The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
G = 
n 
r 2 
*1 
s 2 
h 
G 
1 
H = G“ 1 
(7) 
e 2 fl Si 
e 0 fo 1 
Line based 
pixels 
meters 
Mean 
RMS 
RMS 
X Y 
4.30 6.59 
5.46 10.05 
8.09 
X Y 
7.19 11.03 
9.12 16.83 
13.54 
Table 1. Projective transformation computed based on line 
segments. Image was upscaled to 1.66m pixel size. 
Pntbased 
pixels 
meters 
Mean 
RMS 
RMS 
X Y 
5.81 8.14 
6.39 9.18 
7.91 
X Y 
9.68 13.57 
10.65 15.31 
13.19 
Table 2. Projective transformation computed based on four (4) 
points. Image was upscaled to 1.66m pixel size. 
The calculated mean coordinate differences and RMS values in 
selected 16 check points show that the accuracy of line based 
transformation parameters are equivalent with point based 
transformation. In point based transformation the selected 
ground points located in near comer areas of the satellite image 
to provide a good geometry for computation. So the comparison 
can be considered to be fair regarding to stability of 
computation. The size of the RMS values appear to be rather 
big 5-10 pixels, but one has to bear in mind that image was 
upscaled to 1.66m ground element size, the corresponding RMS 
values would have been 3-6 pixels respect to real ground 
element size. 
The line based method is known to work well in cases were the 
length of the line respect to whole value range is long. 
Therefore a line based transformation was computed in sub 
image area in size of 1 km* lkm. In selected area there were five 
(5) feature lines and the length of the lines was from 200m to 
600m. The same procedure was followed as previously to 
compute the projective transformation. The correspondent 
presentation of accuracy of transformation calculated in three 
check points are depicted in table 3. Equivalently converted to 
RMS values respect to real ground pixels, the corresponding 
values would be 0.3-2 pixels. 
Sub area 
pixels 
meters 
Mean 
RMS 
RMS 
X Y 
0.43 2.40 
0.46 2.71 
1.94 
X Y 
0.71 4.00 
0.76 4.50 
3.23 
Table 3. Line based projective transformation computed in 
bounded area. Image was upscaled to 1,66m pixel size. 
The results show that lines suit well for rectification of a 
smaller image area without any point observations. In all cases 
RMS Y values are six times larger than RMS X values on 
average. This tells something about the nature of QuickBird 
imaging. In row direction (X-axis) the assumption of 
perspective projection is valid which is not true in column 
direction. Also, it is assumed that the area is rather flat, In 
area under inspection the average fluctuation in height was 
around 30m and maximum difference was 60m. 
5. CONCLUSION 
Line based projective transformation was tested in manually 
selected image points and RMS values in those points were 3-6 
pixels. The results were equivalent with point based method 
with four well selected tie points. The test was accomplished 
with QuickBird imagery consisting multispectral channels. The 
experiment does show that it is possible to compute projective 
transformation based only on line segment information with 
real data. This computation was conducted with multispectral 
channel having a ground element size 2.44m-2.88m. More 
potential results could have been expected if the same test 
would have been applied to the panchromatic channel. However, 
the same procedure applied in smaller sub-image area resulted a 
RMS value near to one pixel. The lines do provide good 
opportunity to apply automation by means of feature matching 
and is therefore worth of investigation. 
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