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).