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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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357 26 *
Voc
(c) Profile of the original hyper- (d) Profile ofthe Gram-Schmidt Fu-
spectral image sion image
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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