闫浩文, 张鑫港, 禄小敏, 李蓬勃. DP算法自动实现方法:以河流化简为例[J]. 武汉大学学报 ( 信息科学版), 2024, 49(2): 264-270. DOI: 10.13203/j.whugis20210412
引用本文: 闫浩文, 张鑫港, 禄小敏, 李蓬勃. DP算法自动实现方法:以河流化简为例[J]. 武汉大学学报 ( 信息科学版), 2024, 49(2): 264-270. DOI: 10.13203/j.whugis20210412

DP算法自动实现方法:以河流化简为例

  • 摘要: 曲线化简是自动地图综合的重要内容,但其中广泛应用的DP(Douglas-Peucker)算法却是非自动化的,原因是需要在算法执行之初由人工输入距离阈值ε。为此,首先提出了一个多尺度曲线相似度的计算公式;然后基于该公式,以河流数据为例给出了地图比例尺与曲线目标相似度的函数关系推导方法和曲线目标相似度与ε的函数关系推导方法,进而得出了ε与比例尺的函数关系;最后实现了DP算法的自动化。实验研究表明,利用提出的自动化DP算法可以获得指定地理区域不同比例尺的水系要素的化简结果,化简结果与经验丰富的制图员的手工化简结果的相似度平均值为0.927,相似度总体表现良好,表明了该方法良好的可靠性和较高的智能化。

     

    Abstract:
    Objectives Curve simplification is of importance in automated map generalization; nevertheless, the Douglas-Peucker (DP) algorithm popularly used in map generalization is not automatic, because a key parameter called distance tolerance (ε) must be given by experienced cartographers and needs to be input before execution of the algorithm.
    Methods To solve the problem, this paper proposed a method to automatically calculate ε and by which the automation of the DP algorithm is achieved. The method consists of the following steps: (1) A formula is constructed by the Hausdorff distance for calculating the similarity degree (Ssim) between a curve at a larger scale and its simplified counterpart at a smaller scale. (2) 15 linear rivers are selected, and each of them is manually simplified to get their counterparts at seven different scales. The Ssim of each original river and each of its simplified counterpart at a smaller scale can be obtained using the formula constructed by the Hausdorff distance, and 15×7=105 coordinate pairs consisting of (S,Ssim) can be got, and a function between Ssim and S are constructed by the curve fitting using the coordinates. (3) In the meanwhile, the 15 rivers are simplified using a number of ε, and the Ssim of each original river and each of its simplified counterpart at a smaller scale can be calculated using the formula constructed by the Hausdorff distance. In this way, a number of coordinate pairs (ε,Ssim) are got, and a function between ε and Ssim is constructed by the curve fitting. (4) By the function between Ssim and S and that between ε and Ssim, a formula between ε and S can be deducted. Using the formula ε can be calculated automatically, because in a map generalization task S is usually known. After this step, automation of the DP algorithm is achieved.
    Results The experiment results show that (1) The proposed DP algorithm can automatically simplify the rivers in a specific geographical area to get the results at different scales; and (2) the resulting river curves generated by the proposed DP algorithm have a high degree of similarity with the ones made by experi‍enced cartographers. Their average similarity degree is 0.927.
    Conclusion The proposed DP algorithm can simplify curve features on maps automatically, and the results are highly intelligent and credible. Although only river data is tested in this paper, the principle of the proposed method can be extended to other linear features on maps. Our future work will be on improving the accuracy of the proposed DP algorithm using more river data so that the algorithm can be used in practical map generalization engineering.

     

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