Monotonicity Analysis over Chains and Curves

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dc.creatorKucerovsky, Dan
dc.creatorLemire, Daniel
dc.date2007-01-17
dc.date2007-01-24
dc.date.accessioned2026-07-07T07:42:38Z
dc.date.available2026-07-07T07:42:38Z
dc.descriptionChains 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.
dc.descriptionto appear in Proceedings of Curves and Surfaces 2006
dc.identifierhttps://arxiv.org/abs/math/0701481
dc.identifierhttp://arxiv.org/abs/math/0701481
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/122516
dc.subjectGeneral Mathematics
dc.titleMonotonicity Analysis over Chains and Curves
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