No. which pass by each DEM grid point. This can be
achieved by applying a second order two dimensional
polynomial transformation based on the same control points
which were used to determine the orientation parameters of
SPOT image (Equation 2).
This step gives the approximate image points (i.e. scan-lines
Xi, pixel position y;) for each DEM grid point (1).
ii- Use the computed xi in order to compute the orientation
parameters corresponding to these image coordinates. These
parameters are (Equation 2):
. Satellite instantaneous position.
. Elements of matrices M(L)& M(Q).
iii- Substitute the computed orientation parameters for the
corresponding parameters in the collinearity formula
(Equation 2) and compute new image coordinates (xi and y; ).
Repeat steps (ii) using the new image coordinates and then
repeat step (iii). This repetition can continue until the
difference between the new and the old computed values of
image coordinates becomes less than a specified threshold
(0.25 pixel size is used as threshold in our test and the
solution is always converses before 5 iterations).
As a result of applying the iterative approach given above, the
image coordinates corresponding to each four DEM points
forming a grid will be determined. The positions of the pixels
of the output image (orthoimage) within each DEM grid, on
the original image, can be determined by applying a two
dimensional transformation, where the previously determined
image coordinates of the four DEM grid points are used in
order to compute the parameters of this transformation.
Two different transformations are used:
-Affine transformation, where six parameters are computed.
-Eight parameters transformation. This method needs more
computations compared with the previous method.
2.1.2 Pixel by pixel Technique
In the pixel by pixel technique the determination of the image
coordinates (in the original image plane) corresponding to the
DEM grid points is carried out exactly according to the
method explained in the anchorpoints technique. The
positions of the pixels of the output image (orthoimage)
within each DEM grid, on the original image plane, is
determined applying a three dimensional approach, where the
ground height of each of these pixels is first determined by
interpolation based on the surrounding DEM data. Then the
corresponding positions on the original image are determined
applying the iterative approach given above. The following
four different interpolation methods for height determination
within the grid based on the four surrounding DEM points
are tested in this study:
- Nearest neighbour, - Inverse distance; - Inverse square
distance; and - Bilinear polynomial in the form:
H= a, + ax + ay + asxy
More elaborate algorithms were not tested in this study.
2.2 Step 2
This step involve computing a gray value for every pixel
after being located in the original image plane. A gray value
can be computed by one of the following methods:
2.2.1 Nearest Neighbour
It copies the value (from the original image) of the closest
element. This method has a radiometric advantage, as it
248
keeps the characteristics of the original image. But it has the
disadvantage, that it produces geometric artifact.
2.2.2 Bilinear Interpolation
It interpolates between the gray values of the four
surrounding pixels in order to compute the gray value for the
resampled image. Its advantage is that it does not give
geometric artifacts, but it has a radiometric disadvantage (a
kind of smoothing).
3. TERRAIN CLASSIFICATION BASIS
The roughness factor (RF) is used in order to classify the
different test areas. RF is computed as follows (Balce 1986):
RF 7 (Azave /Adave )*100 (3)
where:
AZave is the average height difference between successive
significant breakpoints
Adave is the average distance between successive significant
breakpoints
The significant breakpoints are determined using the
following criteria:
i- Height difference between any successive points exceeds
Ô interpolation (8 int); and
ii If a point is linearly interpolated between its two
neighboring points, and its computed elevation is compared
with its sampled elevation , the discrepancy exceeds Ó in.
The value of 9 « is a function of aerial triangulation; model
setup; sampling process, and interpolation. Unfortunately
these values are not available for the data used in this study.
Therefore a value of 5m is assumed for 6 int and the terrain
is classified as follows.
The terrain with RF < 10 is considered as flat terrain;
The terrain with RF > 10 and < 20 is considered as
moderate terrain;
The terrain with RF > 20 is considered as rough terrain.
4. EXPERIMENTAL RESULTS
SPOT-1 (level 1A) panchromatic image, with high oblique
mirror looking angle equal to 25 degrees (maximum mirror
looking angle of SPOT images is 27 degrees), is used in this
study. The image was sampled on 12 December 1986 and
cover a part of Nepal. A topographic map produced by
photogrammetric technique with map scale 1:100,000 and
with 100m contour interval was the source of the control
points and DEM data. Twenty seven control points were
identified in the image and digitized from the map. These
points are distributed over an area of 40 by 50 km. The
control points were used in order to compute the 18
orientation parameters of SPOT image (Equation 2). The lack
of accurate control points cause a big residuals in the control
points, which was 47.2 m as the Root Mean Square (RMS) of
the ground vector displacement. Although these residuals are
big, they still in the range of the accuracy of control points
assuming that the map is produced according to the map
standards. This will have a minor effect on the final results of
this study ; because we are comparing different orthoimages
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B4. Vienna 1996
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