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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004
pixel in image space and is in the range of the measurement
accuracy of the initial DTM. With this knowledge we conclude
that the observed area seems to be a Lommel-Seeliger rather
than a Lambert surface. The analysis with image 334, assuming
Lommel-Seeliger, does not converge. Reasons for this
behaviour are discussed in section 3.3.
From one image the scale factor between image and object
coordinate system cannot be determined. Therefore, we fix one
DTM-height at the boundary of the observed area as constant,
to guarantee the determination of absolute DTM-heights. The
reason for choosing a boundary position is, that if there is
height information for the regarded surface, then these height
values come in all probability from the neighbouring region
with sufficient texture computed by means of image matching.
To demonstrate that the algorithm is independent of the chosen
position of the introduced absolute DTM-height, we carried out
analysis no. 3 (table 1) with two other heights. Analysis no. 5 is
computed with a constant height at the centre and analysis no. 6
with a height at the middle of an edge. The normally used
constant DTM-height lies at a corner of the observed area.
Figure 3. Resulting DTM; g_ 335 (height-exaggeration factor 2x)
Figure 3 shows DTM, i3¢ of analysis no. 3. A comparison of
the orthoimage and the model grey values, both computed with
the initial DTM, and the model grey values, computed with
DTM,s 33s, is shown in figure 4.
LX ME m : Ka
Figure 4. Image 338: orthoimage (l.), model grey values of
initial DTM (m.) and of DTM, s, 5s (r.)
In the model grey values of the initial DTM, vertical striping
effects along the measuring directions of the operator can be
seen. This demonstrates that the manually measured DTM is
not of high accuracy. The resulting DTMijs, 3s corresponds
much better to the orthoimage (figure 4 left and right), although
a few visible structures in the images, such as craters and
valleys, are not visible in DTMijs, sss. In a comparison of an
enlargement of the model grey values of DTMis, 338 and the
same enlarged area of the orthoimage (figure 5 centre and right)
some blobs and grid structures are visible. The grid structures
are an indication, that the chosen meshes of the geometric
surface model may not be sufficiently small. We are still
investigating possible reasons for the visible blobs.
à : Lado M = A E i E a
Figure 5. Model grey values of DTMi s 33s (1.), enlargement of
marked area (m.) and same area in orthoimage (r.)
3.3 Error diagnostics
In this section we go into the matter of the non-convergence
using image 334 assuming Lommel-Seeliger reflectance. A
comparison of the orthoimage and the model grey values
calculated with the initial DTM (figure 6) shows, that the grey
value differences are extremely large. The model grey values
are 22 percent darker than the observed grey values. This is
probably a reason that the algorithm computes wrong
DTM-heights and diverges.
Figure 6. Image 334: orthoimage (1.), model grey values (r.)
The following causes are possible reasons for the large grey
value differences:
e incorrect radiometric calibration of image no. 334
e assumption of a wrong reflectance model
With the given information there is no way to separate these
effects from each other. The only possibility is to adjust the
observed values to the model using a simple mathematical
transformation without investigating the physical meaning. To
compensate the encountered radiometric problems a change of
the grey values in image 334 as described in table 2, is carried
out.
Mean model grey value G Mean grey value of orthoimage g
[W:sr'm?] [W:sr m^]
05 eee __ 4.20
Ga Mg
Modification Offset a) [W:sr-m?] Scalefactorm ———
mL. 098 08
m2 2.06 0.29
Table 2. Modification parameters for image 334
The first modification method ml is a change of the grey values
in image 334 with only a scale factor. The second variant m2 is
a linear accommodation of the grey values. The simplest
concept, only an offset, is not uscful, because due to the fact the
G is a linear function of Ar (see equation 4) after using the first
iteration the correction of the unknown reflectance coefficient is
the same as the offset computed a priori. Table 3 shows the
results computed with the modified image 334.
The computation diverges if we use only the scale factor. If we
use the linear change, the algorithm converges. In comparison
to the analysis with image 338 the result with image 334m2 is
