Monotonicity Analysis over Chains and Curves
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.
Reference
Dan Kucerovsky and Daniel Lemire, Monotonicity Analysis over Chains and Curves. Proceedings Curves and Surfaces 2006, 2007. (math.GM/0701481)
Download
- Monotonicity Analysis over Chains and Curves (arxiv pdf)
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BibTeX
@inproceedings{LemireCS2006,
author = {Dan Kucerovsky and Daniel Lemire},
title = {Monotonicity Analysis over Chains and Curves},
booktitle = {Proceedings of Curves and Surfaces 2006},
month = {June},
year = {2007}
}
Author
- Dan Kucerovsky: dan@math.unb.ca
- Daniel Lemire: lemire at acm.org
