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Figure 1 Radiometric differences due to agricultural activities (left pair) and due to clouds and shadows 
(right pair). 
texture. Preliminary investigations have shown that the 
majority of the edges remain stable. However, different 
edges exist due to clouds, shadows, different perspective 
views, new edges within fields due to agricultural 
activities, human intervention, water level, snow 
coverage, changes in the tree canopies etc. (Figure 1). A 
method should be developed to try to detect the different 
edges through consistency checks. 
2. TEST DATA 
A stereo SPOT panchromatic level 1A model over W. 
Switzerland was acquired. The inclination of the sensor's 
optical axis was 23.4? R and 19.2? L respectively, leading 
to a B/H ratio of ca. 0.8. The acquisition dates were 
20.7.1988 and 27.8.1988 with significant radiometric 
differences between the two images, particularly in 
agricultural areas. Figure 1 shows some typical image 
parts with large radiometric differences. The elevation 
range was 350 - 3000 m. The following preprocessing 
was applied to the original digital images: 
e reduction of periodic and chess pattern noise 
e Wallis filtering for contrast enhancement 
136 control and check points were used with Kratky's 
rigorous SPOT model (Kratky, 1989b). 10 for the points 
were used as control points with a linear model of the 
attitude rates of change. The pixel coordinates were 
measured in one image manually and transferred to the 
second one by template matching. The RMS of the check 
points was 9 - 10 m in planimetry and 6 m in height. 
3. MODIFIED MPGC 
MPGC is described in detail in Baltsavias, 1991. It 
combines least squares matching (involving an affine 
geometric transformation and two radiometric 
corrections) and geometric constraints formulated either 
in image or object space. The constraints lead to a 1-D 
search space along a line, thus to an increase of success 
rate, accuracy and reliability, and permit a simultaneous 
determination of pixel and object coordinates. Any 
number of images (more than two) can be used 
simultaneously. The measurement points are selected 
along edges that are nearly perpendicular to the 
geometric constraints line. The approximations are 
derived by means of an image pyramid. The achieved 
917 
accuracy is in the subpixel range. The algorithm provides 
criteria for the detection of observation errors and 
blunders, and adaptation of the matching parameters to 
the image and scene content. 
In the case of matching of SPOT images the geometric 
constraints were formulated as follows. First, given a 
measurement point in one of the images (template image) 
a height approximation is needed. If the existing 
approximations refer to the pixel coordinates, then the 
height is computed by using the pixel coordinates in the 
reference image, the x pixel coordinate in the second 
image and the image to image PMFs. This height Z is 
altered by a height error A Z. Using the heights Z + À Z, 
Z — A Z, the pixel coordinates in the template image are 
projected by the image to image PMFs in the second 
image where they define the geometric constraints 
(epipolar) line. The centre of the patch of the second 
image which is used for matching is forced to move along 
this line by means of a weighted observation equation of 
the form 
v, = (x+Ax)cosB + (y- Ay)sinB-p (1) 
where (x, y) the approximate pixel coordinates of the 
corresponding point in the second image and (A x, A y) 
the unknown x-shift and y-shift. 
Equation (1) is equivalent to the distance of a point 
(x+ A x, y + À y) (the patch centre of the second 
image) from a straight line. The epipolar line is expressed 
by the normal equation of a straight line, where p is the 
distance of the line from the origin and p is the angle 
between the perpendicular to the line and the x-axis. 
If the patch of the second image does not lie on this line, 
then it jumps onto the line right in the first iteration. With 
our data, the epipolar lines are approximately horizontal, 
i.e. any error in the y-direction will be eliminated right in 
the first iteration. An example is shown in Figure 2. Since 
the epipolar lines are horizontal, the measurement points 
must be selected along edges that are nearly vertical in 
order to ensure determinability and high accuracy. Some 
advantages of the geometric constraints will now be 
presented. SPOT images include due their small scale a 
high degree of texture, i.e. edges. Measurement points 
lying along nearly straight edges can not be safely 
determined with other matching techniques, but with our 
approach they can as they lie at the intersection of two