摘要
针对一般的连续参数曲线,提出一种快速计算曲线间Hausdorff距离的方法。由于曲线的近似折线能很好的表示曲线,所以,许多软件中,采用曲线的近似折线绘制曲线。为此,证明了在任意给定误差范围下,可以将曲线间的Hausdorff距离转化为折线间的Hausdorff距离,进一步转化为点到线段间的距离进行计算,并辅之必要的剪枝策略和增量式算法以提高计算效率。该方法计算速度快,逼近度高,基本解决了参数曲线间Hausdorff距离的计算问题,在几何设计、图像匹配、图像识别等领域有广泛应用。
In view of the general continuous parametric curves,a fast method of calculating the Hausdorff distance between curves is proposed in this paper.Because a curve can be indicated by its approximate polyline,many softwares use the approximate polyline to replace the original curve when drawing curves.This paper proves that we can convert calculating the Hausdorff distance between curves into the Hausdorff distance between polylines,and further into the distance between a point and a segment under any given error range.In order to improve the computational efficiency,it also supplement a pruning strategy and incremental algorithm.This method advantages in fast speed and high degree of approximation,and basically solves the problem of calculating the Hausdorff distance between parametric curves.
出处
《图学学报》
CSCD
北大核心
2014年第5期704-708,共5页
Journal of Graphics
