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Monotonicity Analysis over Chains and Curves
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.Comment: to appear in Proceedings of Curves and Surfaces 200
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