346, pp. 1–10.","ista":"Bendich P, Edelsbrunner H, Morozov D, Patel A. 2010. The robustness of level sets. ESA: European Symposium on Algorithms, LNCS, vol. 6346, 1–10.","ama":"Bendich P, Edelsbrunner H, Morozov D, Patel A. The robustness of level sets. In: Vol 6346. Springer; 2010:1-10. doi:<a href=\"https://doi.org/10.1007/978-3-642-15775-2_1\">10.1007/978-3-642-15775-2_1</a>"},"publisher":"Springer","quality_controlled":"1","date_updated":"2024-10-09T20:54:09Z","date_published":"2010-09-01T00:00:00Z","publist_id":"2336","title":"The robustness of level sets","scopus_import":1,"month":"09","status":"public","day":"01","year":"2010","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"publication_status":"published","date_created":"2018-12-11T12:05:30Z","page":"1 - 10","department":[{"_id":"HeEd"}],"doi":"10.1007/978-3-642-15775-2_1"}