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Monotonicity Analysis over Chains and Curves [r-libre/204]

Kucerovsky, Dan, & Lemire, Daniel (2007). Monotonicity Analysis over Chains and Curves. In Curve and surface fitting: Avignon 2006 (p. 180-190). Brentwood, TN, É.-U. : Nashboro Press.

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Item Type: Papers in Conference Proceedings
Refereed: Yes
Status: Published
Abstract: Chains are vector-valued signals sampling a curve. They are important to motion signal processing and to many scientific applications including location sensors. We propose a novel measure of smoothness for chains curves by generalizing the scalar-valued concept of monotonicity. Monotonicity can be defined by the connectedness of the inverse image of balls. This definition is coordinate-invariant and can be computed efficiently over chains. Monotone curves can be discontinuous, but continuous monotone curves are differentiable a.e. Over chains, a simple sphere-preserving filter shown to never decrease the degree of monotonicity. It outperforms moving average filters over a synthetic data set. Applications include Time Series Segmentation, chain reconstruction from unordered data points, Optical Character Recognition, and Pattern Matching.
Depositor: Lemire, Daniel
Owner / Manager: Daniel Lemire
Deposited: 16 Jul 2007
Last Modified: 16 Jul 2015 00:47

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