Measures of data depth have been studied extensively for point data. Motivated by recent work on analysis, clustering, and identifying representative elements in sets of trajectories, we introduce {\em curve stabbing depth} to quantify how deeply a given curve $Q$ is located relative to a given set $\cal C$ of curves in $\mathbb{R}^2$. Curve stabbing depth evaluates the average number of elements of $\cal C$ stabbed by rays rooted along the length of $Q$. We describe an $O(n^3 + n^2 m\log^2m+nm^2\log^2 m)$-time algorithm for computing curve stabbing depth when $Q$ is an $m$-vertex polyline and $\cal C$ is a set of $n$ polylines, each with $O(m)$ vertices.

翻译：数据深度的度量方法已针对点数据进行了广泛研究。受近期关于轨迹集合分析、聚类及代表性元素识别工作的启发，我们提出"曲线刺入深度"（curve stabbing depth）概念，用于量化给定曲线 $Q$ 相对于 $\mathbb{R}^2$ 中曲线集合 $\cal C$ 的嵌入深度。曲线刺入深度通过沿 $Q$ 路径分布的射线刺入 $\cal C$ 中元素的平均数量进行评估。我们描述了一种时间复杂度为 $O(n^3 + n^2 m\log^2m+nm^2\log^2 m)$ 的算法，适用于 $Q$ 为 $m$ 顶点折线且 $\cal C$ 包含 $n$ 条每条含 $O(m)$ 个顶点的折线情形下计算曲线刺入深度。