S), 
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ment 
The most difficult tasks are image matching and the 
generalized bundle adjustment using a proper model for 
the satellite’s movement during the data acquisition. 
Therefore, these are dealt with in more detail in the next 
two chapters. Two projects are described in order to 
demonstrate the capabilities of the method. In contrast 
to many other investigations of SPOT the whole images 
were processed and ample independent control infor- 
mation for a sound statistical accuracy check was availa- 
ble. 
2. IMAGE MATCHING 
Least squares image matching /Forstner 1982/ is known 
to yield the most accurate results. This method has also 
been applied to SPOT imagery /Otto, Chau 1989/. Their 
region growing algorithm has been selected for this pro- 
ject, but has been refined with respect to robustness of 
the results. 
In the following a short explanation of the used algorithm 
is given. One pair of conjugate points is assumed to be 
approximately known. It is called the starting point. By 
matching the template and search matrices surrounding 
the starting point, the exact coordinates of the conjugate 
points and the corresponding geometric and radiome- 
tric transformation parameters are computed. Also the 
correlation coefficient p between the two matrices, the 
semi-major axis of the error ellipse of the points, and the 
differences to the initial values are determined. 
Next, the template and search matrix are shifted by a 
constant amount to the left (this amount is called STEP 
in the following). The matching is then repeated in the 
new position using the results from the starting point as 
initial values. The same is done for the positions to the 
right, on top, and under the starting point. The results 
for all four neighbours of the starting point (coordinates 
of conjugate points, geometric and radiometric trans- 
formation parameters, correlation coefficient) are ente- 
red in a list in the order of decreasing value of p. 
The first point of the list is chosen as new starting point. 
All its remaining neighbours in the distance of STEP are 
attempted to be matched in the same way, and the results 
are entered in the list if certain criteria are fulfilled (see 
below). After matching the neighbours, the new starting 
point is deleted from the list, and the next point is 
467 
processed. The algorithm stops, if the list is empty. In 
this case either all points of the scene have been mat- 
ched, or no point in the neighbourhood fulfils the men- 
tioned criteria. 
The selection of these criteria and the corresponding 
thresholds is essential for the robustness of the algo- 
rithm. In this investigation the following conditions were 
set up for entering a pair of conjugate points into the list: 
- the correlation coefficient must be larger than a 
threshold pxis, 
- the semi-major axis of the error ellipse must be 
smaller than a threshold, 
- the difference to the initial values must be smaller 
than a threshold (this means that the height differen- 
ce between neighbouring points in object space must 
lie below a certain threshold), 
- the number of adjustment iterations must be smaller 
than a threshold. 
If more than one GCP is available, all of them (including 
their neighbours) are matched independently. The re- 
sulting lists are then merged to form a single one. Mat- 
ching is continued using the combined list. 
3. GENERALIZED BUNDLE ADJUSTMENT 
In the generalized bundle adjustment the ground coor- 
dinates of the object points and the exterior orientation 
parameters are simultaneously determined from image 
coordinates of the object points, ground control infor- 
mation and optionally a variety of non-photogrammetric 
data (e.g. GPS or INS measurements of camera positions 
or attitude). Due to the dynamic acquisition mode of a 
line scanner like SPOT each image line basically has its 
own set of six exterior orientation parameters. In practi- 
ce the determination of the exterior orientation parame- 
ters for each line is not possible. For piecewise smooth 
flight paths, their temporal variation can be expressed in 
terms of a mathematical function (e.g. polynomial, cir- 
cular or elliptical arc). The number of unknowns then 
reduces to the number of coefficients of this function. 
A variety of different parameter models for the recon- 
struction of the exterior orientation has been applied in 
the past /e.g. Wu 1986/. The functional model used here 
is based on extended collinearity equations /Hofmann et