The Robustness of Level 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.
Herbert Edelsbrunner is Professor at IST Austria, Arts and Sciences Professor at Duke University, and Founder and Principal at Geomagic, a software company in the field of Digital Shape Sampling and Processing. He graduated from the Graz University of Technology, Austria, in 1982, and he was faculty at the University of Illinois at Urbana-Champaign from 1985 through 1999. His research areas are algorithms, computational geometry, computational topology, and applications in biology. He has published three textbooks in the general area of computational geometry and topology.
In 1991, he received the Alan T. Waterman Award from the National Science Foundation. In 2006, he received an honorary degree from the Graz University of Technology. He is elected member of the American Academy of Arts and Sciences, of the German Academy of Sciences (the Leopoldina), and the Academia Europaea.