Math @ Duke

Publications [#220713] of Paul L Bendich
Papers Published
 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. 5172
(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.


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

