Simplification of Sampled Scalar Fields by Removal of Extrema

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TypeTechnical Report
AbstractWe present Extremal Simplification, a rigorous basis for algorithms that simplify geometric and scientific data. The Eilenberg-Whyburn monotone-light factorization [31] provides a mathematical framework for simplification of continuous functions. We provide conditions on finite data guaranteeing uniqueness of continuous interpolations' topological structure, thereby making continuous methods available in a discrete context. Lower bounds on approximation error are derived. Extremal Simplification is compared to other scalar field simplification methods, including the Reeb graph [4, 5, 28], Morse-Smale complex [1], and the persistence diagram [11, 9].
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AffiliationNRC Institute for Information Technology; National Research Council Canada
Peer reviewedNo
NRC number49359
NPARC number5763548
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Record identifier484c8358-aa22-430a-a743-4d1a9592cdef
Record created2009-03-29
Record modified2016-10-03
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