International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004
5.3.2. Quantitative Evaluation
In general, a good fusion approach should retain the maximum
spatial and spectral information from the original images and
should not damage the internal relationship among the original
bands. Based on these three criteria, correlation coefficients are
used to quantitatively evaluate the image fusion results.
In Table 2, the correlation coefficients between the original
panchromatic image and the fused images (QB Pan + QB XS)
are given as a quality measure. As is shown, the correlation
coefficients are getting larger after fusion, which implies that
the fused image gains information from the original
panchromatic image. The amount of increase varies from 7%
(band 4, near infrared) to 12% (band 1, blue), with the blue
band having the most gain from the panchromatic image.
Table 3 presents the correlation coefficients of the fused images
with their corresponding original images. The higher the value,
the more similar the fused image to the corresponding original
image, which in turn indicates a good spectral information
retain in the fused results. As shown in the table, all bands
except the blue one have a high correlation over 0.93 to their
corresponding original images. The fused blue band has the
lowest correlation of 0.85 to the original blue image. This
property is consistent with the above analysis as the blue band
is most affected in the fusion process by gaining the most
spatial information from the panchromatic image.
Table 4 presents the correlations among the QuickBird
multispectral bands before and after fusion. A good fusion
approach should not considerably change the correlation in the
corresponding bands. As shown in Table 4, the correlation
among all bands but band 4 is subject to a minor change after
fusion. The magnitude of largest correlation change is 0.02,
which is only about 2% of the original correlation. However,
the behavior of band 4 (near infrared) presents different
properties. For both before and after fusion, band 4 has a very
small correlation with all other multispectral bands, with the
maximum correlation being only 0.19. Although the magnitude
of correlation change is still very small (with the largest being
only 0.07), their relative rate can be large (over 200%). This
implies that the near infrared image is the most affected image
in terms of the internal relationship with other bands in the
fusion process.
Table 5 shows the correlation coefficients between each
original multispectral band and the fused ones of QuickBird
image computed for PCA, Brovey, Multiplicative and the
Wavelet transform methods. The larger the correlation
coefficient, the more spectral content is retained from the
original multispectral images. Results in Table shows that the
wavelet transform approach keeps over 90% of the spectral
content of all original multispectral bands except band-1 (blue
band). Among the tested methods, wavelet based approach is
the only one that keeps the most number of bands (3) having a
correlation above 90%. Further examination on Table 5 shows
the magnitudes of correlation change from band to band, that
suggests that the performance of fusion methods is band
selective. A reasonable expectation on a good fusion method is
that they have similar properties across the bands involved.
Results in Table 5 show that the Brovey method results in the
largest range (max — min), whereas the Multiplicative and
wavelet methods yield similarly small ranges (0.04 and 0.07)
across the bands. All the above analysis suggests that the
wavelet based fusion approach provides overall the best results
in the methods used in our study.
1248
XS1 XS2 XS3 XS4
QB | before | 0.6901 | 0.7444 | 0.6753 | 0.6138
Pan | after | 0.7732 | 0.8063 | 0.7352 0.6572
Table 2. Correlation coefficients between the original QB pan
and multispectral bands before and after fusion
XS1
XS2
XS3
X84
0.8501
0.9323
0.9516
0.9374
Table 3. Correlation coefficients between the corresponding
original and fused QB multispectral images
XS1 XS2 XS3 XS4
xs; | Before 1 0.9893 0.9647 | 0.0905
After ] 0.9671 0.9409 | 0.1645
XS2 Before | 0.9893 1 0.0723 | 0.1506
After 0.9671 ] 0.9740 | 0.1889
XS3 Before | 0.9647 0.9723 1 0.0193
After 0.9409 0.9740 ] 0.0593
XS4 Before | 0.0905 0.1596 0.0193 ]
After 0.1645 0.1889 0.0593 1
Table 4. Correlation coefficients among the QB multispectral
bands before and after fusion
Bandi Band2 | Band3 Band4
PCA 0.7743 | 0.7743 | 0.7907 0.9621
Brovey 0.8766 | 0.6302 - 0.4683
Multiplicative | 0.8539 | 0.8777 | 0.8958 0.861
Wavelet 0.8501 | 0.9323 | 0.9516 0.9374
Table 5. Correlation coefficients between original and fused
QB multispectral bands for different fusion methods
Despite the above studies, one correlation coefficient can only
represent the overall quality of the fusion results. In fact, fusion
quality can be higher for certain features than others since they
can give a better response to the fusion algorithm. For this
reason, we suggest to calculate the correlation coefficient for a
small window instead of the entire image. A window that has a
predefined size w (i.e. w = 3 for a 3X3 window) is taken and
the correlation coefficient is calculated for the two images that
falls in this window. In this way, the texture contents at higher
levels of details in the before- and after- fused images can be
directly compared. This process is started from the upper left
corner of the image and continued until whole image is
covered. At the end of this process, a quality matrix made of
the correlation coefficients is created. Brighter places in this
quality matrix suggest better fusion quality than darker places.
Figure 7 shows the quality matrices represented as a grey level
image.
Pan vs. XS Band-1 Pan vs. Fused XS Band-1
Figure 7. Quality matrices before (left) and after (right) fusion
calculated for QB images using 3 x 3 window.
