Simplification of Sampled Scalar Fields by Removal of Extrema

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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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)
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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