Monotonicity Analysis over Chains and Curves

Details Monotonicity Analysis over Chains and Curves Monotonicity Analysis over Chains and Curves

2007-01-17

arxiv.org/abs/math/0701481v2

Mathematics

General Mathematics

to appear in Proceedings of Curves and Surfaces 2006

Scientific paper

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.

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