| 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]. |
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