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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.
File(s) available for this item:| PDF - 0701481.pdf |
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| Item Type: | Papers in Conference Proceedings |
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| 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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