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The absolute values of the Wavelet Fusion and the Segmentation- 
based Fusion are relatively close to the original HyMap data, 
whereas the absolute values of the Gram-Schmidt Fusion exceed 
the original ones by about 50%. This is evidently due to the fact 
that the Gram-Schmidt Fusion adapts the overall brightness to 
the panchromatic image (histogram matching is only performed 
globally), whereas the Wavelet Fusion introduces mostly short- 
wave components of the panchromatic image to the pansharpened 
image. 
  
  
Ó 7 
Lost. 
(b) Profile of RGB orthophoto 
  
image 
  
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(c) Profile of the original hyper- (d) Profile ofthe Gram-Schmidt Fu- 
spectral image sion image 
  
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358 477785 Bil Ta 130 — 149 
Lozotian Location 
  
(e) Profile of the Wavelet Fusion (f) Profile of the Segmentation- 
image based Fusion image 
Figure 8: Profile 3 for different Fusion Methods 
Profile 2 (Figure 8) is of special interest due to the different be- 
haviour of the infrared channel in the Gram-Schmidt and the 
Wavelet Fusion. The small dark strips between the inclined pan- 
els (shadowy areas) on the left building are too small to be re- 
solved in the hyperspectral image, whereas they do appear in the 
panchromatic image. The depths of the corresponding sinks in 
the Wavelet Fusion are more or less independent of the channel, 
whereas for the Gram-Schmidt Fusion they appear to be propor- 
tional to the “continuum” level of the respective channel. The 
Segmentation-based method exhibits its “generalizing” tendency 
again. 
5-3 Quality Measures for the Comparison of the original 
and the pansharpened data 
Some authors propose quality measures based on the differences 
between the original or upsampled hyperspectral data, respec- 
tively, and the pansharpened data. Here we evaluate the root mean 
square error, correlation coefficients and the universal quality in- 
dex proposed by (Wang and Bovik 2002). 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B7, 2012 
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia 
  
    
Root mean square error: 
The root mean square error is used to quantify the average amount 
of distortion in each pixel of the pansharpened images. The root 
mean square is computed between the original hyperspectral im- 
age (resampled to the resolution of the pansharpened hyperspec- 
tral data) and the pansharpened hyperspectral images. The results 
are shown in Table 1: 
  
  
  
  
  
R G B Il D I3 
PCA 465 | 365 | 351 | 821 | 836 | 870 
Gram-Schmidt | 457 | 375 | 349 | 787 | 800 | 804 
Wavelet 269 | 243 | 246 | 369 | 375 | 484 
Seg.-based 231 | 195 [193 305 | 371 490 
  
  
  
  
  
  
Table 1: Root mean square error of different fusion methods com- 
pared to the upsampled original hyperspectral image (reflectivity 
values, range 0-10000) 
The wavelengths of the represented bands are 0.635 um (R), 0.544 
um (G), 0.454 uum (B), 1.50 um (11), 1.805 um (12) and 2.485 um 
(13). It is obvious that for the most wavelengths the grey values 
of the Segmentation-based Fusion are least distorted. 
Correlation Coefficients: 
Table 2 compares the correlations between different channels and 
the panchromatic image. PCA and Gram-Schmidt Fusion show 
the highest correlation values, which means that for these two 
methods the contribution of the panchromatic image is the high- 
est. Particularly high are the correlation coefficients with the 
three infrared channels. On the opposite, the Segmentation-based 
Fusion image is closer to the original hyperspectral image which 
is desirable as the differences between the individual channels are 
levelled out to a lower extent. 
  
  
  
  
  
  
  
  
  
  
RP (GP BP | IP [DP | GBP 
Original data 0.53 | 0.51 | 0.48 | 0.46 | 0.44 | 0.33 
PCA 0.80 | 0.75 | 070 | 0.97 | 0.98 | 0,82 
Gram Schmidt | 0.79 | 0.76 | 0.70 | 0.93 | 0.93 | 0.74 
Wavelet 0.69 | 0.68 | 0.65 | 0.61 | 0.59 | 0.51 
Seg.-based 0.52 | 0.49 | 0.47 | 0.43 | 0.41 | 0.33 
  
  
Table 2: Correlation coefficients between the panchromatic im- 
age and different bands of the original and the pansharpened im- 
ages 
Universal Quality Index: 
Quite common is the Universal Image Quality index Q given by 
(Wang and Bovik 2002): 
40:4 TY Ozy 23 ÿ 2020y 
MS to) +R] oe, TAP +06 
Here x = {x:|i = 1,2,---, N}, y = {yili = 1,2,---, N} de- 
note the original and test image signals, respectively, i is the pixel 
index. Q can be applied to each channel individually. As the last 
term in the defining formula shows, Q can be decomposed into 
three factors which comprise a) the correlation coefficient (corre- 
lation between the two images), b) a similarity measure between 
the arithmetic means z and 7 and c) a similarity measure between 
the standard deviations 0; and oy. 
The “optimal” Q value of 1 e.g. is achieved if the images x and y