基于传统离散Fréchet距离,提出了一种线状要素几何相似性度量方法。推导了基于递归迭代方法计算离散曲线Fréchet距离的计算公式,因传统Fréchet距离仅用一个点对之间的距离来度量相似性存在较大误差,提出了一种基于离散Fréchet距离识别曲线上点与点之间最短路径的方法,通过最短路径计算两条曲线间平均Fréchet距离,以平均Fréchet距离作为两曲线间的相似值。针对传统Fréchet距离不能解决一条曲线的部分与另一条完整曲线之间的相似匹配,基于平均Fréchet距离,提出了“部分-整体”Fréchet距离计算方法。将上述距离应用于地图数据匹配、合并及等高线内插中,取得了较好的效果。
Geometric similarity measurement of linear features is the key to matching map data, fusion, and clustering. This paper presents a new method for geometric similarity measurement of digital map linear features based on the traditional discrete Frechet distance. We derived a formula for computing discrete curves Frechet distance based on recurrence and presents curves similarity measurement model based on average Frechet distance. The average Frfchet distance is obtained by recognizing and computing minimal path between points in two curves, which can avoid biggish error of traditional Frechet distance. Meanwhile, this paper demonstrates that the average Frechet distance delivers higher accuracy, theoretically. In order to measure the partial and overall similarity between two curves, we also present a partial-overall discrete Frfchet distance based on the average Frechet distance. Finally, this Frechet distance was applied to matching map data, fusion and contour interpolation. Experiments were performed to show the feasibility and superiority of the method.