Oca { k Om 
8.7 | 0.271 1.02 | 0251 0.04 | 0.12 | 0.35 
9, dr a, 
  
  
5.8 | 0.21 0.89 | 0.10] 0.02 | 0.08 | 0.14 
  
7.8 | 0.17 | 0.95 | 0.18] 0.03 | 0.11 0.26 
  
21.3 | 0.15 | 0.44 | 1.44 | 0.17 | 0.22 | 2.27 
  
25.3 | 0.20 | 0.69 | 0.38} 0.02 | 0.06 | 0.56 
  
123 019 | 1.11 0.26} 0.03 | 0.11 0.35 
Tab.3: Result of standard deviation adjustment 
  
  
  
  
  
  
  
  
  
The idea is now to separate the correction of the mean from 
that of the standard deviation. Therefore equation (4b) 
cannot be applied directly. The modified steps are (see also 
equation10): 
1. Each greyvalue is reduced by its respective mean m, 
(according to equ. 4b) so that the new mean value 
becomes 0. 
2. The shifted values are scaled by the correction function 
of the standard deviation. 
3. Finally the greyvalues are shifted back by m,,,. 
1 1 
Kr > ——— , Kı: —zZ 
Ki k 
(,*(0 -0,):cos "i $7 5543: 008S. ^1 
m 
m 
Icorr F (9; T uk t Meorr or 
m 
K, 
9cor = g; K, 5 m, K 7 1) 
m (10) 
where the indices ,, and , denote the para- 
meters for the mean and sigma correction, 
respectively. 
We notice immediately that in case of 
equal K, and K, equations (10) and (7) are 
equivalent. The band 4 image corrected by 
this modified approach is shown in figure §& 
10, its scattergram in figure 7. The high EE ^^ 5 
greyvalues for incidence angles >50.1° EE 
(flat terrain) could be reduced significantly, 
while the basic appearance remained the Fig.7 
same. 
8. SUMMARISING REMARKS 
The intended goal of providing an algorithm for an 
approximate topographic normalisation 
that works mostly automatically, 
* delivers accurary measures, 
+ detects automatically how reliably the given model can 
be applied for a given image and finally 
+ yields satisfying results in order to facilitate an a-priori 
classification that can successfully be used for a sub- 
sequent class dependent normalisation 
could be reached by a simple extension of the primitive 
Minnaert BRDF model. We found out, that by introducing 
the skylight term ¢ the Minnaert constant k is always close 
to 1 and therefore does not notably influence the correction 
function. The ¢ term is usually closer to 1 for the short 
EE 
    
A ES sy 
wavelengths and closer to zero for infrareds. Following this 
knowledge one should be able to find appropriate k and ¢ for 
a fairly good normalisation even manually just by trial and 
error. Eventually, we need to emphasizé again, that a high 
quality rectification together with an accurate DTM are 
crucial preconditions for a successful topographic normal- 
isation, independent of whether the normalisation just 
serves as a preprocessing step or it is the final correction 
based on a more sophisticated mathematical and/or 
physical model. 
  
Fig.8: TM Band4, original 
Fig.9: TM Band 4, corrected through equation (7) 
14 International Archives of Photogrammetry and Remote Sensing. Vol. XXXII, Part 7, Budapest, 1998 
  
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