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

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.