A contour interpolation algorithm based on Fréchet distance

doi:10.13474/j.cnki.11-2246.2019.0013

Abstract

Abstract: Contour interpolation is a commonly used method to improve the accuracy of topographic maps,and plays an important role in map synthesis and other fields.In the actual topographic map database,the contour lines have some complete curves and some fracture curves.Existing contour interpolation studies do not consider the processing of such data.For this reason,this paper proposes an interpolation algorithm based on Fréchet distance.Firstly,the calculation method of the contour relationship is proposed.Then the nodes of the contour are evenly encrypted,and the similarity is judged by the Fréchet distance to select the reference contour.Finally,the interpolation is performed according to the “closest point” method.Experiments on actual data in a certain area of Jiangsu province have verified the rationality of the algorithm and have better adaptability and accuracy for the interpolation of the saddle region.

Key words: fracture contour, interpolation, Fréchet distance, saddle

CLC Number:

HAO Zhiwei, LI Chengming, YIN Yong, WU Pengda, WU Wei. A contour interpolation algorithm based on Fréchet distance[J]. 测绘通报, 2019, 0(1): 65-68,74.

References

[1] 杨晓琴.等高线生成算法的研究[D].太原:太原理工大学,2004.
[2] GUL S,KHAN M F.Automatic extraction of contour lines from topographic maps[C]//Digital Image Computing:Techniques and Applications (DICTA).[S.l.]:IEEE,2010:593-598.
[3] ARRIGHI P,SOILLE P.From scanned topographic maps to digital elevation models[J].Proceedings of Geovision,2007,16(91):105-109.
[4] 龚有亮,何玉华,付子傲,等.一种实用的等高线内插算法[J].测绘科学技术学报,2002,19(1):39-40.
[5] 姜波.一种等高线内插的新思路[J].科技通报,2010,26(5):780-781.
[6] 苏广军.基于规则格网的地图等高线快速追踪算法[J].西南师范大学学报(自然科学版),2004,29(5):78-79.
[7] 徐建新,徐地保.等高线内插数学模型的探讨[J].江苏测绘,2000,23(4):31-33.
[8] 胡卫明,吴兵,凌海滨.地图等高线自动内插算法[J].计算机学报,2000,23(8):847-851.
[9] 安晓亚.一种线状要素几何相似性度量方法及其应用[J].武汉大学学报(信息科学版), 2015,40(9):1225-1229.
[10] HUTTENLOCHER D P,KLANDERMAN G A,RUCKLIDGE W A.Comparing images using the Hausdorff distance[J].IEEE Computer Society,1993,15(9):850-863.
[11] FRÉCHET M M.Sur quelques points du calcul fonctionnel[J].Rendiconti del Circolo Matematico di Palermo (1884—1940),1906,22(1):1-72.
[12] 邓敏,钮沭联,李志林.GIS空间目标的广义Hausdorff距离模型[J].武汉大学学报(信息科学版),2007,32(7):641-645.
[13] 朱进.基于运动特征的轨迹相似性度量研究[D].南京:南京师范大学,2015.
[14] EITER T,MANNILA H.Computing discrete Fréchet distance[R].[S.l.]:Technische Universität Wien,1994.
[15] 陈军,赵仁亮.GIS空间关系的基本问题与研究进展[J].测绘学报, 1999,28(2):4-11.
[16] PEUQUET D J.An algorithm for calculating minimum euclidean distance between two geographic features[J].Computers & Geosciences,1992,18(8):989-1001.