apply
(7)
to the
within
en be
gether
ndard
of the
to be
and i
(8)
mean
lue by
(9)
roced-
cy. By
at the
wards
of the
of the
m to
> from
el was
coded
ved
for the
cos-i-
lasses
°), the
ted for
r band
Band 1 Band 4
| m, 0, m, 9,
7,5 54,19 8,74 72,65 18,82
22,5 53,58 7,99 70,06 19,80
37,5 53,49 6,77 64,84 22,55
52,5 51,22 5,87 51,60 19,53
67,5 48,15 4,62 35,27 14,17
82,5 46,02 3,48 19,83 9,61
90,0 45,04 2,11 11,21 4,59
Tab.1: Mean and standard deviation of incidence classes
This leads to seven observation equations per spectral
band (the absolute minimum would be three). The
adjustment for the 6 spectral bands yielded the following
values for the parameters (see also figure 5):
m t k g 0
COIT m { Oy Op
54.6 | 0.82 | 0.98} 0.42 | 0.01 0.17 | 0.59
22.8 | 0.61 0.93} 0.22 | 0.02 | 0.14 | 0.45
20.1 0.54 | 1.081 0.23 | 0.01 0.10 | 0.31
75.4 | 0.13 | 0.97} 1.78 | 0.03 | 0.11 2.50
64.9 | 0.11 1.09} 0.61 0.01 0.05 | 0.84
22.3 | 0.16 | 1.21 0.22 | 0.01 0.05 | 0.20
Tab.2: Result of adjustment for all 6 spectral bands
g
80
60
40
20
0
0? 90° i[°]
Fig.5: Result of adjustment (graph of equ. 4b)
One can clearly see that the Minnaert constant k is always
very close to 1 (= ideal cosine function!), while the skylight
factor ( is always greater than O and significantly greater
than O for all bands in the visible spectrum, in particular in
the blue band (82%). m,,,, the adjusted mean for i=0, is less
important for the correction function. o, shows that the
correction function fits the actual observations with an
accuracy below one greyvalue interval (except band 4,
where the mean error is still very good with 22.5
greyvalues).
7. DISCUSSION AND CONCLUSION
Figures 8 and 9 show the original and topographically
corrected band 4 image, respectively. This part of the whole
image shows a few typical details that need further
discussion:
1. Shadows in areas of incidence angles greater 90° (see
black patches in Fig.3) can also be “corrected” by this
approach. We must bear in mind that those areas are
adjusted to the average mean. The correction is very
unreliable and inaccurate. Not corrected, because not
included in the illumination model used here, are the
cast shadows as one can recognize along the mountain
range in the right upper quarter of the image. The
remainder of the shadow can be seen as dark stripe on
flat terrain. As the algorithm cannot know the origin of
that stripe it is treated like a dark object feature.
2. Dark linear elements along terrain discontinuities or
mountain ridges or sudden changes from dark to bright
resemble the effect of an high pass filter in some way.
Many of this effects are caused by the a slight misalign-
ment between the image content and the terrain model.
A closer check proved that the geometric rectification
was not as accurate as necessary. A displacement of
only one pixel leads to a visible wrong intensity
correction. We conclude that the geometric accuracy is
a crucial point for accurate topographic normalisation, in
particular in mountainous regions.
3. The correction function not only
moves the mean greyvalues within
an incidence class, it, at the same
time, also stretches the associated
standard deviation (see Fig.6). The
effect is that in shaded areas the
contrast is severely enhanced thus
causing bright features within darker
surrounding areas. The following
suggestion of a modified correction
procedure helps to attenuate the un-
realistic contrast enhancement.
Fig.6
The standard deviations of the incidence classes are now
subjected to the same adjustment procedure as the mean
values before. This notion is justified as we must expect and
deduce from the scattergram (Fig.4), that the standard
deviation also depends on the illumination properties.
Therefore, we just apply the same basic rules as for the
mean values. The adjustment is now performed with the i
and o listed in Table 1 (instead of / and m).
The result of this adjustment for our test example of all six
spectral bands is listed in Table 3. The o, column shows
that the functions fits very well the actual “measurements”.
In the worst case (band 4 again) the o, is 2.27 that is about
1096 of the actual standard deviations (see Table 1).
International Archives of Photogrammetry and Remote Sensing. Vol. XXXII, Part 7, Budapest, 1998 13
RR A ET RATER
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