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.
REFERENCES
Barakat, H., Emam, H., Abdel-Wahab, M.,2004. Assesment of
a Developed Combined Point/Line-based Projective Equations.
In: The International Archives of the Photogrammetry, Remote
Sensing and Spatial Information Sciences, Istanbul, Turkey,
Vol. XXXV, Part B3, p. (6)
Habib, A.,1999, Aereal triangulation using point and linear
features. In: The International Archives of Photogrammetry and
Remote sensing, XXXII (Part 3-2W5), pp. 137-141
Heikkinen, J.,1994. Linear feature based approach to map
revision. In: The International Archives of the Photogrammetry,
Remote Sensing, Athens, Georgia, U.S.A. Vol. XXX, Part 4,
pp. 344-351
Heikkila, J., 1991. Use of Linear Features in Digital
Photogrammetry. The Phtotogrammetric Journal of Finland,
vol 12, num 2, pp. 40-56.
Mikhail, E., Bethel, J., McGlone, J.,2001. Introduction to
Modern Photogrammetry, Chapter 4 ’’Mathematical Concept in
Photogrammetry”. John Wiley&Sons,2001, pp. 80-106.
Mikhail, E., Weerawong, K.,1994, Feature-based
photogrammetric object construction. In Proceedings of ASPRS
Annual Convention, Reno, Nevada, U.S.A.
Mulawa, D.,1989, Estimation and Photogrammetric Treatment
of Linear Features. PhD thesis, Purdue University, p. (312)
Mulawa, D., Mikhail, E.,1988. Photogrammetric treatment of
linear features. In: The International Archives of the
1098