The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
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evaluated in [5]. In addition, a 3-D transformation model, based 
on the collinearity condition, is used in [6] to generate 
orthophotos from IKONOS stereo images using 1 meter to 20 
meters DEMs. Results reported an accuracy of 2 to 4 meters 
using 13 panchromatic and multispectral IKONOS images over 
seven test sites. 
A large amount of research has been devoted to efficiently 
improve the accuracy of the spatial data generated using the 
satellite imageries. For example, different methods are 
presented in [7] to improve the accuracy of the ground 
coordinates using IKONOS stereo images with Ground Control 
Points (GCPs) by either refining the vendor-provided IKONOS 
Rational Function Coefficients (RFCs) or refining the derived 
ground coordinates. The accuracy of the 3D ground point 
coordinates was improved to 1 to 2 meters after the refinement. 
The same results were obtained [8] after removing the 
systematic errors in the computed coordinates. In addition, 
results in [9] showed an improved planemetric accuracy of 0.3- 
0.6 meter and elevation accuracy of 0.5-0.9 meter using less 
than 10 GCPs after removing the biases in the RPCs. Several 
researchers investigated the potential of rectifying a single 
IKONOS panchromatic images. The use of a single Geo 
panchromatic IKONOS image for large-scale mapping is 
evaluated in [10], [11], [12] and [13]. The results recommended 
that IKONOS images could be used to provide 1:10000 scale 
maps. In addition, the results suggested using IKONOS 
panchromatic images to provide preliminary and provisional 
versions of 1:5000 scale maps. 
Additional investigation has been conducted to rectify IKONOS 
images using linear features. The 2D and 3D affine and 
conformal transformation models are used to model the 
relationship between object space and image space linear 
features in [14]. The underlying principle of the models is that 
the line unit vector components of a line segment could replace 
the point coordinates in the representation of the ordinary 2D 
and 3D affine and conformal models. Experiments with 
synthetic and real data were conducted. For the real data, a 
group of 12 GCLs were established by connecting some GCPs 
in the data set. A set of 16 GCPs were used as checkpoints. 
Results showed an average RMSE of several meters in the X 
and Y coordinates of the check points using 4 to 12 GCLs. 
3. LINEAR FEATURES BASED TRANSFORMATION 
MODELS 
Many photogrammetric models have been developed based on 
point features. However, image information can be represented 
in other forms such as linear features. Linear features are 
relatively easier to detect and extract from digital images than 
point features. Hence, photogrammetric models need to be 
expanded to accommodate linear features. In this case, given 
two corresponding linear features in two different spaces, the 
relation between the parameters of the two linear features are 
derived rigorously using the transformation parameters between 
the two spaces. Straight lines in a 2D space is characterized by 
two independent parameters [17]. These two parameters could 
be formulated using different representations. For this research, 
the linear feature is characterized using equation 1. However, 
the equation is not valid for a straight line passing through the 
origin. 
ax + by + \ = 0 (1) 
Where x and y are the planemetric coordinates of any point on 
the line, and a and b are the line parameters. 
3.1 Six Parameters Transformation 
The line-based 6-parameter transformation model is described 
using equation (2). 
a 2Pl + b 2P4 
aj = 
a 2P3+ b 2P6 +A 
i (2) 
a 2 P2 + h 2 P5 
b, = 
a 2 P3 + b 2P6+ 1 
where p , p , p , p , p , and p are the 6 transformation 
1 2 3 4 5 6 
parameters, 
a] and b] are the line parameters in space 1. 
a 2 and b 2 are the line parameters in space 2. 
Several forms, based on point features and line features, of the 
projective transformation model are used to rectify different 
satellite images in [15]. These images include LANDSAT7, 
SPOT4, IRS-ID, IKONOS images. For the LANDSAT7, results 
showed an RMSE of about 16 meters using either the point- or 
line- based projective transformation models. For SPOT4, 
results showed an RMSE of about 13 meters. For the IRS-ID, 
results showed an RMSE of about 8 meters. For IKONOS, 
results showed an RMSE less than 2 meters. In all experiments, 
the combined point/line-based projective transformation model 
showed approximately the same results as the point- and line- 
based projective transformation models. 
Straight lines are used in [16] to register multi-source satellite 
images including IKONOS, Quickbird, Orbview, and SPOT-5. 
Results showed that the 6 parameters transformation model can 
be used to register satellite images with narrow angular filed of 
view. In addition, the results showed that the 2D similarity 
transformation model could be used in low accuracy 
applications. 
3.2 Eight Parameters Transformation 
The line-based 8-parameters transformation model can be 
described using equation (3). 
where 
a 2 Pi+ b 2P4+p 7 
a l = : 
P3 + P6 + 1 
“2P2 +b 2P5 + P8 
(3) 
b l= — 
P3 + P6+ 1 
p ,p ,p ,p ,p ,p ,p , and p are the 8 transformation 
1 2 3 4 5 6 7 8 
parameters, 
a| and bi are the line parameters in space 1. 
a 2 and b 2 are the line parameters in space 2. 
3.3 Direct Linear Transformation 
The point-based DLT transformation model is described using 
equation (4).