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inclination angles of the plane. Thus, geometric 
constraints can be formulated by using the known pixel 
coordinates of all corner points, their heights (which are a 
function of the height at the patch centre and the plane 
parameters) and the PMFs (note that their coefficients are 
the same for all points). The unknowns to be solved for 
are the plane parameters and the height at the patch 
centre. This approach is an indirect object-based 
matching approach. It has the advantage that permits the 
determination of the local surface parameters (and not 
just the height at the patch centre), and that it constrains 
the 4 corners, i.e. restricts the affine geometric 
transformation. Using an inclined plane model, which is 
implicitly implied by the affine transformation of the 
current approach, the new approach also results in 
computational advantages as the number of unknowns 
reduces from 6 to 3. However, the problem to be solved is 
the a priori determination of a suitable surface model. 
4, DATA PREPROCESSING AND SELECTION 
OF MEASUREMENT POINTS 
First, the gradient magnitude images are computed. To 
reduce weak edges due to noise, which is very noticeable 
in SPOT images, all gradients with a magnitude less than 
a threshold T can be set equal to T. The threshold is 
selected as a function of the mean and the standard 
deviation of the gradient magnitude image (in this case T 
= mean - standard deviation). The same function should 
be used for both images to ensure equal treatment. The 
threshold should not be too high otherwise (a) useful 
texture is deleted, and (b) the edges are broken and 
significant differences between the two images occur due 
to different edge strength. This approach eliminates noise 
but also low texture which is however not very likely to 
lead to accurate matching results. An example is shown 
in Figure 5. 
As already mentioned, the measurement points are 
selected along edges nearly perpendicular to the epipolar 
lines. In order not to reduce the number of the selected 
points too much (and thus their density, which influences 
the DTM accuracy), points along edges with an angle of 
145° with the perpendicular to the epipolar line should 
also be selected. To avoid clustering of good points a 
thin-out window for non-maxima suppression can be 
defined. To avoid selecting points lying at small and faint 
noisy edges the points are selected in the first level of the 
image pyramid. Our approach is to match the same 
number of points in all pyramid levels. Thus, a selected 
point must have the aforementioned properties in all 
pyramid levels. Generally, the approach to be followed is 
to detect good points in all levels of the image pyramid of 
the template image and keep the points that appear in all 
pyramid levels. However, these SPOT images had a lot of 
texture and this was expressed in all pyramid levels. By 
going up in the image pyramid, the relative number of 
selected points was actually increasing. 
To avoid selecting points at regions of radiometric 
differences, especially the ones with a large area extent 
(like clouds), the following approach can be used. Using 
the PMFs and an average height of the scene (derived 
either from a priori knowledge or from the average height 
of the control points used in the rigorous SPOT model), 
or a polynomial transformation derived from the pixel 
coordinates of the control points, the search image is 
registered with the template image. If the registration 
were perfect, a simple subtraction of the two images 
would give us the different edges. Since the registration 
is not perfect, an image pyramid is created so that at the 
highest level the misregistration error is within pixel 
range. Then through subtraction, the different edges are 
detected by binarising the difference image with an 
absolute threshold. This binary image can eventually be 
dilated in order to avoid selecting points whose patch 
would partially fall inside areas with radiometric 
differences. These disturbance areas are projected in all 
pyramid levels and convolved with the selected points in 
order to clean the selected points. An example is shown 
in Figure 6. 
5. DERIVATION OF APPROXIMATIONS 
In this test the approximations were either given 
manually or derived from a given DTM. The proposed 
general approach is the following. After the PMFs are 
computed an average height is used in order to determine 
the position of the selected points in the search image. To 
check the quality of these approximations the 136 points 
  
Figure 5 Grey level image (left), gradient magnitude image (middle), thresholded gradient 
magnitude image (right) 
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