一种基于Fréchet距离的断裂等高线内插算法

等高线内插是提高地形图精度的一个常用手段，在地图综合等领域中有很重要的作用。在实际地形图数据库中，等高线除了存在完整的计曲线以外，还有一部分断裂的首曲线。已有的等高线内插研究中未考虑对此类数据的处理，为此，本文提出了一种基于Fréchet距离的断裂等高线内插算法。首先提出了等高线度量关系的计算方法，然后对等高线的节点均匀加密，并利用Fréchet距离进行相似度判断以选择参考等高线，最后根据“最近点”的方式进行插值。通过对江苏某地区实际数据的试验，验证了该算法的合理性，对于鞍部地区的内插，有更好的适应性和准确性。

A contour interpolation algorithm based on Fréchet distance

Contour interpolation is a commonly used method to improve the accuracy of topographic maps,and plays an important role in map synthesis and other fields.In the actual topographic map database,the contour lines have some complete curves and some fracture curves.Existing contour interpolation studies do not consider the processing of such data.For this reason,this paper proposes an interpolation algorithm based on Fréchet distance.Firstly,the calculation method of the contour relationship is proposed.Then the nodes of the contour are evenly encrypted,and the similarity is judged by the Fréchet distance to select the reference contour.Finally,the interpolation is performed according to the “closest point” method.Experiments on actual data in a certain area of Jiangsu province have verified the rationality of the algorithm and have better adaptability and accuracy for the interpolation of the saddle region.