期刊
DISCRETE & COMPUTATIONAL GEOMETRY
卷 37, 期 1, 页码 103-120出版社
SPRINGER
DOI: 10.1007/s00454-006-1276-5
关键词
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The persistence diagram of a real-valued function on a topological space is a multiset 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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