Approach to Automating DP Algorithm：Taking River Simplification as a Example

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 ($\epsilon$) must be given by experienced cartographers and needs to be input before execution of the algorithm.

To solve the problem, this paper proposed a method to automatically calculate $\epsilon$ 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 ($S_{\mathrm{s}\mathrm{i}\mathrm{m}}$) 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 $S_{\mathrm{s}\mathrm{i}\mathrm{m}}$ 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$\times$7=105 coordinate pairs consisting of ($S,S_{\mathrm{s}\mathrm{i}\mathrm{m}}$) can be got, and a function between $S_{\mathrm{s}\mathrm{i}\mathrm{m}}$ and $S$ are constructed by the curve fitting using the coordinates. (3) In the meanwhile, the 15 rivers are simplified using a number of $\epsilon$, and the $S_{\mathrm{s}\mathrm{i}\mathrm{m}}$ 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 ($\epsilon ,S_{\mathrm{s}\mathrm{i}\mathrm{m}}$) are got, and a function between $\epsilon$ and $S_{\mathrm{s}\mathrm{i}\mathrm{m}}$ is constructed by the curve fitting. (4) By the function between $S_{\mathrm{s}\mathrm{i}\mathrm{m}}$ and $S$ and that between $\epsilon$ and $S_{\mathrm{s}\mathrm{i}\mathrm{m}}$, a formula between $\epsilon$ and $S$ can be deducted. Using the formula $\epsilon$ can be calculated automatically, because in a map generalization task $S$ is usually known. After this step, automation of the DP algorithm is achieved.

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.

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.