链和曲线上的单调性分析
Monotonicity Analysis over Chains and Curves
摘要：
链是对曲线进行采样的向量值信号。它们对于运动信号处理和包括位置传感器在内的许多科学应用都很重要。通过推广标量值单调性的概念，提出了一种新的链曲线光滑性度量。单调性可以通过球的逆像的连通性来定义。这个定义是坐标不变的，可以在链上有效地计算。单调曲线可以是不连续的，但连续单调曲线是可微的。在链上，一个简单的球保持过滤器，永远不会减少单调性的程度。它在合成数据集上优于移动平均滤波器。应用包括时间序列分割、无序数据点的链重建、光学字符识别和模式匹配。
英文摘要：
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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