Brooks, M. and Watson, L. (2007) Simplification of Sampled Scalar Fields by Removal of Extrema. Technical Report. National Research Council Canada.
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Publisher's URL: http://nparc.cisti-icist.nrc-cnrc.gc.ca/npsi/ctrl?action=shwart&index=an&req=5763548&lang=en
Abstract
We 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].
| Item Type: | Research Reports or Papers (Technical Report) |
|---|---|
| Status: | Published |
| Glasgow Author(s) Enlighten ID: | Watson, Professor Liam |
| Authors: | Brooks, M., and Watson, L. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Publisher: | National Research Council Canada |
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