Lucr ări Știin țifice vol. 58 (1) 2015, seria Agronomie [616787]

Lucr ări Știin țifice – vol. 58 (1) 2015, seria Agronomie

171

VERTICAL ACCURACY EVALUATION
OF DIGITAL TERRAIN MODELS CREATED BASED ON LINE-FOL LOWING
DIGITIZATION OF CONTOUR MAPS

Ersilia-Valeria ONIGA 1, Mihaela CÂRDEI 1

e-mail: [anonimizat]

Abstract

Digital terrain models are used in wide variety of domains and applications, of which the most importa nt are:
orthorectification of aerial and satellite images, space object model ling, passageways designing, achieving slopes
exhibition maps, hydrological modeling, etc. There are several techniques for dat a acquisition in order to create digital
terrain models, such as photogrammetry, radargramme try, interferometry, airborne laser scanning, surve ying and
geodetic and cartographic digitization. By using ca rtographic digitization, digital terrain models are c reated based on the
digitized contour maps on existing maps, which were brought in digital format by scanning process, thi s method
involving low costs and being reach of a large numb er of users. It must therefore assess the vertical accuracy of digital
ter rain models created by this method. To achieve resu lts, first were created the digital terrain models based on contour
maps and points of known elevations manually digiti zed on plans at 1: 1000 scale and maps at 1: 25000 scale, using an
interpolation grid side of 5m and spline bicubic in terpolation method. Then, were determined with prec ision, by GNSS
technology, the coordinates of 18 control points. B ased on the grid nodes elevations, using the spline bicubic
interpolation method, were calculated the eleva tions of the 18 control points and then the differe nces between them and
those accurately obtained by GNSS technology. By pe rforming a statistical analysis of these difference s, the vertical
precision of digital terrain models created from co ntour maps was determined.

Key words : digital terrain model, line-following digitization, contour maps, accuracy evaluation

1 Technical University „Gheorghe Asachi” from Iasi Digital terrain models are used in wide
variety of domains and applications, of which the
most important are: orthorectification of aerial an d
satellite images, space object modelling,
passageways designing, achieving slopes
exhibition maps, hydrological modeling, etc. (Dana
I. F., 2010). There are several techniques for data
acquisition in order to create digital terrain mode ls,
such as photogrammetry, radargrammetry,
interferometry, airborne laser scanning, surveying
and geodetic and cartographic digitization. (Li Z.
et. al , 2005), the digital terrain models accuracy
being different for each type of data.
There are four possible approaches for
assessing the height accuracy of the digital terrai n
models, namely: Prediction by production
(procedures), Prediction by area, Evaluation by
cartometric testing și Evaluation based on control
points (Li Z. et. al , 2005).
This paper proposes to assess the vertical
accuracy of digital terrain models created by line-
following digitization of contour maps, by doing a
statistical analysis based on the known elevations
of control points.
MATERIAL AND METHOD

Trapezoids corresponding to the study area, at
1:1000 scale, respectively 1:25000 scale, have been
georeferenced, using as reference points the
trapezoids corners and intersection points of the
kilometric grid, with the help of TopLt software ( figure
1).
First, corresponding to trapezoids at 1:25000
scale, the geographical coordinates of trapezoids
corners and the Gauss planimetric rectangular
coordinates of kilometric grid intersection points, have
been transformed into planimetric rectangular Stere o
-70 coordinates using the Matlab programming
language.
Second, corresponding to trapezoids at 1:1000
scale, the geographical coordinates of trapezoids
corners and the planimetric rectangular coordinates
of kilometric grid intersection points, given in „L ocal
Iasi” projection system, have been transformed into
planimetric rectangular Stereo -70 coordinates usin g
the GOLIATH software.
Given the fact that, in order to georeference
one raster image at 1:25000 scale, 97 points have
been used and to georeference one raster image at
1:1000 scale, 70 points have been used, third degre e
polynomial transformation method was used to
optimize local accuracy (Imbroane A.M.,2012).

Universitatea de Știin țe Agricole și Medicin ă Veterinar ă Ia și

172

(a) (b)
Figure 1 The process of georeferencing the maps at 1:25000 s cale (a) and plans at 1:1000 scale
(b) corresponding to the study area

Then, the contour maps were digitized, on
plans at 1:1000 scale namely L-35-32-C-a-2-I-2-a, L-
35-32-C-a-2-I-2-b, L-35-32-C-a-2-I-2-c and L-35-32-
C-a-2-I-2-d ( figure 2 ), respectively on maps at 1:
25000 scale, namely L-35-32-C-a and L-35-32-A-c,
corresponding to the study area, using the “ AutoCAD
Map 3D 2010” software ( figure 3 ). Also, the points
with known elevations, which are marked on plans
and maps, were extracted.
In order to assess the vertical accuracy of
surfaces created based on contour maps, digitized o n
maps at 1: 25000 scale and plans at 1:1000 scale,
the spline bicubic interpolation method was used and
18 control points, measured using the GNSS
technology.
The coordinates inventory, was obtained with
the help of a program of „LISP” type, that extract s
from AutoCAD, the vertices tridimensional
coordinates.
The program is presented here:

(defun c:3dvertexes (/ doc spc ss file sel pts)
(vl-load-com)
(setq doc (vla-get-ActiveDocument
(vlax-get-Acad-Object))
spc (if (zerop (vla-get-activespace doc))
(if (= (vla-get-mspace doc) :vlax-
true)
(vla-get-modelspace doc)
(vla-get-paperspace doc))
(vla-get-modelspace doc)))
(if (and (setq ss (ssget '((0 .
"*POLYLINE"))))
(setq file
(getfiled "Output File"
(if *load *load "") "csv;txt" 9))) (progn
(setq *load file file (open file "a"))
(vlax-for Obj (setq sel (vla-get-
ActiveSelectionSet doc))
(setq pts
(vlax-list->3D-point
(vlax-get Obj 'Coordinates)
(cond ((eq (vla-get-ObjectName
Obj) "AcDbPolyline"))) Obj))
(mapcar
(function
(lambda (x)
(write-line
(strcat
(rtos (car x) 2 2) (chr 44)
(rtos (cadr x) 2 2) (chr 44)
(rtos (caddr x) 2 2)) file)
(vla-addPoint spc (vlax-3D-point
x)))) pts))
(princ
(strcat "\n<< Points from "
(itoa (vla-get-Count sel)) " Polylines
written to file >>"))
(close file)
(vla-delete sel)))
(princ))

(defun vlax-list->3D-point (lst x Obj / oLst)
(while lst
(setq oLst
(cons (list (car lst) (cadr lst)
(if x (vla-get-Elevation Obj) (ca ddr
lst))) oLst)
lst ((if x cddr cdddr) lst)))
oLst)

Lucr ări Știin țifice – vol. 58 (1) 2015, seria Agronomie

173

Figure 2 The necessary data used to create the digital terra in models: contours maps and points with known
elevations, digitized on plans at 1:1000 scale

Figure 3 The contours maps digitized on plans at 1:25000 sc ale used to create the digital terrain models and
control points measured using the GNSS technology

RESULTS AND DISCUSSIONS

In order to represent the 3D terrain surfaces,
an interpoation grid was created using the spline
bicubic interpolation method, based on the data
digitized on plans at 1:1000 scale, respectively on
maps at 1:25000 scale.
An important step in determining the
interpolation grid is the choice of the cell size
or the network step. Analyzing the specialty
literature, the best way to choose the step of
the cell network is iterative testing and after
evaluating its results the best decision is taken.
When choosing the network step is envisaged
the interpolated surface shape, its degree of kneading and the source points distribution in
the generated model.
Thus, for this case study, the 5m grid
step was chosen, resulting a grid of 58×78
lines and 4524 nodes.
Surfaces resulted after the interpolation
process by spline bicubic interpolation method,
with the grid step of 5 m, of points belonging to t he
contour maps digitized on plans at 1:1000 scale
and maps at 1:25000 scale, are presented in figure
4 and figure 5 , where the blue points represents the
polylines vertices and also the points with known
elevations and the red points represents the contro l
points. LEGEND:

– contour map
digitized on plans at
1:1000 scale;
– points with
known elevations,
extracted from plans at
1:1000 scale;
– control points
measured using the
GNSS technology.
LEGEND:

– contour map
digitized on plans at
1:1000 scale;
– control points
measured using the
GNSS technology.

Universitatea de Știin țe Agricole și Medicin ă Veterinar ă Ia și

174
6.957 6.958 6.959 6.96 6.961 6.962
x 10 5
6.3205 6.321 6.3215 6.322 6.3225 6.323 6.3235 6.324
x 10 540 45 50 55 60 65
Est [m] Metoda de interpolare spline bicubica
Nord [m]
Altitudini normale [m]
44 46 48 50 52 54 56 58 60 62

(a) (b)
Figure 4 (a) The surface corresponding to the study area, obtain ed by spline bicubic interpolation me thod, with
5 m grid size, based on points that belong to conto ur maps digitized on plans at 1:1000 scale and (b) detail

6.957 6.9575 6.958 6.9585 6.959 6.9595 6.96 6.9605 6.961 6.9615
x 10 56.3205 6.321 6.3215 6.322 6.3225 6.323 6.3235 6.324
x 10 540 45 50 55 60 65
Est [m] Metoda de interpolare spline bicubica
Nord [m] Altitudini normale [m]
44 46 48 50 52 54 56 58 60 62

(a) (b)
Figure 5 The surface corresponding to the study area, obtain ed by spline bicubic interpolation metho d, with 5
m grid size, based on points that belong to contour maps digitized on maps at 1:25000 scale and (b) de tail

In order to assess the vertical accuracy of the
surfaces created based on contour maps, the
standard deviation for each control point was
calculated with the following equation:

2
1n
i( x x )
n =−∑
(1) where x is the values average and n is the values
total number.
The deviations average in absolute value
from the mean was calculated with the equation:
11n
ix x n=−∑
(2)

Lucr ări Știin țifice – vol. 58 (1) 2015, seria Agronomie

175 where x is the values average and n is the values
total number.
Differences obtained between the normal
altitudes of the 18 control points, measured by
GNSS technology and those obtained by
interpolation, based on contour maps digitized on plans at 1:1000 scale and maps at 1:25000 scale,
are presented in table 1 .
The differences distribution histogram were
calculated in Matlab and are presented in Figure 6.

Table1
Differences obtained between the normal altitudes o f the 18 control points, measured by GNSS technology and
those obtained by interpolation, based on contour m aps digitized on plans at 1:1000 scale and maps at 1:25000
scale
Differences between normal altitudes calculated in control points
Plans at 1:1000 scale Maps at 1:25000 scale
1 0.142 10 -0.212 1 0.103 10 0.293
2 -0.191 11 -0.171 2 -0.919 11 -0.300
3 0.027 12 0.404 3 -0.847 12 -0.264
4 0.121 13 -0.575 4 0.001 13 -0.006
5 0.374 14 -0.871 5 0.692 14 -0.984
6 0.889 15 -0.840 6 0.581 15 0.531
7 0.103 16 -0.280 7 1.394 16 0.573
8 0.149 17 0.150 8 -0.521 17 -0.854
9 0.490 18 -0.843 9 0.103 18 -0.699

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 200.2 0.4 0.6 0.8 11.2 1.4 1.6 1.8 2
Normal altitudes diferences calculated in control p oints Frequency

normal altitudes deviations
normal distribution

(a) (b)

Figure 6 The differences distribution histograms, calculate d between the normal altitudes of the 18 control
points, measured by GNSS technology and those obtaine d by interpolation, based on contour maps digitized
on plans at 1:1000 scale (a) and maps at 1:25000 sc ale (b)

We can observe that, in the case of the
differences calculated based on plans at 1:1000
scale, respectively on maps at 1:25000 scale, for
four control points, respectively 1 control point,
from the total of 18 control points, differences
deviate greatly from the average value. This may
be due to the fact that errors might have
occurred in the digitization process, given that the study area is the central area of Iasi, an
area dominated by buildings (Li Z. et. al , 2005 ).
The statistical results obtained for the data
sets resulted by contour maps digitization on plans
at 1:1 000 scale, repectively on maps at 1:25000
scale, using a 5 m grid step and spline bicubic
interpolation method, are presented in table 2
(Chirila C. et al ., 2013):

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176
Table 2
Statistical analysis of the data sets obtained by co ntour maps digitization on plans at 1:1 000 scale, repectively
on maps at 1:25000 scale
Scara Control
points Standard
deviation
(cm) Maximum value of
the deviation
(cm) Deviations average in
absolute value
from the mean
(cm)
1:1000 18 0.47 0.89 0.39
14 0.28 0.57 0.23
1:25000 18 0.66 1.39 0.57
14 0.57 0.98 0.51

CONCLUSIONS

The vertical accuracy calculation of
digital terrain models created based online-
following digitizations of contour maps, is
done by testing a sufficient number of control
points uniformly distributed on the considered
study area.
Data sets were statistically analyzed by
the correlation between normal altitudes of
control points determined by GNSS
technology and those calculated by
interpolation.
In the case of the data set obtained by
contour maps digitization on plans at 1:1000 scale,
the standard deviation was 28 cm.
In the case of the data set obtained by
contour maps digitization on maps at 1:25000
scale, the standard deviation was 57 cm. REFERENCES

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*** – www.topolt.com
*** – www.mathworks.com