一种改进的移动曲面拟合DEM插值方法
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摘要
针对传统曲面移动拟合法中定权方式仅以采样点与待插点的距离作为权重,而忽略采样点方向性和分布对DEM插值精度的影响问题,将Shepard加权模型引入曲面移动拟合法中进行分区定权,并在此基础上对采样点的方向性和分布进行约束,提出改进的曲面移动拟合插值方法。以湖南城市学院玉壶山作为研究对象,利用线性内插法、自然邻点插值法、曲面移动拟合法和本文方法对采样点数据进行插值生成DEM,并采用数值精度指标、等值线、坡度和坡向值以及剖面值对不同算法插值结果进行分析和评价。实验结果表明,在地貌类型为丘陵和山地的混合地区,本文方法内插出的DEM效果相对较好,DEM具有良好的连续性,能够较好地模拟出研究区的真实地形。
The surface moving fitting( SMF) method has been widely used in DEM interpolation. However, the weight in traditional surface moving fitting algorithms is only determined by the distances between scattered points and insertion points, and the influences of DEM interpolation accuracy on the direction and distribution of scattered points are neglected. The Shepard weighted model is introduced into the surface moving fitting method to define weights in different intervals, the direction and distribution of scattered points are constrained, and an improved interpolation method for surface moving fitting is proposed in this paper. Yuhu hill in Hunan City University is taken as the study area which includes hilly region and mountain land. Linear, natural neighbor interpolation( NNI), surface moving fitting and the improved method are used to generate DEM based on scattered data, and spatial interpolation results and accuracies of four interpolation algorithms are analyzed and evaluated by using numerical prccilion index, contour, slope and aspect values, and profile values. The experimental results show that DEM interpolated by the improved interpolation method is much more precise than those of the other three interpolation algorithms in hill and mountain regions, and the contours derived from it has good continuity which can accurately reflect the real terrain better.
The surface moving fitting( SMF) method has been widely used in DEM interpolation. However, the weight in traditional surface moving fitting algorithms is only determined by the distances between scattered points and insertion points, and the influences of DEM interpolation accuracy on the direction and distribution of scattered points are neglected. The Shepard weighted model is introduced into the surface moving fitting method to define weights in different intervals, the direction and distribution of scattered points are constrained, and an improved interpolation method for surface moving fitting is proposed in this paper. Yuhu hill in Hunan City University is taken as the study area which includes hilly region and mountain land. Linear, natural neighbor interpolation( NNI), surface moving fitting and the improved method are used to generate DEM based on scattered data, and spatial interpolation results and accuracies of four interpolation algorithms are analyzed and evaluated by using numerical prccilion index, contour, slope and aspect values, and profile values. The experimental results show that DEM interpolated by the improved interpolation method is much more precise than those of the other three interpolation algorithms in hill and mountain regions, and the contours derived from it has good continuity which can accurately reflect the real terrain better.
引文
[1]黄长军,夏红梅,杜梓维.南方典型丘陵区域DEM高程插值方法研究[J].湖南城市学院学报(自然科学版),2018,27(3):1-6.HUANG C J,XIA H M,DU Z W.Discussion on different DEM interpolation methods in typical hilly area of southern China[J].Journal of Hunan City University(Natural Science),2018,27(3):1-6.
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[9]陈玉莹,胡兴树,熊小青.GNSS控制网坐标移动转换的三次曲面拟合法[J].测绘科学,2016,41(10):1-3.CHEN Y Y,HU X S,XIONG X Q.Three cubic surface fitting method for mobile coordinate conversion in the GNSS control network[J].Science of Surveying and Mapping,2016,41(10):1-3.
[10]徐遵义,姜玉祥,赵亮,等.改进的Shepard算法及其在重力异常插值中的应用[J].武汉大学学报(信息科学版),2010,35(4):477-480.XU Z Y,JIANG Y X,ZHAO L,et al.Improved shepard method and its application in gravity field data interpolation[J].Geomatics and Information Science of Wuhan University,2010,35(4):477-480.
[11]NIE H,ZENG L,LUO X N.A partial approximation shepard method based on about messy data[J].Journal of Matlientatical Research and Exposition,2003,23(2):237-240.
[12]陈吉龙,刘洪斌,武伟.用等高线内插DEM的不同算法的误差分析[J].测绘科学,2009,34(4):174-176.CHEN J L,LIU H B,WU W.Error analyses on DEM interpolation based on contour[J].Science of Surveying and Mapping,2009,34(4):174-176.
[13]LIU K,DING H,TANG G A,et al.An object-based approach for two-level gully feature mapping using high-resolution dem and imagery:A case study on hilly loess plateau region,China[J].Chinese Geographical Science,2017,27(3):415-430.
[14]兰玉芳,徐霞,胡英敏.等高线内插DEM算法的质量评价[J].地理与地理信息科学,2012,28(4):25-28.LAN Y F,XU X,HU Y M.Quality assessment on different DEM interpolation algorithms based on contours[J].Geography and Geo-information Science,2012,28(4):25-28.
[15]刘爱利,丁浒,田丹,等.基于坡度和坡向分析的DCT域DEM数字水印算法[J].武汉大学学报(信息科学版),2016,41(7):903-910.LIU A L,DING H,TIAN D,et al.A DCT DEM digital watermarking algorithm based on the analysis of slope and aspect[J].Geomatics and Information Science of Wuhan University,2016,41(7):903-910.
[16]贾旖旎,汤国安,刘学军.高程内插方法对DEM所提取坡度、坡向精度的影响[J].地球信息科学学报,2009,11(1):40-46.JIA Y N,TANG G A,LIU X J.The impact of elevation interpolation on the accuracy of gradient and aspect from DEMs[J].Journal of Geo-Information Science,2009,11(1):40-46.
[2]张锦明,郭丽萍,张小丹.反距离加权插值算法中插值参数对DEM插值误差的影响[J].测绘科学技术学报,2012,29(1):51-56.ZHANG J M,GUO L P,ZHANG X D.Effects of interpolation parameters in inverse distance weighted method on DEM accuracy[J].Journal of Geomatics Science and Technology,2012,29(1):51-56.
[3]蔺爱军.利用二次曲面移动拟合法进行DEM内插的精度探讨[J].测绘技术装备,2003,5(2):23-25.LIN A J.Discussion on accuracy of DEM interpolation using quadric surface moving fitting method[J].Geomatics Technology and Equipment,2003,5(2):23-25.
[4]冯园,赵牡丹,张鹏,等.顾及梯田的DEM地形特征研究[J].水土保持研究,2017,24(4):32-37.FENG Y,ZHAO M D,ZHANG P,et al.Study on topographic features of the terraces DEM[J].Research of Soil and Water Conservation,2014,24(4):32-37.
[5]潘攀,王光霞,张华.DEM建模方法的研究与实践[J].测绘科学技术学报,2007,24(1):61-64.PAN P,WANG G X,ZHANG H.Study and practice of DEMgeneration[J].Journal of Geomatics Science and Technology,2007,24(1):61-64.
[6]张伟,覃庆炎,简兴祥.自然邻点插值算法及其在二维不规则数据网格化中的应用[J].物探化探计算技术,2011,33(3):291-295.ZHANG W,TAN Q Y,JIAN X X.Natural neighbour interpolation and its application to 2D grid of irregular data[J].Computing Techniques for Geophysical and Geochemical Exploration,2011,33(3):291-295.
[7]王建民.基于Kriging下的移动曲面拟合法研究[J].测绘科学,2012,37(4):160-161;170.WANG J M.Moving surface fitting models based on Kriging method[J].Science of Surveying and Mapping,2012,37(4):160-161;170.
[8]杨晓云,顾利亚,岑敏仪,等.基于不同大小窗口的移动曲面拟合法探测不规则DEM粗差的一种方法[J].测绘学报,2005,34(2):148-153.YANG X Y,GU L Y,CEN M Y,et al.A method based fitting of moving quadric surface with variable windows for detecting gross errors in irregular DEM[J].Acta Geodaetica et Cartographica Sinica,2005,34(2):148-153.
[9]陈玉莹,胡兴树,熊小青.GNSS控制网坐标移动转换的三次曲面拟合法[J].测绘科学,2016,41(10):1-3.CHEN Y Y,HU X S,XIONG X Q.Three cubic surface fitting method for mobile coordinate conversion in the GNSS control network[J].Science of Surveying and Mapping,2016,41(10):1-3.
[10]徐遵义,姜玉祥,赵亮,等.改进的Shepard算法及其在重力异常插值中的应用[J].武汉大学学报(信息科学版),2010,35(4):477-480.XU Z Y,JIANG Y X,ZHAO L,et al.Improved shepard method and its application in gravity field data interpolation[J].Geomatics and Information Science of Wuhan University,2010,35(4):477-480.
[11]NIE H,ZENG L,LUO X N.A partial approximation shepard method based on about messy data[J].Journal of Matlientatical Research and Exposition,2003,23(2):237-240.
[12]陈吉龙,刘洪斌,武伟.用等高线内插DEM的不同算法的误差分析[J].测绘科学,2009,34(4):174-176.CHEN J L,LIU H B,WU W.Error analyses on DEM interpolation based on contour[J].Science of Surveying and Mapping,2009,34(4):174-176.
[13]LIU K,DING H,TANG G A,et al.An object-based approach for two-level gully feature mapping using high-resolution dem and imagery:A case study on hilly loess plateau region,China[J].Chinese Geographical Science,2017,27(3):415-430.
[14]兰玉芳,徐霞,胡英敏.等高线内插DEM算法的质量评价[J].地理与地理信息科学,2012,28(4):25-28.LAN Y F,XU X,HU Y M.Quality assessment on different DEM interpolation algorithms based on contours[J].Geography and Geo-information Science,2012,28(4):25-28.
[15]刘爱利,丁浒,田丹,等.基于坡度和坡向分析的DCT域DEM数字水印算法[J].武汉大学学报(信息科学版),2016,41(7):903-910.LIU A L,DING H,TIAN D,et al.A DCT DEM digital watermarking algorithm based on the analysis of slope and aspect[J].Geomatics and Information Science of Wuhan University,2016,41(7):903-910.
[16]贾旖旎,汤国安,刘学军.高程内插方法对DEM所提取坡度、坡向精度的影响[J].地球信息科学学报,2009,11(1):40-46.JIA Y N,TANG G A,LIU X J.The impact of elevation interpolation on the accuracy of gradient and aspect from DEMs[J].Journal of Geo-Information Science,2009,11(1):40-46.
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