URE 
A comparison of both sets of data after the conversion 
into absolute reflectance shows that the spectral signatures 
obtained from the field measurements and the correspon- 
ding signatures of the LANDSAT-TM fits well. As an 
example Fig. 1 shows the comparison for sand and num- 
[ERU 
S (Rj =) 
=] 
rms = i 
n 
(2) 
ulitic limestone. Rj - modelled reflectance 
m R5 = measured reflectance 
After this step the spectral signature of the selected end- n = number of bands 
members in the LANDSAT-TM image had to be determined. 
Finally, the spectral unmixing was carried out. In Fig. 2 
the sequence of all steps for the processing of the data is 
shown. 
2 SPECTRAL MIXTURE ANALYSIS 
This method has been described in HILL (1994), SABOL 
et al. (1992) and SMITH et al. (1990). The spectral signa- 
ture of a pixel arises from the weighted sum of the indi- 
vidual components of its surface. The unknown quantities 
  
  
  
To compensate differences in brightness due to surface 
roughness and artefacts of the relief shadow had to be 
included as an endmember. Since there is no spectral in- 
formation in this endmember the fractions of all other 
endmembers have to be normalized (to unity, saine the 
fraction of shadow (Eq. 3 and 4)). 
[=1/ (=F) (3) 
= fraction of the endmember SHADOW 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
ii Fj (Eq. 1) are determined by a least-square method. 
2$CODy. (n-1) (4) 
sults of n Y 5sf-d 
"NS FH RES E: T 
: J=1 
Entmi- f. — normalization factor 
pektro- with the condition Fj = fraction of endmember j 
durch- A : 
ledaten E (1) For the spectral unmixing of the LANDSAT-TM image 
fitting of experimental data was performed for all combi- 
> Fn nations of endmembers. The combination with the lowest 
jl rms was selected for the final result. A pixel was classi- 
ated be- fied as unmixed if the rms was «29. This value is about 
covered Fi = fraction of the endmember j three times the noise level. 
(mainly Ri = reflectance of the mixed spectrum in band i 
between REj = reflectance of the endmember j in band i As the final result of the unmixing the fractions of the 
d ground £i = residual error in band i individual endmembers and the rms were obtained for 
pectra of every pixel in the image. 
[S spec The rms (Eq. 2) provides the difference between the 
tired on measured and the modelled spectrum. The rms should be 
(spectro- in the range of the noise level, in case of the processed 
the data LANDSAT-TM image it is 0.56% absolute reflectance. 
1g of the 
orrection 
a correc- 
c (BACH field spectra LANDSAT-TM image 
[C "S^ fO in instrument units in digital numbers 
method. 7 i 
conversion to 
absolute reflectance conversion to absolute reflectance 
- conversion to spectral radiance 
- atmospheric correction 
simulation of - correction of the adjajency effects 
the 6 TM bands 
| | 
determination of LANDSAT-TM image 
the endmembers in absolute reflectance 
spectral signatures of the endmembers 
in the LANDSAT-TM image 
| 
2.4 spectral unmixing of the 
LANDSAT-TM image 
from the 
Fig. 2: Single steps for the processing of the two data sets 
227 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B7. Vienna 1996