Math @ Duke
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Publications [#42085] of John Harer
Papers Published
- D. Cohen-Steiner, H. Edelsbrunner and J. Harer., Stability of persistence diagrams.,
Discrete Comput. Geom., vol. 37
(2007),
pp. 103-120
(last updated on 2007/12/16)
Author's Comments: D. Cohen-Steiner, H. Edelsbrunner and J. Harer. .
Abstract: The persistence diagram of a real-valued
function on a topological space is a
multi-set of points in the extended plane.
We prove that under mild assumptions on the
function, the persistence diagram is stable:
small changes in the function imply only
small changes in the diagram. We apply this
result to estimating the homology of sets in
a metric space and to comparing and
classifying geometric shapes.
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