Publications [#220713] of Paul L Bendich

Papers Published

1. Paul Bendich, Herbert Edelsbrunner, Dmitriy Morozov, and Amit Patel, Homology and Robustness of Level and Interlevel Sets, edited by Gunnar Carlsson, Homology, Homotopy, and Applications, vol. 15 no. 1 (March, 2013), pp. 51-72
   (last updated on 2013/12/17)

   Abstract:
   Given a continuous function f : X → R on a topological space, we consider the preimages of intervals and their homol- ogy groups and show how to read the ranks of these groups from the extended persistence diagram of f. In addition, we quan- tify the robustness of the homology classes under perturbations of f using well groups, and we show how to read the ranks of these groups from the same extended persistence diagram. The special case X = R^3 has ramifications in the fields of medical imaging and scientific visualization.