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Topological persistence and simplification. (English) Zbl 1011.68152
Summary: We formalize a notion of topological simplification within the framework of a filtration, which is the history of a growing complex. We classify a topological change that happens during growth as either a feature or noise depending on its lifetime or persistence within the filtration. We give fast algorithms for computing persistence and experimental evidence for their speed and utility.

MSC:
68U10 Computing methodologies for image processing
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