Department of Mathematics Search | Help | Login | |

Math @ Duke

 ....................... ....................... Webpage

## Publications [#303523] of Paul L Bendich

Papers Published

1. Bendich, P; Edelsbrunner, H; Morozov, D; Patel, A, Homology and robustness of level and interlevel sets, Homology, Homotopy and Applications, vol. 15 no. 1 (2013), pp. 51-72 [1102.3389v1], [doi]
(last updated on 2018/10/23)

Abstract:
Given a function $f: \Xspace \to \Rspace$ on a topological space, we consider the preimages of intervals and their homology groups and show how to read the ranks of these groups from the extended persistence diagram of $f$. In addition, we quantify 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 $\Xspace = \Rspace^3$ has ramifications in the fields of medical imaging and scientific visualization.

dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320