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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004
2. METHODOLOGY
The proposed method comprises two major parts. The first part
is to build up the satellite orientation by using the ground
control points. The second part is to use the orbit parameters to
perform the orthorectification, in which a “Patch
Backprojection" method is proposed. The model error of
*Patch Backprojection" will also be evaluated in this section.
2.1 Orbit Modeling
In the modeling of orientation parameters, the position vectors
and the attitudes of the satellite are expressed with low order
polynomials in terms of sampling time. Due to the extremely
high correlation between two groups of orbital parameters and
attitude data, we only adjust the orbital parameters followed by
a collocation procedure to compensate for the local systematic
errors. Two steps are included in the orientation modeling.
The first step is to initialize the orientation parameters using on-
board ephemeris data. We then fit the orbital parameters with
low order polynomials using GCPs (Chen and Teo, 2002).
Once the trend functions of the orbital parameters are
determined, the fine-tuning of an orbit is performed by using
Least Squares Filtering technique (Mikhail and Ackermann,
1982).
2.2 Image Orthorectification
The objective of image orthorectification is to determine the
corresponding image pixel for a ground element. In addition to
providing the traditional pixel-by-pixel procedure, we proposed
a "Patch Backprojection" method and a patch size optimization
approach as well. It is demonstrated that the indirect method
performs better than the direct method in terms of quality and
efficiency (Kim et al, 2001). Thus, we select the indirect
method to determine the corresponding image pixels from a
ground element.
2.2.1 Pixel-by-pixel Backprojection
Figure 1 shows the geometry of indirect method. Given a
ground point A, we can create a vector r(t) from ground point A
to image point a. The vector r(t) vector is located on the
principle plane and n(t) is the normal vector on the principal
plane. The mathematics show that, at time t, r(t) is orthogonal
to the normal vector n(t). When r(t) is perpendicular to n(t),
the inner product of r(t) and n(t) is zero. The function f(t) is
defined to characterize the coplanarity condition.
ft)»r(t) in(t )20 (1)
We apply Newton-Raphson method to solve the nonlinear
equation (1), and to determine the sampling time t for ground
point A. Using the trigonometric calculation, the image
coordinate respect to ground point can be determinate from the
principal plane. After determining the corresponding image
point for ground element, the grey value on the orthoimage is
calculated by image resampling, while the orthoimage is done
by pixel-by-pixel backprojection.
587
Satellite Orbit after precision normal vector n(t) Projection Center
correction
Satellite CCD array
scanning surface
Principal
plane
Ground surface
X
Figure 1. Illustration of indirect method
2.2.2 Patch Backprojection
The indirect method in pixel-by-pixel way is very time
consuming. Thus, we proposed a “Patch Backprojection”
method to minimize the orthorectification computation load
with negligible model error. The proposed method is based on
the following two assumptions: (1) the relief displacements in a
small area with moderate terrain variations are linear, and (2)
the mapping geometry between image coordinates and object
coordinates may be expressed by affine transformation when a
small area is considered.
The procedure of the patch backprojection is illustrated in
Figure 2. We first divide the area of interest into a number of
equal-sized tiles. Selecting the lowest elevation in the tile, the
corners of the tile are projected on the image to form a set of
anchor points. Another set of anchor points with the highest
elevation are generated in the same manner. Assuming that the
relief displacement in a small tile is linear, a groundel within
the tile is projected into the image space according to the
groundel elevation and the two associated anchor point sets.
Pu
Indirect
Method /
d rd
L1,51
5
Affine Transformation
(Parameter 1)
(b)
E,N,Hmin
kc cui
Indirect — /
Method
Á
(E,N)
Affine Transformation
i rf >
E,N.Hmax (Parameter lj L2,S2
(a) (c)
(mr Parameter = — 38 7
é j |
N = f /
Tr Prange) / T /
E,NH' LS
(d)
Figure 2. Illustration of patch backprojection
(a) Tiles with equal size
(b) Anchor point generation for the top layer
(c) Anchor point generation for the bottom layer
(d) Interpolation
