Given a set of polygonal curves, we present algorithms for computing a middle curve that serves as a representative for the entire set of curves. We require that the middle curve consists of vertices of the input curves and that it minimizes the maximum discrete Fréchet distance to all input curves. We consider three different variants of a middle curve depending on in which order vertices of the input curves may occur on the middle curve, and provide algorithms for computing each variant.

中文翻译：

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基于离散Fréchet距离的中间曲线

给定一组多边形曲线，我们提出了用于计算中间曲线的算法，该中间曲线可以代表整个曲线集。我们要求中间曲线由输入曲线的顶点组成，并且要最大程度地减少到所有输入曲线的最大离散Fréchet距离。我们根据输入曲线的顶点在中间曲线上出现的顺序来考虑中间曲线的三种不同变体，并提供用于计算每种变体的算法。