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：数据深度度量已被广泛研究于点数据。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"曲线刺穿深度"概念，用于量化给定曲线$Q$相对于$\mathbb{R}^2$中曲线集合$\cal C$的深度位置。曲线刺穿深度评估沿$Q$长度方向根生的射线刺穿$\cal C$中元素的平均数量。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，当$Q$为$m$顶点折线且$\cal C$为$n$条折线（每条含$O(m)$个顶点）的集合时，该算法可计算曲线刺穿深度。