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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008
Given the image parameters which have calculated by the true
IKNOS and SOPT imageries using the affine model and the
ground coordinates for the artificial points, (transformation
parameters is given by experiments of Ahmed Shaker), the
image coordinates (xl, yl), (x2, y2) of each point on the stereo
artificial imageries were calculated for the three terrain
conditions. This means that the data of the image is completely
consistent with the ground point coordinate, which is perfect
tool for testing 3D affine LBTM. In order to make the artificial
data as the real one, the errors were added on both image space
coordinates and object space coordinates, which are about lm
to 2m for ground coordinates and 0.5m to lm for stereo image
coordinates.
Two kinds of artificial ground control lines were simulated
individually for three conditions of terrain, which are shown in
Figure 4: parallel lines and random lines. So there will be total
six models here, three terrains, and every terrain have two
kinds of line attitudes. Fifth well-distributed ground control
lines of every kind were established for three condition in the
object coordinate system, the coordinates of two end points on
the lines was estimated in the software of Arcmap. After
creating TIN in Arcmap according to the distribution and
coordinates of the aritificial GCPs and overlapping the line
layer on the created TIN, the coordinates of the end points of
lines will be simulated on that interface. The lengths for
parallel lines for three conditions of terrains were from about
110 meters to 1300 meters and for random lines were from
about 130 meters to 1500 meters. The coordinates for the GCLs
of stereo images are also calculated by parameters as the GCPs,
and add errors individually. These six models will evaluate the
terrain and attitudes of lines influence for the accuracy of 3D
transformation model, the part of GCPs will be considered as
the checkpoints for the final accuracy analysis.
For the results obtained, the results of three sets of artificial
data cannot be calculated. There are two types of lines
distribution for every condition of terrain, but the results of one
of these types cannot be computed by the software for 3D
affine LBTM arithmetic. The three sets of artificial data are
parallel lines, only the type of random line for the three
conditions of terrain can be calculated in the software, and
obtained results for RMS errors.
So for the artificial data sets, only three groups of results can
be compared for different conditions of terrain, flat, hilly and
mountainous terrain. The lines attitudes influence of data sets
for the model cannot be discussed in this research. The results
of this developed model of artificial data for random lines of
terrain conditions are listed in Table 1. The numbers of
checkpoints of every terrain are all 30 points, and the numbers
of ground control lines are increased from 4 lines (at 4 comers
of test-area ) to 50 lines, after changing the order of lines,
which makes lines well-distributed on the artificial area when
selection numbers of GCLs, the RMS errors are obtained
adding every two lines from four to fifty lines. And the RMS
errors range is listed here from the RMS errors for three
different directions of ground coordinate using four lines to
using fifty lines.
Terrain
condition
No. of
GCLs
No. of
Chkpts
RMS errors (m)
X
Y
Z
Flat
4-50
30
9.95-0.78
5.39-2.53
15.76-3.61
Hilly
450
30
4.55-0.90
0.95 - 2.42
4.19-0.57
Mountainous
450
30
8.13-3.19
20.59 - 5.03
7.66-6.14
Table 1: Results of the 3D affine LBTM of artificial data
(b) Random lines
Figure 4: Distribution of the artificial ground control lines
4. EXPERIMENT RESULT AND ANALYSIS
4.1 Results of the artificial data
As introduced in third part, six sets of artificial stereo image
data were derived from the actual orientation parameters of
three pairs of IKONOS and SPOT imageries for three
conditions of terrain and artificial object coordinates of 30
well-distributed points individually. The established GCLs for
the different attitudes and terrain of artificial data sets are
presented in Figure 4. The results of root mean square (RMS)
error for X, Y, Z direction on the ground, when use different
numbers of GCLs, have been calculated by the software of 3D
affine LBTM in Matlab database, which is written and
performed by Ahmed Shaker (2004).
As showed in the table, when the numbers of GCLs reach to a
certain numbers, the RMS errors are nearly in tolerance. The
next part 4.2 will discuss the effects of the increasing of ground
control lines, and comparing the result of different conditions
of terrain for three different ground directions and the result of
different ground directions for three different conditions of
terrain.
4.2 Compare of different directions of ground coordinate
The research for rectification effects of different terrain
conditions will be discussed by the comparing of X, Y and Z
directions of ground coordinates. As showed in Figure 5, the
trends of RMS errors with the increasing of the numbers of
GCLs in different directions are described for every conditions
of terrain. For every condition of terrain, various trends of
RMS errors with the increasing of the numbers of GCLs are
presented with different colours in different directions. With
the increasing of the numbers of GCLs from 4 to 50, the
various trends of RMS errors are becoming flat and mild when
the lines’ number reach to a specifically value.
For the flat terrain, the maximum RMS error of the three
directions is over 15m, this value is similar to the requirement
of tolerance. Behind the numbers of GCLs from 4 to 12, the
various of the trend line of three directions is relative sharp,
especially for the numbers of 6, the RMS errors can be less
then 5m on all the three directions when the numbers of GCLs
more than 14, after the GCLs number over 28, the trends of
lines are mildest. As shown in Figure 5a, the lowest line is the
