CN102930146B - 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 fidelity precision of digital elevation model

Technical field

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

Background technology

Current, digital elevation model (Digital Elevation Model, DEM) research of precision mainly concentrates on numerical precision assessment aspect, conventional numerical precision appraisal procedure comprises medial error method, transfer function method, covariance function method, image analysis is (see 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 [J] of digital elevation model accuracy assessment. Earth Information Science, 2003, (3): 64-70. Tang Xinming, Lin Zongjian, Wu Lan. the Accuracy Assessment setting up DEM based on level line and spot elevation inquires into [J]. sensor information, 1999, (3): 7-10.ZHOU Xinghua, ZHAO Jixian, et al.Research on Interpolationand Accuracy Assessment ofDEM [J] .Science of Surveying and Mapping, 2005, 30 (5). soup Guoan, Tao Yang, Wang Chun. level line register differences and the applied research in DEM quality assessment [J]. mapping circular, 2007, (7): 65-67.), and based on the synthetic determination method of terrain representation error (see 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, Deng. the research [J] of digital elevation model topograph precision. mapping journal, 2004, 33 (2): 168-173.).

Fidelity is that to judge whether DEM maintains that actual three dimensions or initial three-dimensional data have (great see Shen in the standard of the conflict free three-dimensional feature of adjacent area and elevation logical consistency, Jing Xin prosperous .DEM high-fidelity problem analysis [J]. Surveying Engineering, 2011, 20 (1): 30-32.), this is medial error method exactly, transfer function method, covariance function method and image analysis etc. are difficult to the problem determining to solve, namely the fidelity of DEM to initial landform cannot be determined, therefore the derived contour maps method assessed based on " visual acuity " becomes the main method of DEM form accuracy evaluation, derived contour maps method effectively can reject local rough error, ensure the total quality of dem data preferably.But derived contour maps method workload is comparatively large, and mostly is qualitative description, lack quantitative description index, cause being affected by human factors larger.

Many scholars propose different qualitative assessment indexs, in order to realize the quantitative description of derived contour maps.Soup Guoan etc. are (see soup Guoan Tao Yang, Wang Chun. level line register differences and the applied research in DEM quality assessment [J]. mapping circular, 2007, (7): 65-67.) according to the regulation of " when 1:1 ten thousand dem data derived contour maps checks; level line skew of the same name is not more than 1/2 contour interval ", level line register differences index quantification assessment DEM precision is used.Jiang Fan (study [D] see river sail .DEM surface modeling and precision assessment method. Zhengzhou: Institute of Surveying and Mapping of information engineering university, 2006,6.), the ((Zhu Changqing such as Zhu Changqing, Wang Zhiwei, bang inkstone. based on the DEM accuracy evaluation model [J] of reconstruction contour. Wuhan University Journal (information science version), 2008,33 (2): 153-156.) propose with the difference in areas between original level line and reconstruction contour and original level line length ratio (i.e. reconstructed error), as DEM accuracy evaluation index.Wang Zhiwei (Wang Zhiwei. based on the DEM error model Study and appliance [D] of reconstruction contour. Zhengzhou: Institute of Surveying and Mapping of information engineering university, 2007,6. on the basis of reconstructed error) propose isocontour maximum reconstructed offset error and average maximum reconstructed offset error two indices, utilize this two indices to reflect the degree of agreement of DEM and actual landform in regional area.(the Wang Guangxia such as Wang Guangxia, Bian Shuli, Zhang Yinbao. with the research [J] of playback level line assessment DEM precision. Surveying and mapping technology 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 reconstruction contour on terrain feature is expressed.Above-mentioned research has all made useful exploration to the qualitative assessment of derived contour maps method.

No matter utilize level line register differences or utilize the index quantification assessment DEM fidelities such as level line reconstructed error, all must solve two key issues.One is the generation of high-fidelity reconstruction contour, although higher based on the efficiency of algorithm of DEM reconstruction contour, robustness is better, but the quality of reconstruction contour is unsatisfactory, especially flat region or DEM size larger time, ambiguousness and broken line phenomenon relatively serious (Wang Chun, pottery kiss, Jia Dunxin, Zhu Xuejian. Regular Grid DEM Topographical Description Morphology Research on Accuracy [J]. the geography information world, 2008,1:46-52.).Two is isocontour couplings of the same name, owing to not being man-to-man simple relation between original level line and reconstruction contour, but one-to-many, the many-one even complex relationship of 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 poor.

What is more important, various evaluation index does not all form the DEM fidelity precision evaluation criteria of system, although can assess same Experimental Area, different interpolation algorithm set up DEM between difference, but cannot determine whether DEM fidelity quality has reached to produce and the demand of application, and then the critical problem such as optimum range of the multiple dimensioned conversion of DEM cannot be determined.

Summary of the invention

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

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

1) for an Experimental Area, water system is reference element, and 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 side-play amount medial error membership function, f _max(Δ D) is maximum offset membership function, A ∈ [0.1,0.3], B ∈ [0.7,0.9];

Work as DEM _s>2 & & DEM _{Δ h}during >80:

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

Work as DE _ms≤ 2 & & DEM _{Δ h}when≤80:

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

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

Work as DEM _s>2 & & DEM _{Δ h}during >80:

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

Work as DEM _s≤ 2 & & DEM _{Δ h}when≤80:

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

Wherein zmf is Z-shaped membership function, and it is a kind of function based on spline interpolation, and parameter a, b respectively define starting point and the terminal 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 use fuzzy mathematics to set up, and sets up the criterion that water system and reconstruct valley route fit side-play amount membership function follow and comprise: Linear element displacement criterion and Scale criterion;

Linear element displacement criterion: when the side-play amount medial error of water system and Feature line is within 0.3mm, thinks that sleeving fastening degree is better, is namely subordinate to angle value and reaches more than 0.8; When the side-play amount medial error of water system and Feature line is 0.4mm, thinks that sleeving fastening degree is general, be namely subordinate to angle value about 0.5; When the side-play amount medial error of water system and Feature line is greater than 0.4mm, thinks that sleeving fastening degree is poor, be namely subordinate to angle value below 0.5;

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

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

Mean inclination criterion: Experimental Area mean inclination is less shows that the level line feature in region is not obvious, therefore can relax Linear element displacement criterion; When mean inclination be less than 2 °, the discrepancy in elevation be less than 80m time, the side-play amount on the spot that the medial error threshold value again revising 0.4mm is corresponding in different scale topomap; When landform map scale is 1:10000, the medial error threshold value correspondence of 0.4mm on the spot side-play amount is 11.2m; When landform map scale is 1:50000, the medial error threshold value correspondence of 0.4mm on the spot side-play amount is 40m; When landform map scale is 1:100000, the medial error threshold value correspondence of 0.4mm on the spot side-play amount is 56.6m; When landform map scale is 1:250000, the medial error threshold value correspondence of 0.4mm on the spot side-play amount is 71.6m; When landform map scale is 1:1000000, the medial error threshold value correspondence of 0.4mm on the spot side-play amount is 143.2m;

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

Improvement of visual effect criterion: between the different scale digital elevation model of same experiment area, if visualization effect is similar, the side-play amount so calculated is subordinate to angle value and there is not difference significantly; Between the same yardstick digital elevation model in different experiments area, if visualization effect is similar, the side-play amount so calculated is subordinate to angle value and there is not difference significantly equally.

Method of the present invention makes full use of the regulation of Linear element displacement in cartographic generaliztion specification, for water system and terrain reconstruction valley route, calculate side-play amount medial error value between the two and peak excursion value, use fuzzy mathematics method to set up water system and reconstruct valley route fit side-play amount membership function, finally determine that the fit of single digital elevation model is subordinate to angle value.The method not only may be used for the fidelity precision qualitative assessment of digital elevation model, and may be used for the optimum range determining the multiple dimensioned conversion of digital elevation model.

Accompanying drawing explanation

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

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

Fig. 3 is non-plains region of the present invention maximum offset membership function schematic 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 that the fit result improvement of visual effect of the regional different scale DEM of the same experiment of the present invention and water system compares;

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

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

Embodiment

Below in conjunction with accompanying drawing, the present invention will be further described in detail.

As shown in Figure 1, wherein A ', B ', C ', D ' are the point of crossing of reconstruction contour 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 by with the point of crossing reconstructing valley route and reconstruction contour for foundation, ' B, C ' C, D ' D that calculates the vertical range of each point of crossing to corresponding water system as the bias of water system and landform fit, as A ' A, B.Co-existing in 4 in Fig. 1 can for the water system calculated and the point of crossing reconstructing valley route, and wherein maximum offset is 42.56m, and minimum offset is 3.66m, and side-play amount medial error is 21.76m.

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

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

Criterion one: Linear element displacement criterion

Cartographic generaliztion specification clear stipulaties " planimetric position of Linear element except the displacement undertaken by cartographic generaliztion principle, medial error must control within ± 0.3mm ".Therefore, when the side-play amount medial error of water system and Feature line is within 0.3mm, can think that sleeving fastening degree better (be namely subordinate to angle value and reach more than 0.8); When the side-play amount medial error of water system and Feature line is 0.4mm, sleeving fastening degree general (being namely subordinate to angle value about 0.5) can be thought; When the side-play amount medial error of water system and Feature line is greater than 0.4mm, sleeving fastening degree poor (being namely subordinate to angle value below 0.5) can be thought.

Criterion two: Scale criterion

The impact of DEM scale factor must be considered when setting up side-play amount membership function.Mapping geography information office of country defined 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 medial error threshold value 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 relation between side-play amount on the spot

In practice process, if simple utilization criterion one judges the sleeving fastening degree of water system and landform, so experimental result will cause serious deviation when different DEM yardstick, namely along with the increase of DEM yardstick, and the increase of the actual fit side-play amount of water system and landform non-specifically is obvious.Using table 1 as judgment criterion, the side-play amount obtaining large scale DEM is subordinate to the situation that angle value is better than small scale.

As can be seen from Figure 5, when DEM yardstick is 12.5m, fit skew medial error value is 7.7649m, the criterion formulated according to table 1, and the side-play amount of 7.7649m is very huge; And when DEM yardstick is 200m, fit skew medial error is 36.9228m, now for judging that its standard is 300m, be 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 almost ubiquity in all Experimental Areas, therefore criterion two must be revised.

Square root regularity method is a kind of quantity method of disposal of cartographic generalization that German Topfer proposes, and the quantity produced due to the conversion of engineer's scale for solving derived map and newly organized map simplifies problem.He thinks: the root of the ratio of derived map and newly organized map two kinds of scale denominators is the quantity of the map elements that newly organized map should be chosen, namely

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

Wherein N _newfor the map elements quantity of newly making picture, N _orignfor the map elements quantity of source map, M _newfor newly organized map scale denominator, M _orignfor source map scale denominator.

Square root regularity method is applicable to the On The Choice solving map elements quantity, the map elements number of research object mainly in different scale map.When supposing that map elements is uniformly distributed, then the mean distance between different scale map elements meets 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 for the mean distance of newly making picture between map elements, for the mean distance of newly making picture between map elements.

Consider the dimensional discrepancy between new compilation and source map, also should increase correction factor C in formula (2), 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 scope correction factor.Such as new compilation for 1:10 ten thousand and source map is 1:5 ten thousand time, then C gets 4.Therefore according to formula (3) amendment table 1, as shown in table 2.

Table 2 topomap engineer's scale, DEM yardstick and relation between side-play amount (according to the amendment of square root regularity method) on the spot

Criterion three: mean inclination criterion

The impact considering Experimental Area mean inclination is needed when setting up side-play amount membership function.Experimental Area mean inclination is less means that the level line feature in this region is not obvious, does not have too large meaning at the sleeving fastening degree of level line feature unconspicuous regional study water system and landform, in most cases can give tacit consent to water system and landform sleeving fastening degree is better.Specifying in cartographic generaliztion specification in " Plain landforms " can by " the displacement medial error of Linear element be loosened to ± 0.6mm within ".Therefore " topomap engineer's scale, DEM yardstick and the 0.4mm relation between side-play amount on the spot " of Plain landforms is as shown in table 3.

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

Criterion four: maximum fit side-play amount criterion

The impact considering maximum fit side-play amount is needed when setting up side-play amount membership function.Side-play amount medial error is the dispersion degree of water system and landform fit side-play amount from whole meaning, does not consider the impact of single point of crossing.Suppose to there is N number of point of crossing for calculating, wherein most of side-play amount is less, and the side-play amount of a certain point of crossing is comparatively large, then the medial error finally calculated may be less.Now cannot reflect the impact on fit precision of peak excursion value.Therefore, the impact of maximum offset should be considered, in side-play amount membership function, namely occupy the ratio of 20%.

Criterion five: improvement of visual effect criterion

The effect considering visualization is needed when setting up side-play amount membership function.First, between the regional different scale DEM of same experiment, if visualization effect is similar, then the side-play amount calculated is subordinate to angle value should not exist larger difference.As shown in Figure 6.Secondly, between the same scale DEM in different experiments area, if visualization effect is similar, then the side-play amount calculated is subordinate to angle value also should not exist larger difference, as shown in Figure 7.

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

1. side-play amount medial error membership function

Work as DEM _s>2 & & DEM _{Δ h}during >80 (as shown in Figure 2, wherein each bar curve is from left to right followed successively by the medial 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 & & DEM _{Δ h}when≤80:

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

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

2. maximum offset membership function

Work as DEM _s>2 & & DEM _{Δ h}during >80 (as shown in Figure 3, wherein each bar curve is from left to right 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 & & DEM _{Δ h}when≤80:

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

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

After determining side-play amount medial error membership function and maximum offset medial error membership function, just can according to the proportionate relationship determination side-play amount membership function of two membership functions, that is:

f(ΔD)＝A*f _RMSE(ΔD)+B*f _Max(ΔD)（4）

Wherein A ∈ [0.1,0.3], B ∈ [0.7,0.9].

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

The first step: data encasement

Source data based on 1:5 ten thousand topographic map data choosing four regional 25.6Km × 25.6Km such as Yongan, Jilin, Dengfeng, Henan, Fujian vest, Zhangye, Gansu respectively, and calculate corresponding topograph parameter (table 4), represent hills, low mountain, Zhong Shan and high mountain respectively.

Regional topograph parameter tested by table 4

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

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

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

Second step: calculate side-play amount and be subordinate to angle value

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

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

(2.3) calculate water system respectively and reconstruct valley route fit side-play amount and be subordinate to angle value.

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

(3.1), in all Experimental Areas, calculate fit precision based on multiple dimensioned dem data and be subordinate to angle value there is different performances.As shown in Figure 8, the fit precision that 25m and 50m DEM calculates is best, and the fit precision that 12.5m DEM calculates is the poorest.Show in the multiple dimensioned dem data set up for benchmark with 1:5 ten thousand contour line data, the reproduction of 25m and 50m DEM to elevation information implicit in raw data is most suitable, and again to demonstrate the best scale setting up DEM based on 1:5 ten thousand contour line data be 25m is rational.When showing to carry out scaling down conversion based on 25m DEM simultaneously, under to push away 1 grade be completely reasonably, under push away 2-3 grade then need consideration, because 100m and 200m DEM calculates in fit precision the logic error (namely water system crosses over topographical crest, water system leap mountain top, water system leap saddle etc. three kinds, and its peak excursion value is 9999.0) that there is landform and express; But when carrying out scaling up conversion based on 25m DEM, experiment shows without any meaning, i.e. fit accuracy computation result extreme difference, illustrate that elevation information implicit in 1:5 ten thousand contour line data can not be supplemented by different DEM interpolation algorithm (even stability, robustness interpolation algorithm all preferably), unique method increases new elevation information, otherwise utilize any interpolation algorithm raising DEM precision to be all futile.

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

In the multiple dimensioned DEM in each Experimental Area of table 5, water system and landform fit are subordinate to angle value

The invention has the advantages that:

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

(2) the landform fidelity precision that the present invention not only may be used for single dem data quantitatively measures, and may be used for the optimum range of determining that multiple dimensioned DEM changes, ensure that the scope of application of multiple dimensioned DEM; And the difference of selection according to water system reference data, may be used for assessing the DEM synthesis precision that different integration algorithm is set up.

Claims (3)

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

1) choose Experimental Area, experimentally the topographic map data in region calculates topograph parameter and lowest elevation, the highest elevation and the mean inclination in this region; Extract the water system line data of Experimental Area, as reference data, the reconstruct valley route information extracting the multiple dimensioned dem data of Experimental Area, as comparing data, sets up water system and reconstruct valley route fit side-play amount membership function f (△ D):

f(△D)＝A*f _RMSE(△D)+B*f _Max(△D)

F _rMSE(△ D) is side-play amount medial error membership function, f _max(△ D) is maximum offset membership function, A ∈ [0.1,0.3], B ∈ [0.7,0.9];

Work as DEM _s>2 & & DEM _{△ h}during >80:

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

Work as DEM _s≤ 2 & & DEM _{△ h}when≤80:

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

Wherein △ D is the side-play amount medial error value of Experimental Area, DEM _sizefor digital elevation model yardstick, DEM _sfor the mean inclination of Experimental Area, DEM _{△ h}for the discrepancy in elevation of Experimental Area;

Work as DEM _s>2 & & DEM _{△ h}during >80:

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

Work as DEM _s≤ 2 & & DEM _{△ h}when≤80:

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

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

2) based on Experimental Area, finding the water system line for comparing and the match point of reconstruct valley route, calculating the side-play amount of each match point, and then obtaining the side-play amount medial error Δ D of Experimental Area;

3) calculate f (△ 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 use fuzzy mathematics to set up, and sets up the criterion that water system and reconstruct valley route fit side-play amount membership function follow and comprise: Linear element displacement criterion and Scale criterion;

Linear element displacement criterion: when the side-play amount medial error of water system and Feature line is within 0.3mm, thinks that sleeving fastening degree is better, is namely subordinate to angle value and reaches more than 0.8; When the side-play amount medial error of water system and Feature line is 0.4mm, thinks that sleeving fastening degree is general, be namely subordinate to angle value about 0.5; When the side-play amount medial error of water system and Feature line is greater than 0.4mm, thinks that sleeving fastening degree is poor, be namely subordinate to angle value below 0.5;

Scale criterion: according to the displacement criterion of Linear element, and with reference to square root regularity, revise the side-play amount on the spot that the medial error threshold value of 0.4mm is corresponding in different scale topomap; When landform map scale is 1:10000, the medial error threshold value correspondence of 0.4mm on the spot side-play amount is 5.6m; When landform map scale is 1:50000, the medial error threshold value correspondence of 0.4mm on the spot side-play amount is 20m; When landform map scale is 1:100000, the medial error threshold value correspondence of 0.4mm on the spot side-play amount is 28.3m; When landform map scale is 1:250000, the medial error threshold value correspondence of 0.4mm on the spot side-play amount is 35.8m; When landform map scale is 1:1000000, the medial error threshold value correspondence of 0.4mm on the spot side-play amount is 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;

Mean inclination criterion: Experimental Area mean inclination is less shows that the level line feature in region is not obvious, therefore can relax Linear element displacement criterion; When mean inclination is less than when the discrepancy in elevation is less than 80m, again revise the side-play amount on the spot that the medial error threshold value of 0.4mm is corresponding in different scale topomap; When landform map scale is 1:10000, the medial error threshold value correspondence of 0.4mm on the spot side-play amount is 11.2m; When landform map scale is 1:50000, the medial error threshold value correspondence of 0.4mm on the spot side-play amount is 40m; When landform map scale is 1:100000, the medial error threshold value correspondence of 0.4mm on the spot side-play amount is 56.6m; When landform map scale is 1:250000, the medial error threshold value correspondence of 0.4mm on the spot side-play amount is 71.6m; When landform map scale is 1:1000000, the medial error threshold value correspondence of 0.4mm on the spot side-play amount is 143.2m;

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

Improvement of visual effect criterion: between the different scale digital elevation model of same experiment area, if visualization effect is similar, the side-play amount so calculated is subordinate to angle value and there is not difference significantly; Between the same yardstick digital elevation model in different experiments area, if visualization effect is similar, the side-play amount so calculated is subordinate to angle value and there is not difference significantly equally.