CN102930146A - Method for quantitatively evaluating fidelity precision of digital elevation model - Google Patents

Abstract

The invention relates to a method for quantitatively evaluating fidelity precision of a digital elevation model. The method is used for solving the problem that a contour playback method can only qualitatively evaluate the fidelity precision due to the absence of a fidelity precision standard of the digital elevation model during quantitative evaluation. According to the method, regulation on linear element displacement in an integrated drawing standard is fully utilized, and a water system and a terrain reconstruction valley line are taken as an example; the method comprises the following steps of: calculating an error value and a maximum offset value in offset between the water system and the terrain reconstruction valley line; establishing a subordinating degree function of a combined offset value between the water system and the terrain reconstruction valley line by employing a fuzzy mathematics method; and finally, determining a matched subordinating degree value of a single digital elevation model. The method can be used for quantitatively evaluating the fidelity precision of the digital elevation model and can be used for determining a proper range of multi-scale transformation of the digital elevation model.

Description

A kind of method of qualitative assessment digital elevation model fidelity precision

Technical field

The present invention relates to a kind of method of qualitative assessment digital elevation model fidelity precision.

Background technology

Current, digital elevation model (Digital Elevation Model, DEM) research of precision mainly concentrates on numerical precision assessment aspect, numerical precision appraisal procedure commonly used comprises the middle theory of error, transfer function method, the covariance function method, image analysis is (referring to Ke Zhengyi, He Jianbang, the pond Milky Way. digital terrain model [M]. Beijing: China Science Tech Publishing House, 1993. Hu Peng, Wu Yanlan, Hu Hai. the basic theories of digital elevation model accuracy assessment [J]. Earth Information Science, 2003, (3): 64-70. Tang Xinming, Lin Zongjian, Wu Lan. the Accuracy Assessment of setting up DEM based on level line and spot elevation is inquired into [J]. sensor information, 1999, (3): 7-10.ZHOU Xinghua, ZHAO Jixian, et al.Research on Interpolation and Accuracy Assessment ofDEM[J] .Science of Surveying and Mapping, 2005,30 (5). soup Guoan, pottery Yang, Wang Chun. level line register differences and the applied research [J] in the DEM quality assessment. the mapping circular, 2007, (7): 65-67.), and based on the synthetic determination method of topograph error (referring to soup Guoan, Gong Jianya, Chen Zhengjiang, Cheng Yanhui, Wang Zhanhong. the Accuracy of DEM Terrain Representation modeling effort [J]. mapping journal, 2001,30 (4): 361-365. Wang Guang rosy clouds, Zhu Changqing, Shi Wenzhong, etc. the research [J] of digital elevation model topograph precision. the mapping journal, 2004,33 (2): 168-173.).

Fidelity is to judge that the standard at the conflict free three-dimensional feature of adjacent area and elevation logical consistency whether DEM kept actual three dimensions or original three-dimensional data to have is (great referring to the Shen, the prosperous .DEM high-fidelity of Jing Xin problem analysis [J]. Surveying Engineering, 2011,20 (1): 30-32.), this is the middle theory of error exactly, transfer function method, covariance function method and image analysis etc. are difficult to determine the problem of solution, can't determine that namely DEM is to the fidelity of initial landform, therefore become the main method of DEM form accuracy evaluation based on the derived contour maps method of " vision precision " assessment, the derived contour maps method can effectively be rejected local rough error, guarantees preferably the total quality of dem data.But derived contour maps method workload is larger, and mostly is qualitative description, lacks the quantitative description index, causes being affected by human factors larger.

Many scholars have proposed different qualitative assessment indexs, in order to realize the quantitative description of derived contour maps.Soup Guoan etc. are (referring to the Tao of soup Guoan Yang, Wang Chun. level line register differences and the applied research [J] in the DEM quality assessment. the mapping circular, 2007, (7): 65-67.) according to the regulation of " when 1:1 ten thousand dem data derived contour maps check; level line skew of the same name is not more than 1/2 contour interval ", use level line register differences index quantification assessment DEM precision.Jiang Fan (referring to river sail .DEM surface modeling and precision assessment method research [D]. Zhengzhou: mapping institute of information engineering university, 2006,6.), the ((Zhu Changqing such as Zhu Changqing, Wang Zhiwei, the bang inkstone. based on the isocontour DEM accuracy evaluation of reconstruct model [J]. Wuhan University Journal (information science version), 2008,33 (2): 153-156.) propose with the ratio (be reconstructed error) of the area difference between original level line and reconstruct level line with original level line length, as DEM accuracy evaluation index.Wang Zhiwei (Wang Zhiwei. based on the isocontour DEM error model research of reconstruct and application [D]. Zhengzhou: mapping institute of information engineering university, 2007,6.) propose isocontour maximum reconstructed offset error and average two indexs of maximum reconstructed offset error on the basis of reconstructed error, utilized the degree of agreement of these two interior DEM of index reflection regional areas and actual landform.(the Wang Guangxia such as Wang Guangxia, Bian Shuli, Zhang Yinbao. with the research [J] of playback level line assessment DEM precision. survey and draw scientific and technical journal, 2010,27 (1): 9-13.) same on the basis of reconstructed error, increase important geography line playback offsets error criterion and reflect original level line and the difference of reconstruct level line on terrain feature is expressed.Above-mentioned research has all been made useful exploration to the qualitative assessment of derived contour maps method.

No matter utilize the level line register differences or utilize the index quantification such as level line reconstructed error assessment DEM fidelity, all must solve two key issues.The one, the isocontour generation of high-fidelity reconstruct, although higher based on the isocontour efficiency of algorithm of DEM reconstruct, robustness is better, but the isocontour quality of reconstruct is unsatisfactory, especially in the flat region or DEM size when larger, ambiguousness and broken line phenomenon relatively more serious (Wang Chun, the kiss of making pottery, Jia Dunxin, Zhu Xuejian. Regular Grid DEM Topographical Description Morphology Research on Accuracy [J]. the geography information world, 2008,1:46-52.).The 2nd, isocontour coupling of the same name, owing to be not man-to-man simple relation between original level line and the reconstruct level line, but the complex relationship of one-to-many, many-one even multi-to-multi, there is certain difficulty in isocontour coupling of the same name.These two key issues all may need a large amount of edit operations, cause derived contour maps method operability relatively poor.

What is more important, various evaluation indexes all do not form the DEM fidelity accuracy evaluation standard of system, although can assess the difference between the DEM that same Experimental Area, different interpolation algorithm sets up, but can't determine whether DEM fidelity quality has reached the demand of producing and using, and then can't determine the critical problems such as optimum range of the multiple dimensioned conversion of DEM.

Summary of the invention

The purpose of this invention is to provide a kind of method of utilizing water system and landform to overlap right qualitative assessment digital elevation model fidelity precision, in order to solve in the qualitative assessment, owing to lack digital elevation model fidelity accuracy standard, the problem that the derived contour maps method can only qualitative evaluation.

For achieving the above object, the solution of the present invention is: a kind of method of qualitative assessment digital elevation model fidelity precision, and step is as follows:

1) for an Experimental Area, water system is reference element, and the reconstruct valley route is comparison element, sets up water system and reconstruct valley route fit side-play amount membership function f (Δ D):

f(ΔD)＝A*f _RMSE(ΔD)+B*f _Max(ΔD)

f _RMSE(Δ D) is error membership function in the side-play amount, f _Max(Δ D) is the maximum offset membership function, A ∈ [0.1,0.3], B ∈ [0.7,0.9];

Work as DEM _s2﹠amp; ﹠amp; DEM _{Δ h}80 o'clock:

$f_{\mathrm{RMSE}}\left(\mathrm{\ΔD}\right)=\left\{\begin{array}{cc}1/(1+\exp (0.9902*(\mathrm{\ΔD}-5.6)))& {\mathrm{DEM}}_{\mathrm{size}}=12.5\\ 1/(1+\exp (0.2273*(\mathrm{\ΔD}-20.0)))& {\mathrm{DEM}}_{\mathrm{size}}=25\\ 1/(1+\exp (0.1899*(\mathrm{\ΔD}-28.3)))& {\mathrm{DEM}}_{\mathrm{size}}=50\\ 1/(1+\exp (0.1575*(\mathrm{\ΔD}-35.8)))& {\mathrm{DEM}}_{\mathrm{size}}=100\\ 1/(1+\exp (0.0788*(\mathrm{\ΔD}-71.6)))& {\mathrm{DEM}}_{\mathrm{size}}=200\end{array}\right.$

Work as DE _Ms≤ 2﹠amp; ﹠amp; DEM _{Δ h}≤ 80 o'clock:

$f_{\mathrm{RMSE}}\left(\mathrm{\ΔD}\right)=\left\{\begin{array}{cc}1/(1+\exp (0.9902*(\mathrm{\ΔD}-11.2)))& {\mathrm{DEM}}_{\mathrm{size}}=12.5\\ 1/(1+\exp (0.2273*(\mathrm{\ΔD}-40.0)))& {\mathrm{DEM}}_{\mathrm{size}}=25\\ 1/(1+\exp (0.1899*(\mathrm{\ΔD}-56.6)))& {\mathrm{DEM}}_{\mathrm{size}}=50\\ 1/(1+\exp (0.1575*(\mathrm{\ΔD}-71.6)))& {\mathrm{DEM}}_{\mathrm{size}}=100\\ 1/(1+\exp (0.0788*(\mathrm{\ΔD}-143.2)))& {\mathrm{DEM}}_{\mathrm{size}}=200\end{array}\right.$

Wherein Δ D is error amount in the side-play amount of Experimental Area, DEM _SizeBe digital elevation model yardstick, DEM _sBe the mean inclination of Experimental Area, DEM _{Δ h}The discrepancy in elevation for the Experimental Area;

Work as DEM _s2﹠amp; ﹠amp; DEM _{Δ h}80 o'clock:

$f_{\mathrm{Max}}\left(\mathrm{\ΔD}\right)=\left\{\begin{array}{cc}\mathrm{zmf}(\mathrm{\ΔD},\left[\begin{array}{cc}5.6& 11.2\end{array}\right])& {\mathrm{DEM}}_{\mathrm{size}}=12.5\\ \mathrm{zmf}(\mathrm{\ΔD},\left[\begin{array}{cc}20& 40\end{array}\right])& {\mathrm{DEM}}_{\mathrm{size}}=25\\ \mathrm{zmf}(\mathrm{\ΔD},\left[\begin{array}{cc}28.3& 56.6\end{array}\right])& {\mathrm{DEM}}_{\mathrm{size}}=50\\ \mathrm{zmf}(\mathrm{\ΔD},\left[\begin{array}{cc}35.8& 71.6\end{array}\right])& {\mathrm{DEM}}_{\mathrm{size}}=100\\ \mathrm{zmf}(\mathrm{\ΔD},\left[\begin{array}{cc}71.6& 143.2\end{array}\right])& {\mathrm{DEM}}_{\mathrm{size}}=200\end{array}\right.$

Work as DEM _s≤ 2﹠amp; ﹠amp; DEM _{Δ h}≤ 80 o'clock:

$f_{\mathrm{Max}}\left(\mathrm{\ΔD}\right)=\left\{\begin{array}{cc}\mathrm{zmf}(\mathrm{\ΔD},\left[\begin{array}{cc}11.2& 22.4\end{array}\right])& {\mathrm{DEM}}_{\mathrm{size}}=12.5\\ \mathrm{zmf}(\mathrm{\ΔD},\left[\begin{array}{cc}40& 80\end{array}\right])& {\mathrm{DEM}}_{\mathrm{size}}=25\\ \mathrm{zmf}(\mathrm{\ΔD},\left[\begin{array}{cc}56.6& 113.2\end{array}\right])& {\mathrm{DEM}}_{\mathrm{size}}=50\\ \mathrm{zmf}(\mathrm{\ΔD},\left[\begin{array}{cc}71.6& 143.2\end{array}\right])& {\mathrm{DEM}}_{\mathrm{size}}=100\\ \mathrm{zmf}(\mathrm{\ΔD},\left[\begin{array}{cc}143.2& 286.4\end{array}\right])& {\mathrm{DEM}}_{\mathrm{size}}=200\end{array}\right.$

Wherein zmf is the Z-shaped membership function, and it is a kind of function based on spline interpolation, and parameter a, b have defined respectively starting point and the terminal point of spline interpolation.

2) calculate f (Δ D), determine the fidelity of the digital elevation model of given Experimental Area.

Described water system and reconstruct valley route fit side-play amount membership function are to use fuzzy mathematics to set up, and set up the criterion that water system and reconstruct valley route fit side-play amount membership function follow and comprise: wire key element displacement criterion and Scale criterion;

Wire key element displacement criterion: when error is in 0.3mm in the side-play amount of water system and terrain feature line, think that sleeving fastening degree is better, namely the degree of membership value reaches more than 0.8; When error is 0.4mm in the side-play amount of water system and terrain feature line, think that sleeving fastening degree is general, namely the degree of membership value is about 0.5; When error is greater than 0.4mm in the side-play amount of water system and terrain feature line, think that sleeving fastening degree is relatively poor, namely the degree of membership value is below 0.5;

Scale criterion: according to the displacement criterion of wire key element, and with reference to square root regularity, revise the side-play amount on the spot of middle error threshold correspondence in the different scale topomap of 0.4mm; When the landform map scale was 1:10000, the middle error threshold correspondence of 0.4mm on the spot side-play amount was 5.6m; When the landform map scale was 1:50000, the middle error threshold correspondence of 0.4mm on the spot side-play amount was 20m; When the landform map scale was 1:100000, the middle error threshold correspondence of 0.4mm on the spot side-play amount was 28.3m; When the landform map scale was 1:250000, the middle error threshold correspondence of 0.4mm on the spot side-play amount was 35.8m; When the landform map scale was 1:1000000, the middle error threshold correspondence of 0.4mm on the spot side-play amount was 71.6m.

Setting up the criterion that water system and landform fit side-play amount membership function follow also comprises: mean inclination criterion, maximum fit side-play amount criterion and improvement of visual effect criterion;

The mean inclination criterion: the Experimental Area mean inclination is less to show that the level line feature in zone is not obvious, therefore can relax wire key element displacement criterion; When mean inclination less than 2 °, the discrepancy in elevation during less than 80m, the middle error threshold of again revising 0.4mm corresponding side-play amount on the spot in the different scale topomap; When the landform map scale was 1:10000, the middle error threshold correspondence of 0.4mm on the spot side-play amount was 11.2m; When the landform map scale was 1:50000, the middle error threshold correspondence of 0.4mm on the spot side-play amount was 40m; When the landform map scale was 1:100000, the middle error threshold correspondence of 0.4mm on the spot side-play amount was 56.6m; When the landform map scale was 1:250000, the middle error threshold correspondence of 0.4mm on the spot side-play amount was 71.6m; When the landform map scale was 1:1000000, the middle error threshold correspondence of 0.4mm on the spot side-play amount was 143.2m;

Maximum fit side-play amount criterion: the ratio that the maximum offset membership function accounts for water system and landform fit side-play amount membership function is 10% to 30%;

The improvement of visual effect criterion: between the different scale digital elevation model of same experiment area, if the visualization effect is similar, there is not significantly difference in the side-play amount degree of membership value that calculates so; Between the same yardstick digital elevation model in different experiments area, if the visualization effect is similar, there is not significantly difference equally in the side-play amount degree of membership value that calculates so.

Method of the present invention takes full advantage of the regulation of wire key element displacement in the cartographic generaliztion standard, take water system and terrain reconstruction valley route as example, calculate error amount and peak excursion value in the side-play amount between the two, use fuzzy mathematics method to set up water system and reconstruct valley route fit side-play amount membership function, finally determine the fit degree of membership value of single digital elevation model.The method not only can be used for the fidelity precision qualitative assessment of digital elevation model, and can be used for determining the optimum range of the multiple dimensioned conversion of digital elevation model.

Description of drawings

Fig. 1 is water system of the present invention and terrain reconstruction valley route deflection graph;

Fig. 2 is error membership function synoptic diagram in the side-play amount of non-plains region of the present invention;

Fig. 3 is non-plains region of the present invention maximum offset membership function synoptic diagram;

Fig. 4 a is the mountain valley line chart according to dem data reconstruct of test block, Yongan, Jilin of the present invention;

Fig. 4 b is the mountain valley line chart according to dem data reconstruct of test block, Dengfeng, Henan of the present invention;

Fig. 4 c is the mountain valley line chart according to dem data reconstruct of vest test block, Fujian of the present invention;

Fig. 4 d is the mountain valley line chart according to dem data reconstruct of test block, Zhangye, Gansu of the present invention;

Fig. 5 is the fit result of the regional different scale DEM of the same experiment of the present invention and water system;

Fig. 6 is the as a result improvement of visual effect comparison of fit of the regional different scale DEM of the same experiment of the present invention and water system;

Fig. 7 is the as a result improvement of visual effect comparison of fit of the different experiments same scale DEM in area of the present invention and water system;

Fig. 8 is water system of the present invention and landform fit experimental result example.

Embodiment

The present invention will be further described in detail below in conjunction with accompanying drawing.

As shown in Figure 1, wherein A ', B ', C ', D ' are the point of crossing of reconstruct level line and reconstruct valley route, and A, B, C, D are respectively A ', B ', C ', D ' to the corresponding closest approach of water system line; The present invention will be take reconstruct valley route and the isocontour point of crossing of reconstruct as foundation, calculates each point of crossing to the bias as water system and landform fit of the vertical range of corresponding water system, such as A ' A, B ' B, C ' C, D ' D.Co-existing in 4 among Fig. 1 can be for the water system of calculating and the point of crossing of reconstruct valley route, and wherein maximum offset is 42.56m, and minimum offset is 3.66m, and error is 21.76m in the side-play amount.

Side-play amount in the experiment with computing zone between water system and the reconstruct valley route just can realize the quantitative measurement of water system and reconstruct valley route sleeving fastening degree.The side-play amount that but different experiments is regional, different scale DEM obtains there are differences, and judges that the quality of water system and landform sleeving fastening degree and another Experimental Area is difficult in a certain Experimental Area this moment, therefore must set up unified judgment models.And the water system and the landform fit side-play amount membership function that use fuzzy mathematics to set up are to select preferably.

Water system and reconstruct valley route fit side-play amount membership function must be followed following five basic norms.

Criterion one: wire key element displacement criterion

Cartographic generaliztion standard clear " planimetric position of wire key element except the displacement of being undertaken by the cartographic generaliztion principle, middle error must be controlled at ± 0.3mm in ".Therefore, when error is in 0.3mm in the side-play amount of water system and terrain feature line, can think sleeving fastening degree better (being that the degree of membership value reaches more than 0.8); When error is 0.4mm in the side-play amount of water system and terrain feature line, can think sleeving fastening degree general (being that the degree of membership value is about 0.5); When error is greater than 0.4mm in the side-play amount of water system and terrain feature line, can think sleeving fastening degree relatively poor (being that the degree of membership value is below 0.5).

Criterion two: Scale criterion

Must consider the impact of DEM scale factor when setting up the side-play amount membership function.Mapping geography information office of country has stipulated the optimum DEM yardstick corresponding relation (table 1) that corresponding proportion chi topomap is set up in 1998.Therefore, be the judgment criterion that criterion one is set up equally, the middle error threshold of 0.4mm represents different side-play amounts on the spot in the DEM of different scale.

Table 1 topomap engineer's scale, DEM yardstick and side-play amount Relations Among on the spot

In the practice process, if simple utilization criterion one is judged the sleeving fastening degree of water system and landform, experimental result will cause serious deviation when different DEM yardstick so, and namely along with the increase of DEM yardstick, the increase of the actual fit side-play amount of water system and landform is not obvious especially.As judgment criterion, the side-play amount degree of membership value that obtains large scale DEM is better than the situation of small scale with table 1.

As can be seen from Figure 5, when the DEM yardstick was 12.5m, error amount was 7.7649m in the fit skew, and according to the criterion that table 1 is formulated, the side-play amount of 7.7649m is very huge; And when the DEM yardstick was 200m, error was 36.9228m in the fit skew, was used for this moment judging that its standard is 300m, was undoubtedly very accurately fit.But from improvement of visual effect, the fit successful of 12.5m DEM is better than the situation of 200m DEM.This departing from phenomenon ubiquity in all Experimental Areas almost, so criterion two must be revised.

The square root regularity method is the quantity method of disposal of a kind of cartographic generalization of proposing of German Topfer, is used for solving derived map and newly organized map because the quantity simplification problem that the conversion of engineer's scale produces.He thinks: the root of the ratio of two kinds of scale denominators of derived map and newly organized map is the quantity of the map elements that should choose of newly organized map, namely

$\frac{N_{\mathrm{new}}}{N_{\mathrm{orign}}}=\sqrt{\frac{M_{\mathrm{orign}}}{M_{\mathrm{new}}}}---\left(1\right)$

N wherein _NewBe the map elements quantity of new compilation, N _OrignBe the map elements quantity of source map, M _NewBe newly organized map scale denominator, M _OrignBe the source map scale denominator.

The square root regularity method is applicable to solve the On The Choice of map elements quantity, and research object mainly is the map elements number in the different scale map.When supposing that map elements evenly distributes, then the mean distance between the different scale map elements meets the square root regularity method equally, namely

$\frac{{\stackrel{\‾}{D}}_{\mathrm{orign}}}{{\stackrel{\‾}{D}}_{\mathrm{new}}}=\sqrt{\frac{M_{\mathrm{orign}}}{M_{\mathrm{new}}}}---\left(2\right)$

Wherein Be the mean distance between the new compilation map elements,

Be the mean distance between the new compilation map elements.

Consider the dimensional discrepancy between new compilation and the source map, also should in formula (2), increase correction factor C, namely

$\frac{{\stackrel{\‾}{D}}_{\mathrm{orign}}}{{\stackrel{\‾}{D}}_{\mathrm{new}}}=\sqrt{C*\frac{M_{\mathrm{orign}}}{M_{\mathrm{new}}}}---\left(3\right)$

Wherein C is the scope correction factor.When for example new compilation was 1:5 ten thousand for 1:10 ten thousand and source map, then C got 4.Therefore revise table 1 according to formula (3), as shown in table 2.

Table 2 topomap engineer's scale, DEM yardstick and side-play amount Relations Among (revising according to the square root regularity method) on the spot

Criterion three: mean inclination criterion

Need to consider the impact of Experimental Area mean inclination when setting up the side-play amount membership function.The Experimental Area mean inclination is less to mean that this regional level line feature is not obvious, does not have too large meaning at the sleeving fastening degree of the unconspicuous regional study water system of level line feature and landform, in most cases can give tacit consent to water system and the landform sleeving fastening degree is better.In the cartographic generaliztion standard regulation " Plain landforms " in can with " in the displacement of wire key element error be loosened to ± 0.6mm in ".Therefore " topomap engineer's scale, DEM yardstick and 0.4mm be the side-play amount Relations Among on the spot " of Plain landforms is as shown in table 3.

Table 3 topomap engineer's scale, DEM yardstick and side-play amount Relations Among (Plain landforms) on the spot

Criterion four: maximum fit side-play amount criterion

Need to consider the impact of maximum fit side-play amount when setting up the side-play amount membership function.Error is the dispersion degree of water system and landform fit side-play amount from the whole meaning in the side-play amount, does not consider the impact of single point of crossing.Suppose to exist N can supply the point of crossing of calculating, wherein most of side-play amounts are less, and the side-play amount of a certain point of crossing is larger, and the middle error that then finally calculates may be less.Can't reflect the impact on the fit precision of peak excursion value this moment.Therefore, should consider the impact of maximum offset, namely in the side-play amount membership function, occupy 20% ratio.

Criterion five: improvement of visual effect criterion

Need to consider the effect of visualization when setting up the side-play amount membership function.At first, between the regional different scale DEM of same experiment, if the visualization effect is similar, should there be larger difference in the side-play amount degree of membership value that then calculates.As shown in Figure 6.Secondly, between the same scale DEM in different experiments area, if the visualization effect is similar, should there be larger difference in the side-play amount degree of membership value that then calculates yet, as shown in Figure 7.

First and second must strictly observe in above-mentioned five criterions, third and fourth, five belong to the fine adjustments effect.Therefore with reference to above-mentioned five criterions, can set up water system and reconstruct valley route side-play amount membership function, by error membership function f in the side-play amount _RMSE(Δ D) and maximum offset membership function f _Max(Δ D) forms:

1. error membership function in the side-play amount

Work as DEM _s2﹠amp; ﹠amp; DEM _{Δ h}80 o'clock (as shown in Figure 2, wherein each bar curve from left to right is followed successively by the middle error membership function figure of 12.5m, 25m, 50m, 100m, 200mDEM):

$f_{\mathrm{RMSE}}\left(\mathrm{\ΔD}\right)=\left\{\begin{array}{cc}1/(1+\exp (0.9902*(\mathrm{\ΔD}-5.6)))& {\mathrm{DEM}}_{\mathrm{size}}=12.5\\ 1/(1+\exp (0.2273*(\mathrm{\ΔD}-20.0)))& {\mathrm{DEM}}_{\mathrm{size}}=25\\ 1/(1+\exp (0.1899*(\mathrm{\ΔD}-28.3)))& {\mathrm{DEM}}_{\mathrm{size}}=50\\ 1/(1+\exp (0.1575*(\mathrm{\ΔD}-35.8)))& {\mathrm{DEM}}_{\mathrm{size}}=100\\ 1/(1+\exp (0.0788*(\mathrm{\ΔD}-71.6)))& {\mathrm{DEM}}_{\mathrm{size}}=200\end{array}\right.$

Work as DEM _s≤ 2﹠amp; ﹠amp; DEM _{Δ h}≤ 80 o'clock:

$f_{\mathrm{RMSE}}\left(\mathrm{\ΔD}\right)=\left\{\begin{array}{cc}1/(1+\exp (0.9902*(\mathrm{\ΔD}-11.2)))& {\mathrm{DEM}}_{\mathrm{size}}=12.5\\ 1/(1+\exp (0.2273*(\mathrm{\ΔD}-40.0)))& {\mathrm{DEM}}_{\mathrm{size}}=25\\ 1/(1+\exp (0.1899*(\mathrm{\ΔD}-56.6)))& {\mathrm{DEM}}_{\mathrm{size}}=50\\ 1/(1+\exp (0.1575*(\mathrm{\ΔD}-71.6)))& {\mathrm{DEM}}_{\mathrm{size}}=100\\ 1/(1+\exp (0.0788*(\mathrm{\ΔD}-143.2)))& {\mathrm{DEM}}_{\mathrm{size}}=200\end{array}\right.$

Wherein Δ D is error amount in the side-play amount of each Experimental Area, DEM _SizeBe DEM Grid size, DEM _sBe the mean inclination of each Experimental Area, DEM _{Δ h}The discrepancy in elevation for each Experimental Area.

2. maximum offset membership function

Work as DEM _s2﹠amp; ﹠amp; DEM _{Δ h}80 o'clock (as shown in Figure 3, wherein each bar curve from left to right is followed successively by the maximum offset membership function figure of 12.5m, 25m, 50m, 100m, 200mDEM):

$f_{\mathrm{Max}}\left(\mathrm{\ΔD}\right)=\left\{\begin{array}{cc}\mathrm{zmf}(\mathrm{\ΔD},\left[\begin{array}{cc}5.6& 11.2\end{array}\right])& {\mathrm{DEM}}_{\mathrm{size}}=12.5\\ \mathrm{zmf}(\mathrm{\ΔD},\left[\begin{array}{cc}20& 40\end{array}\right])& {\mathrm{DEM}}_{\mathrm{size}}=25\\ \mathrm{zmf}(\mathrm{\ΔD},\left[\begin{array}{cc}28.3& 56.6\end{array}\right])& {\mathrm{DEM}}_{\mathrm{size}}=50\\ \mathrm{zmf}(\mathrm{\ΔD},\left[\begin{array}{cc}35.8& 71.6\end{array}\right])& {\mathrm{DEM}}_{\mathrm{size}}=100\\ \mathrm{zmf}(\mathrm{\ΔD},\left[\begin{array}{cc}71.6& 143.2\end{array}\right])& {\mathrm{DEM}}_{\mathrm{size}}=200\end{array}\right.$

Work as DEM _s≤ 2﹠amp; ﹠amp; DEM _{Δ h}≤ 80 o'clock:

$f_{\mathrm{Max}}\left(\mathrm{\ΔD}\right)=\left\{\begin{array}{cc}\mathrm{zmf}(\mathrm{\ΔD},\left[\begin{array}{cc}11.2& 22.4\end{array}\right])& {\mathrm{DEM}}_{\mathrm{size}}=12.5\\ \mathrm{zmf}(\mathrm{\ΔD},\left[\begin{array}{cc}40& 80\end{array}\right])& {\mathrm{DEM}}_{\mathrm{size}}=25\\ \mathrm{zmf}(\mathrm{\ΔD},\left[\begin{array}{cc}56.6& 113.2\end{array}\right])& {\mathrm{DEM}}_{\mathrm{size}}=50\\ \mathrm{zmf}(\mathrm{\ΔD},\left[\begin{array}{cc}71.6& 143.2\end{array}\right])& {\mathrm{DEM}}_{\mathrm{size}}=100\\ \mathrm{zmf}(\mathrm{\ΔD},\left[\begin{array}{cc}143.2& 286.4\end{array}\right])& {\mathrm{DEM}}_{\mathrm{size}}=200\end{array}\right.$

Wherein zmf is the Z-shaped membership function, and it is a kind of function based on spline interpolation, and parameter a, b have defined respectively starting point and the terminal point of spline interpolation.

Determine in the side-play amount in the error membership function and maximum offset just can to determine the side-play amount membership function according to the proportionate relationship of two membership functions, that is: after the error membership function

f(ΔD)＝A*f _RMSE(ΔD)+B*f _Max(ΔD)（4）

A ∈ [0.1,0.3] wherein, B ∈ [0.7,0.9].

Below take 1:5 ten thousand topographic map datas as example, and by reference to the accompanying drawings the specific embodiment of the present invention is described in further detail.

The first step: data are prepared

Choose respectively 1:5 ten thousand topographic map datas of four regional 25.6Km * 25.6Km such as Yongan, Jilin, Dengfeng, Henan, Fujian vest, Zhangye, Gansu as the elementary sources data, and calculate corresponding topograph parameter (table 4), represent respectively hills, low mountain, Zhong Shan and high mountain.

The regional topograph parameter of table 4 experiment

(1.1) according to the Experimental Area of selecting, extract respectively and should be mutually water system line data, as reference data; In the Experimental Area, choose at random, equably simultaneously the measurement that experiment sample district is used for the fit precision;

(1.2) best scale of determining the DEM that 1:5 ten thousand topomap are set up is 25m;

(1.3) use the DEM interpolation algorithm to set up respectively the dem data that yardstick is respectively 12.5m, 25m, 50m, 100m, 200m.

Second step: calculate side-play amount degree of membership value

(2.1) the reconstruct valley route information of the multiple dimensioned dem data of extraction is shown in Fig. 4 a, 4b, 4c and 4d;

(2.2) based on experiment sample district, searching can be used for the water system line of comparison and the match point of reconstruct valley route, calculates corresponding side-play amount;

(2.3) calculate respectively water system and reconstruct valley route fit side-play amount degree of membership value.

The 3rd step: analyze the fit precision of single DEM, and determine the optimum range of multiple dimensioned conversion

(3.1) in all Experimental Areas, calculate fit precision degree of membership value based on multiple dimensioned dem data and have different performances.As shown in Figure 8, the fit precision that 25m and 50m DEM calculate is best, and the fit precision that 12.5m DEM calculates is the poorest.Show in the multiple dimensioned dem data of setting up take 1:5 ten thousand contour line datas as benchmark, 25m and 50m DEM are optimum to the reproduction of implicit elevation information in the raw data, have verified that again the best scale of setting up DEM based on 1:5 ten thousand contour line datas is that 25m is rational.Show simultaneously when carrying out the scaling down conversion based on 25m DEM, under to push away 1 grade be fully reasonably, under push away 2-3 grade then need the consideration, because 100m and 200m DEM calculate the logic error (be that water system is crossed over topographical crest, water system is crossed over three kinds of mountain top, water system leap saddles etc., its peak excursion value is 9999.0) that exists landform to express in the fit precision; But when being based on 25m DEM and carrying out the scaling up conversion, experiment shows without any meaning, it is as a result extreme difference of fit accuracy computation, illustrate in 1:5 ten thousand contour line datas that implicit elevation information can not be replenished by different DEM interpolation algorithms (even stable, robustness all preferably interpolation algorithm), unique method is to increase new elevation information, all is futile otherwise utilize any interpolation algorithm to improve the DEM precision.

(3.2) mean inclination of Experimental Area is more smooth, and the DEM change of scale is " gently " more; The fit degree of membership value that each scale DEM data in Yongan, Jilin calculate in the table 5 is better than other Experimental Areas on the whole, show smooth zone of landform mean inclination, difference is less when carrying out multi-scale transform, more can realize " gently " conversion of DEM yardstick; But in the larger zone of landform mean inclination, difference becomes large in the process of carrying out multi-scale transform, and scaling up can not meet the demands owing to there is more elevation information, and then there is a limited range in scaling down, i.e. 1-2 yardstick.Also can know something about the variation of the terrain feature factors such as the minimum elevation during from the DEM change of scale, maximum elevation, mean inclination.The variation relation of DEM yardstick and the terrain feature factor generally shows as: along with the increase of DEM yardstick, minimum elevation becomes large, maximum elevation diminishes, mean inclination diminishes, gradually regional smoothization in whole zone, this Changing Pattern is comparatively fierce in the comparatively complicated zone of landform, then milder in the comparatively simple zone of landform, being reflected in the variation of contour information also is so, finally shows on the sleeving fastening degree so same.

Water system and landform fit degree of membership value among the multiple dimensioned DEM in each Experimental Area of table 5

The invention has the advantages that:

(1) the present invention is based on cartographic generaliztion standard principle, use fuzzy membership function, realized utilizing water system and landform sleeving fastening degree quantitative evaluation DEM landform fidelity precision.

(2) the present invention not only can quantitatively measure for the landform fidelity precision of single dem data, and can be used for determining the optimum range of multiple dimensioned DEM conversion, guarantee the scope of application of multiple dimensioned DEM; And according to the difference of the selection of water system reference data, the DEM synthesis precision that can set up for assessment of different integration algorithms.

Claims (3)

1. the method for a qualitative assessment digital elevation model fidelity precision is characterized in that step is as follows:

1) for an Experimental Area, water system is reference element, and the reconstruct valley route is comparison element, sets up water system and reconstruct valley route fit side-play amount membership function f (Δ D):

f(ΔD)＝A*f _RMSE(ΔD)+B*f _Max(ΔD)

f _RMSE(Δ D) is error membership function in the side-play amount, f _Max(Δ D) is the maximum offset membership function, A ∈ [0.1,0.3], B ∈ [0.7,0.9];

Work as DEM _s2﹠amp; ﹠amp; DEM _{Δ h}80 o'clock:

$f_{\mathrm{RMSE}}\left(\mathrm{\ΔD}\right)=\left\{\begin{array}{cc}1/(1+\exp (0.9902*(\mathrm{\ΔD}-5.6)))& {\mathrm{DEM}}_{\mathrm{size}}=12.5\\ 1/(1+\exp (0.2273*(\mathrm{\ΔD}-20.0)))& {\mathrm{DEM}}_{\mathrm{size}}=25\\ 1/(1+\exp (0.1899*(\mathrm{\ΔD}-28.3)))& {\mathrm{DEM}}_{\mathrm{size}}=50\\ 1/(1+\exp (0.1575*(\mathrm{\ΔD}-35.8)))& {\mathrm{DEM}}_{\mathrm{size}}=100\\ 1/(1+\exp (0.0788*(\mathrm{\ΔD}-71.6)))& {\mathrm{DEM}}_{\mathrm{size}}=200\end{array}\right.$

Work as DEM _s≤ 2﹠amp; ﹠amp; DEM _{Δ h}≤ 80 o'clock:

$f_{\mathrm{RMSE}}\left(\mathrm{\ΔD}\right)=\left\{\begin{array}{cc}1/(1+\exp (0.9902*(\mathrm{\ΔD}-11.2)))& {\mathrm{DEM}}_{\mathrm{size}}=12.5\\ 1/(1+\exp (0.2273*(\mathrm{\ΔD}-40.0)))& {\mathrm{DEM}}_{\mathrm{size}}=25\\ 1/(1+\exp (0.1899*(\mathrm{\ΔD}-56.6)))& {\mathrm{DEM}}_{\mathrm{size}}=50\\ 1/(1+\exp (0.1575*(\mathrm{\ΔD}-71.6)))& {\mathrm{DEM}}_{\mathrm{size}}=100\\ 1/(1+\exp (0.0788*(\mathrm{\ΔD}-143.2)))& {\mathrm{DEM}}_{\mathrm{size}}=200\end{array}\right.$

Wherein Δ D is error amount in the side-play amount of Experimental Area, DEM _SizeBe digital elevation model yardstick, DEM _sBe the mean inclination of Experimental Area, DEM _{Δ h}The discrepancy in elevation for the Experimental Area;

Work as DEM _s2﹠amp; ﹠amp; DEM _{Δ h}80 o'clock:

$f_{\mathrm{Max}}\left(\mathrm{\ΔD}\right)=\left\{\begin{array}{cc}\mathrm{zmf}\left(\begin{array}{c}\mathrm{\ΔD},\left[\begin{array}{cc}5.6& 11.2\end{array}\right]\end{array}\right)& {\mathrm{DEM}}_{\mathrm{size}}=12.5\\ \mathrm{zmf}\left(\begin{array}{c}\mathrm{\ΔD},\left[\begin{array}{cc}20& 40\end{array}\right]\end{array}\right)& {\mathrm{DEM}}_{\mathrm{size}}=25\\ \mathrm{zmf}\left(\begin{array}{c}\mathrm{\ΔD},\left[\begin{array}{cc}28.3& 56.6\end{array}\right]\end{array}\right)& {\mathrm{DEM}}_{\mathrm{size}}=50\\ \mathrm{zmf}\left(\begin{array}{c}\mathrm{\ΔD},\left[\begin{array}{cc}35.8& 71.6\end{array}\right]\end{array}\right)& {\mathrm{DEM}}_{\mathrm{size}}=100\\ \mathrm{zmf}\left(\begin{array}{c}\mathrm{\ΔD},\left[\begin{array}{cc}71.6& 143.2\end{array}\right]\end{array}\right)& {\mathrm{DEM}}_{\mathrm{size}}=200\end{array}\right.$

Work as DEM _s≤ 2﹠amp; ﹠amp; DEM _{Δ h}≤ 80 o'clock:

$f_{\mathrm{Max}}\left(\mathrm{\ΔD}\right)=\left\{\begin{array}{cc}\mathrm{zmf}\left(\begin{array}{c}\mathrm{\ΔD},\left[\begin{array}{cc}11.2& 22.4\end{array}\right]\end{array}\right)& {\mathrm{DEM}}_{\mathrm{size}}=12.5\\ \mathrm{zmf}\left(\begin{array}{c}\mathrm{\ΔD},\left[\begin{array}{cc}40& 80\end{array}\right]\end{array}\right)& {\mathrm{DEM}}_{\mathrm{size}}=25\\ \mathrm{zmf}\left(\begin{array}{c}\mathrm{\ΔD},\left[\begin{array}{cc}56.6& 113.2\end{array}\right]\end{array}\right)& {\mathrm{DEM}}_{\mathrm{size}}=50\\ \mathrm{zmf}\left(\begin{array}{c}\mathrm{\ΔD},\left[\begin{array}{cc}71.6& 143.2\end{array}\right]\end{array}\right)& {\mathrm{DEM}}_{\mathrm{size}}=100\\ \mathrm{zmf}\left(\begin{array}{c}\mathrm{\ΔD},\left[\begin{array}{cc}143.2& 286.4\end{array}\right]\end{array}\right)& {\mathrm{DEM}}_{\mathrm{size}}=200\end{array}\right.$

Wherein zmf is the Z-shaped membership function, and it is a kind of function based on spline interpolation, and parameter a, b have defined respectively starting point and the terminal point of spline interpolation.

2) calculate f (Δ D), determine the fidelity of the digital elevation model of given Experimental Area.

2. method according to claim 1, it is characterized in that, described water system and reconstruct valley route fit side-play amount membership function are to use fuzzy mathematics to set up, and set up the criterion that water system and reconstruct valley route fit side-play amount membership function follow and comprise: wire key element displacement criterion and Scale criterion;

Wire key element displacement criterion: when error is in 0.3mm in the side-play amount of water system and terrain feature line, think that sleeving fastening degree is better, namely the degree of membership value reaches more than 0.8; When error is 0.4mm in the side-play amount of water system and terrain feature line, think that sleeving fastening degree is general, namely the degree of membership value is about 0.5; When error is greater than 0.4mm in the side-play amount of water system and terrain feature line, think that sleeving fastening degree is relatively poor, namely the degree of membership value is below 0.5;

Scale criterion: according to the displacement criterion of wire key element, and with reference to square root regularity, revise the side-play amount on the spot of middle error threshold correspondence in the different scale topomap of 0.4mm; When the landform map scale was 1:10000, the middle error threshold correspondence of 0.4mm on the spot side-play amount was 5.6m; When the landform map scale was 1:50000, the middle error threshold correspondence of 0.4mm on the spot side-play amount was 20m; When the landform map scale was 1:100000, the middle error threshold correspondence of 0.4mm on the spot side-play amount was 28.3m; When the landform map scale was 1:250000, the middle error threshold correspondence of 0.4mm on the spot side-play amount was 35.8m; When the landform map scale was 1:1000000, the middle error threshold correspondence of 0.4mm on the spot side-play amount was 71.6m.

3. method according to claim 2 is characterized in that, sets up the criterion that water system and landform fit side-play amount membership function follow and also comprises: mean inclination criterion, maximum fit side-play amount criterion and improvement of visual effect criterion;

The mean inclination criterion: the Experimental Area mean inclination is less to show that the level line feature in zone is not obvious, therefore can relax wire key element displacement criterion; When mean inclination less than 2 °, the discrepancy in elevation during less than 80m, the middle error threshold of again revising 0.4mm corresponding side-play amount on the spot in the different scale topomap; When the landform map scale was 1:10000, the middle error threshold correspondence of 0.4mm on the spot side-play amount was 11.2m; When the landform map scale was 1:50000, the middle error threshold correspondence of 0.4mm on the spot side-play amount was 40m; When the landform map scale was 1:100000, the middle error threshold correspondence of 0.4mm on the spot side-play amount was 56.6m; When the landform map scale was 1:250000, the middle error threshold correspondence of 0.4mm on the spot side-play amount was 71.6m; When the landform map scale was 1:1000000, the middle error threshold correspondence of 0.4mm on the spot side-play amount was 143.2m;

Maximum fit side-play amount criterion: the ratio that the maximum offset membership function accounts for water system and landform fit side-play amount membership function is 10% to 30%;

The improvement of visual effect criterion: between the different scale digital elevation model of same experiment area, if the visualization effect is similar, there is not significantly difference in the side-play amount degree of membership value that calculates so; Between the same yardstick digital elevation model in different experiments area, if the visualization effect is similar, there is not significantly difference equally in the side-play amount degree of membership value that calculates so.

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