2003-2004 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Shi, WZ

Wan, GX

Zhang, GQ

Zhu, CQ

PolyU Institutional Repository

? 33 ?　? 2 ? ?　?　?　? Vol.33 , No.2　2004 ? 5 ? ACTA GEODAETICA e t CARTOGRAPHICA SINICA May , 2004　　????:1001-1595(2004)02-0168-06 ?????:P207　　　　?????:A???????????????王光霞1 , 朱长青1 , 2 , 史文中3 , 张国芹2(1.????????? ???? ,?? ?? 450052;2.??????????????? ,?? ??430077;3.?????? ??????????????????? , ??)The Further Study on the Accuracy of DEMTerrain RepresentationWANG Guang-x ia1 , ZHU Chang-qing1 , 2 , SHI Wen-zhong 3 , ZHANG Guo-qin2(1.Zhengzhou Institute of Surveying and Mapping , Zhengzhou 450052 , China;2.I nstitute of Geodesy andGeophysics , Chinese Academy of Science , Wuhan 430077 , China;3.Advanced Research Centre for Spatial In-formation Technology , Department of Land Surveying and Geo-Informatics , The Hongkong Poly technic Univer-sity , Hong Kong , China)Abstract:The relation between DEM terrain representa tion erro r(E t)and the variation of DEM resolution(R)and mean profile curvature(V)is studied.And a new fo rmula on the relation fo r RMS E t , R and V is describedas:RMSE t =(0.006 1 V+0.002 7)R+0.001 0 V2-0.064 9 V +0.569 5On the o ther hand , a fo rmula on the relation fo r RMS E t , R and slope W is described as:RMS E t=(0.000 1W2+0.003 1W +0.030 1)R+0.000 8W2-0.050 8W+0.355 9The analy sis of the formulae show s tha t there is high accuracy by the developed formulae.Key words:DEM;error;space resolution;mean profile curvature;slope?　?:对数字高程模型(DEM)的地形描述误差(E t)与空间分辨率(R)和平均剖面曲率(V)的关系进行研究 , 得到地形描述误差的均方差值与 R 、 V 的函数关系公式:RMSE t =(0.006 1 V +0.002 7)R +0.001 0 V2-0.064 9V +0.569 5。进一步 ,还得到地形描述误差的均方差值与 R 、坡度 W 的函数关系公式:RMSE t =(0.000 1W 2+0.003 1W +0.030 1)R +0.000 8W 2-0.050 8W +0.355 9。分析结果表明 ,所得公式具有好的效果 。　　????:2003-07-21;????:2003-11-30????:???????????????????????(WKL(01)0101);??????? ,????????????(40176032 , 40174006)????:???(1962-),? ,????? ,?? ,?????????? 、??????。???:DEM;误差;空间分辨率;平均剖面曲率;坡度1　引　言??????(DEM)????????????????? ,??????? DEM ???????? ,?????????。?? DEM??? ,?????? ,? Monckton[ 1]?? DEM????? 、???????????????。Kidner[ 2]???????DEM ???????。??? ,???[ 3]???????????????? DEM ?????。????????????? ,????????? ,?????????????? E t ??? 、???? 、?????????????? ,??? 6????? E t?????(RMSE)???????????RMSE t =y =0.213 9 x -0.427 8(?? , P=34.80 , S =27.5)y =0.133 4 x -0.310 1(?? , P=21.24 , S =20.7)y =0.099 9 x -0.225 3(?? , P=15.47 , S =15.1)y =0.055 1 x +0.109 4(?? , P=8.87 , S =7.15)y =0.037 8 x +0.206 3(?? , P=5.96 , S =2.42)y =0.118 1 x -0.277 0(???? , P=18.48 , S =14.3)(1)?? , P ????? , S ????? 。??(1)?? y =ax+b ,??? a , b???????? ,????????a=0.006 3V +0.006 6 (2)b=-0.022V +0.241 5 (3)??? 2 ????????????????? ,????? DEM ???????????????????RMSE t =(0.006 3 V+0.006 6)R -0.022 V+0.241 5 (4)????????R =(RMSE t +0.022V -0.241 5)/(0.006 3V +0.006 6) (5)?? ,??? DEM ??????????????? DEM ??? 。?? ,???(4)?????????? ,???????????????? 。?? ,????? ,??????(? 1?? 2)???(4)??? E t ???? 1?? 。????????? ,??????????????? 。? 1　?????????? DEM??[ 1]Tab.1　Major topographic variables and the accuracy of original DEMs?? ?? ?? ?? ?? ???????? ???? ???? ???? ????? ????? ??????????? ????/ m 　425 　224 　227 　824 2 614　 　662????/ m 　　2.42 　　7.15 　 15.1 　 20.7 　 　27.5 　 14.3????/(°) 5.96 8.87 15.47 21.24 34.80 18.48???/ m 0.39 0.64 1.15 1.52 2.82 1.35?? DEM ?? ???/ m 0.28 0.57 1.04 1.41 2.16 1.23????/ m 0.24 0.41 0.91 1.03 2.09 1.11? 2　??????? Et ????(RMSE)???[ 1]Tab.2　RMS E t of different terrain types???/ m ?? ?? ?? ?? ??????10 0.599 0.678 0.856 1.012 1.378 0.93820 0.975 1.237 1.831 2.350 3.571 2.10230 1.350 1.796 2.805 3.687 5.763 3.22640 1.726 2.355 3.779 5.025 7.955 4.43150 2.101 2.914 4.754 6.363 10.148 5.59560 2.476 3.474 5.728 7.701 12.340 6.75970 2.852 4.033 6.703 9.039 14.533 7.92480 3.227 4.592 7.677 10.376 16.725 9.08890 3.602 5.151 8.651 11.714 18.917 10.252100 3.978 5.710 9.626 13.052 21.110 11.417　　?? 1 ?? ,?? RMS E t ? 3 ,????(4)??????????? 40 ,?????????? ,???? 50?? 。??????? ,??????? 。?? ,??(4)???(5)??????????? 。????? 1 、? 2?? ,?????(2)?????(3)??? ,????????????? ,?????? DEM ??????????????????? ,???? DEM ????????????????? 。??????????????? ,???????????????。169? 2 ?　　　　　　　　　　　????:???????????????? 1　???? DEM ???????(4)????Fig.1　The calculated result by formula(4)and statisticdata fo r terrain2　DEM 误差与空间分辨率和平均剖面曲率关系公式　　?????(4)???(5)??? ,?????DEM ??????????????????? ,?????????? 。2.1　??????(4)???(5)??????(1)???a ,b ??????????? 。?? ,????????????(4)???(5)????。? 2?? 3??????(1)??? a , b???????????。? 2　??????? a ????　　Fig.2　The relation between profile curvature andcoefficient a? 3　??????? b ????　　Fig.3　The relation between profile curvature andcoefficient b?? 2?? ,?? a ?????????????? ,??????????????????a=0.006 1V +0.002 7 (6)??? 3?? ,?? b?????????????? ,??????????????? ,???? DEM ??????????????????。??? ,?? 3?? ,?? b ???????????????? ,????????????????。???????? ,???? b??????????????b=0.001 0 V2-0.064 9 V+0.569 5 (7)? 4?????????????? b ?????????? 。?4　?? b ?????????(????????? ,?????????)Fig.4　The approach of profile curvature against coefficientb(the straight line is the linear approach , and thecurv e is the square approach)????(6),??(7),????(1),????DEM ?????????????????????170 ?　?　?　?　　　　　　　　　　　　　　　　　　? 33 ?RMSE t =(0.006 1 V+0.002 7)R +0.001 0V 2-0.064 9V +0.569 5 (8)?????R =(RMSE t -0.001 0V 2+0.064 9V -0.569 5)/(0.006 1 V+0.002 7) (9)?? ,???? DEM ??????????????? DEM ???。2.2　?????? 4?? ,??????? b ?????????????????b??????????。?? ,???????????????????????????? 。?? ,????(6),??(7)????? 。???? 3。? 3　????????????????Tab.3　The correction coefficient of regression againstprof ile curvature?? a ??????? b ???????[ 1]???? 0.989 9 0.842 5???? 0.998 9 0.988 2?? 3?? ,???(2)、(3)?? ,??(6)?????(7)????????。?? ,????(2)、(3)???(6)、(7)????? ,????????。??????MSE =】∑Ni=1(h i -h i′)2/ N〈?? , hi ????? , hi′?????????? ,N ???????。?4 ???????(2),??(3)???(6),??(7)????? 。?? 4?? ,??(6)?????(7)?????????。? 4　??????Tab.4　The error of approach curve?? a ??????? b ???????[ 1]???? 0.003 0 0.040 4???? 0.000 8 0.014 3?? ,??? 2????????? E t ???? ,???(8)???[ 1]???(4)??????。? 1??????????????(4)???(8)????? ,?? 1??? ,??(8)???? 。??????? ,???????。?? ,???????????????????????(4)???(8)?????????????? ,????????(? 5)。? 5　??(4)???(8)?????????Tab.5　The comparision result for formula(4)and(8)with the original data?? ?? ?? ?? ?? ??????(4) 0.313 9 0.344 9 0.428 1 0.502 5 0.680 1 0.464 4??(8) 0.089 1 0.025 8 0.098 1 0.123 1 0.159 2 0.120 5　　?? 5 ?? ,?????????? DEM??????????????????????????? ,????? 、?????????????????? 。3　DEM误差与空间分辨率和坡度关系公式　　????(1),??? DEM ?????????????????? 。3.1　???????(1)??? a , b???????????????????? 。?? a ??? ,????????????????a=0.006 8W +0.011 2 (10)?? ,?????????? ,?????????a=0.000 1W2+0.003 1W+0.030 1(11)???? b ??? , ??????? ,???????????????????b=-0.026 6W +0.231 9 (12)b=0.000 8W 2-0.050 8W +0.355 9 (13)?5 ,? 6??????????????????????? 。171? 2 ?　　　　　　　　　　　????:???????????????? 5　?? a ????????Fig.5　The approach of slope against coefficient a? 6　?? b ????????Fig.6　The approach of slope against coefficient b　　?? 5 ,? 6?? ,????????????????。?? ,????????????????????? DEM ???????????????RMSE t =(0.000 1W2+0.003 1W+0.030 1)R+0.000 8W2-0.050 8W +0.355 9 (14)?? ,??(14)?R =(RMSE t -0.000 8W 2+0.050 8W -0.355 9)/(0.000 1W 2+0.003 1W +0.030 1) (15)?? ,???? DEM ??????????????? DEM ???。3.2　???????????? ,??????(10)～ ??(13)????? ,???? 6。? 6　????Tab.6　The correction coefficient of regression against slope?? a ??? ?? b ??????? 0.949 1 0.903 0?????? 0.969 9 0.958 3? 6????? ,????????????????。?? ,??? 2????????? E t ???? ,???(14)?????? 。? 7 ????????????????????(14)?????????????? ,????????。? 7　??(14)?????????Tab.7　The contact result for formula(14)in this paper with the original data?? ?? ?? ?? ?? ??????(14) 0.052 8 0.042 3 0.066 8 0.183 8 1.429 4 1.320 0　　?? 7?? ,??(14)??? 、?? 、?? 、?????????????????? ,?????????????? 。?????????????? a , b ????????????????。4　结　论??? DEM ?????????????????????????????? ,????????????? ,?????? DEM ???????????????????。???? ,?????????????????? ,?????????。?? ,??????????????????? R 、?? W ???????? ,???????????? ,???????????。??????? ,????????? DEM??????????????? 、??????? ,? DEM ???????????????????。????????? ,??????????? ,???????????? 。172 ?　?　?　?　　　　　　　　　　　　　　　　　　? 33 ?参考文献:[ 1] 　MONCKTON C.An Investigation into the SpatialStructure of Er ro r in Digital Elevation Da ta [ M ] .London:Taylor and F rancis , 1994.[ 2] 　KIDNER D B.High-order Interpolation of RegularG rid Digital Elevation Models[ J] .I nterna tional Jour-nal of Remo te Sensing , 2003 , 21(14):2 981-2 987.[ 3] 　TANG Guo-an , GONG Jian-ya, et al.A Simulationon the Accuracy of DEM Terrain Representation[ J] .Acta Geodaetica e t Cartographica Sinica , 2001 , 30(4):361-365.(in Chinese)[ 4] 　WU Gong-fu , AN Wan-fu , Liu Jing-hai.Data Analy-sis Method [ M ] .Beijing:China S tatistics Press ,1992.(in Chinese)英文摘要的几点要求　　????????? ,?????????? ,?:????? 、????? 、??。???????? , ??? , ???????????????。 ???????????????? , ????????? , ???????????? ,????????????。?????????? ,????? , ?????“??” ,“????”?“????”???。 ????????? 150 wo rds。????????? ,???????。???????????? ,??????? 。??????1.????????:? “ It is reported…” , “ Exten-sive investigations show that …”“ The author discusses …”“ This paper concerned with …” ;????? “ In this pa-per , ” ????????? , ?“ in detail” , “ briefly” ,“ here” , “ new” , “mainly”?????。2.???????????????????;3.?????????(Background Information);???????????????????????? , ???????????????????????。4.?????????? ,??? , ???????????;5.?????? ,?“??????????????????????????” , “????????…” ,“???????????????”??????????;6.??????????????????;7.?????????????? ,?:?? ??at a temperature of 250℃ to 300℃ at 250℃-300℃at a high pressure of 2000 psig at 2000 psigat a high temperature of 1500 ℃ at 1500℃discussed and studied in detail discussed　　8.???????????(Title)??。????1.??????? ,?? , ??;2.?????????????;3.??????????? , ???????????;? “ The structure of dislocation cores in GaP was in-vestigated by weak-beam electron microscopy.The disloca-tio ns are dissocia ted into two Shokley partials with separa-tio ns of 80 ±10 and 40±10 A in the pure edge and screwcases respectively.The results show that…”4.???????????????? , ?????????????????。??:? measurement accuracy ?? measuring accura-cy;? experimental results ?? experiment results.?????????????????? ,??? of ??。??:? measurement accuracy ?? accuracy of mea-surement;? camera cur tain shutter ?? curtain shutter ofcamera;? equipment structure?? structure of equipment.5.???????????????????;??:? Thickness of plastic sheets w as measured ??Measurement of thickness of plastic sheet w as made.6.?????? , ???? ,?????????。7.?????????????????? , ?????????????? ,????????? , ???????(?????)。??? The chlorine-containing propylene-based po ly-mer of high meld index ?? The chlorine containing highmelt index propylene based polymer.8.?????????????;9.????? 、???????????;10.???????;11.????? ,??????????;? Adsorption nitrobenzene on copper chromite investi-gation ?? Adso rption of nitrobenzene on copper chromitewas investigated.12.??????? , ??????????????;13.????? ,?????????;??:??:The decolorization in solutions of the pigment indioxane , which w ere exposed to 10 hr o f UV ir radiation , w asno longer irreversible.??:When the pigment was dissolvedin dio xane , decolorization was ir reversible after 10hr of UVirradiation.14.????;?? increased ?? has been found to increase;? theresults show ?? from the experimental results , it can beconcluded tha t.15.????????????????? , ??????????????;16.?????? , ???????? , ????????????。17.???????“?××” 、“??××”?“????××”???。??????1.??? home made ??“ ??” ???? , homemade???????“????”????。2.???????? , ?????????。3.????????????。?????????。?? , ??? because??????“??”???? ,because?????????????。???“ XX areanaly zed and studied(discussed)” 。???“????(??)”??????。?“XX are analyzed”????。?????? not only…but also ????“??” …“??” ???? , ? and ???。4.????????。????????????? 、????????? ,??????????? ,????????????????。???????????????????????????????????????? , ???????????。5.? ? ? ? ? ? ? ? ? ?(Abbreviations andAcronyms)。??????????????? , ? radar、laser、CAD? , ??????。??????????????? ,???? 、???????????????。173? 2 ?　　　　　　　　　　　????:???????????????

The further study on the accuracy of DEM terrain representation

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