用嵌套逼近加速多边形曲线的简化
Speeding up Simplification of Polygonal Curves using Nested Approximations
摘要：
我们开发了一个多分辨率的方法来解决多边形曲线逼近的问题。我们从理论上和实验上证明，如果在任意两个连续的分辨率级之间使用的简化算法A满足一定的条件，那么多分辨率算法MR的复杂度将低于A的复杂度。特别是，我们表明，如果A有一个O（N2/K）的复杂性（减少搜索动态解决方案的方法的复杂性），其中N和K分别是初始和最终的段数，MR的复杂性是在O（N）。我们实验比较MR的结果与最佳的“全搜索”动态规划解决方案和经典的合并和分裂的方法。实验评估证实了理论推导，并表明，所提出的方法在2D海岸地图上评估，要么表现出较低的复杂性，或提供多边形近似接近初始曲线。
英文摘要：
We develop a multiresolution approach to the problem of polygonal curve approximation. We show theoretically and experimentally that, if the simplification algorithm A used between any two successive levels of resolution satisfies some conditions, the multiresolution algorithm MR will have a complexity lower than the complexity of A. In particular, we show that if A has a O(N2/K) complexity (the complexity of a reduced search dynamic solution approach), where N and K are respectively the initial and the final number of segments, the complexity of MR is in O(N).We experimentally compare the outcomes of MR with those of the optimal "full search" dynamic programming solution and of classical merge and split approaches. The experimental evaluations confirm the theoretical derivations and show that the proposed approach evaluated on 2D coastal maps either shows a lower complexity or provides polygonal approximations closer to the initial curves.
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