引用本文: 程绵绵, 孙群, 李少梅, 徐立. 多尺度点群广义Hausdorff距离及在相似性度量中的应用[J]. 武汉大学学报 ( 信息科学版), 2019, 44(6): 885-891.
CHENG Mianmian, SUN Qun, LI Shaomei, XU Li. Generalized Hausdorff Distance of Multi-scale Point Group and Its Application in Similarity Measurement[J]. Geomatics and Information Science of Wuhan University, 2019, 44(6): 885-891.
 Citation: CHENG Mianmian, SUN Qun, LI Shaomei, XU Li. Generalized Hausdorff Distance of Multi-scale Point Group and Its Application in Similarity Measurement[J]. Geomatics and Information Science of Wuhan University, 2019, 44(6): 885-891.

## Generalized Hausdorff Distance of Multi-scale Point Group and Its Application in Similarity Measurement

• 摘要: 多尺度点群相似度计算在制图综合过程控制及结果评价中具有重要作用。针对现有方法的不足，提出一种基于广义Hausdorff距离的多尺度点群相似度计算方法。在传统Hausdorff距离基础上，建立距离相似度计算公式；给出拓扑距离的定义及计算方法，建立基于拓扑Hausdorff距离的拓扑相似度计算公式；以点群最小外包圆为基础建立方向关系参考框架，给出方向距离定义，建立基于方向Hausdorff距离的方向相似度计算公式，并得出总相似度计算公式。通过多尺度点群相似度计算实验及综合结果评价实验，验证了所述方法的可行性和有效性。

Abstract: Multi-scale point group similarity calculation plays an important role in process control and result evaluation of cartographic generalization. In view of the shortcomings of the existing methods, a multi-scale point group similarity calculation method based on generalized Hausdorff distance is proposed. On the basis of the traditional Hausdorff distance, the calculation formula of distance similarity is built. The definition and calculation method of topology distance is qiven, the calculation formula of topology similarity is built using the topological Hausdorff distance. The direction distance definition is also given, the direction relation reference frame is established based on the smallest enclosing disk of point group. The direction distance definition is provided and the calculation formula of direction similarity is established by using the direction Hausdorff distance. And the calculation formula of total similarity is obtained. By multi-scale point group similarity computation experiment and point group generalization evaluation experiment, the feasibility and effectiveness of the method are verified.

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