Environmental Engineering Reference
In-Depth Information
the linear model, having
N
r
×
N
c
rows and (
N
+
1) columns,
N
r
and
N
c
being the Pan dimensions.
The
N
×
(
N
+
1) parameters are jointly optimally estimated
in the MMSE sense at degraded resolution (both
P
and MS
are filtered by the corresponding MTF filters), as shown by the
following least squares (LS) solution:
case study
α
=
β
=
1, i.e., spatial and spectral distortions are
given the same weight.
Table 10.1 reports
D
λ
,
D
s
and QNR values for the selected
algorithms measured on the QuickBird image. Concerning the
EXP image, as expected from its definition,
D
λ
is very near
to 0 while
D
s
is moderate. Concerning GS algorithm, QNR is
comparable with the expanded MS image but lower than the
QNR values of the other methods. As a general consideration,
all other algorithms perform very well and the indices exhibit
similar values. GSA-CA obtains the highest QNR score and is also
the best concerning spectral distortion
D
λ
.GLP-CAobtainsthe
best result concerning spatial distortion. GMMSE exhibits a low
spectral distortion, practically equal to GSA-CA; this determines
a good score that is intermediate between GSA-CA and GLP-CA.
Table 10.2 reports
D
λ
,
D
s
and QNR values for the selected
algorithms measured on the IKONOS image. Apart from the
expanded MS image that is comparable, all the algorithms
obtain scores that are a little bit lower than QuickBird. This
occurs because of some residual local subpixel mis-registrations
between the Pan and the MS image. The presence of misregis-
tration artifacts explains why GLP-CA scores on IKONOS are
less competitive than the scores of the other algorithms. In fact
GLP-CA is based on MRA and suffers frommisregistration more
than the other algorithms that are CS based, as already recognized
in the research community. GSA-CA and GMMSE obtain the
best QNR with nearly the same score. GSA-CA exhibits the best
D
s
while the best
D
λ
is obtained by GMMSE. As in the case of
QuickBird, GMMSE exhibits a very stable behaviour.
Qualitative analysis has been performed by visual inspection
on the test areas. From these areas two 512
γ
k
=
(
H
L
H
L
)
−
1
H
L
(
MS
k
−
MS
L
k
)
k
=
1, 2,
...
,
N
(10.8)
Where
H
L
is the observation matrix formed by image data
with resolution reduced by means of proper MTF filtering. The
MMSE solution is stable because of the high dimensionality of
H
L
. Constraints can be imposed on the MMSE solution in order
to obtain positive weights, but such a choice usually causes a little
degradation in performances.
By observing Eq. 10.4, one may conclude that the method
follows a component substitution approach since the Pan image
is not filtered. However, it is evident from Equation 10.8 and
from Fig. 10.3, that the MMSE fusion method adopts MRA
for parameter estimation. As a conclusion, the MMSE Pan-
sharpening algorithm may be classified as a hybrid component-
substitution/MRA fusion method.
10.5
Results
Four Pan-sharpening algorithms have been selected for com-
parison purposes. The GLP-CA scheme has been selected as
representative of MRA advanced techniques, the GSA-CA algo-
rithmhas been chosen among the CS schemes, while the GMMSE
scheme with global gain is the representative of hybrid MRA/CS
schemes. A fourth algorithm, the GS method as implemented in
ENVI, has been reported in order to provide a reference with
a well-established and rather efficient scheme. Also the plain
resampled MS image (EXP) is reported as reference.
Results of the algorithms are reported for two different test
images. The first is an 11-bit QuickBird satellite scene consisting
of an MS image of Trento area in Northern Italy, with spatial
sampling interval (SSI) of 2.8 m and of a Pan image with an
SSI of 0.7 m. The whole scene has been fused by means of
the four selected algorithms and quantitative results have been
reported for a fused image of 1520
512 details have
been extracted from the Pan image, the expanded MS original
and the four selected Pan-sharpening algorithms. These images
are displayed in Figs 10.4 and 10.6, respectively.
The 512
×
512 details have been selected in such a way to
contain some buildings with sharp edges and vegetated areas as
well, in which color distortion may appear.
×
TABLE 10.1
Spatial distortion
D
s
, spectral distortion
D
λ
and
quality with no reference (QNR) index are reported for the selected
algorithms for the QuickBird test image. The best results are
showninbold.
1520 pixels where urban
feature are more concentrate. The second data set consists of an
11-bit IKONOS satellite MS image, referring to Umbria Region
in Central Italy, with an SSI of 4 m and of a Pan image with
an SSI of 1 m. Also in this case the whole scene has been fused
and quantitative results refer to a 2048
×
Metric
EXP
GS
GSA-CA
GLP-CA
GMMSE
D
s
0.1474
0.1031
0.0441
0.0334
0.0532
D
λ
0.0011
0.0721
0.0623
0.0875
0.0630
×
2048 subimage where
QNR
0.8431
0.8322
0.8963
0.8820
0.8872
urban features appear.
Quantitative results have been judged by the novel metric
quality with no reference (QNR) that is computed at full scale
even if the reference is not available as occurs in this case
(Alparone
et al
., 2008). QNR is based on the invariance of the
Q index defined by (Wang and Bovik 2002) and measures the
quality of the fusion process by merging two factors, denoted as
D
λ
and
D
s
, which quantify the spectral and spatial distortions
of the fused products, respectively.
D
λ
and
D
s
should be ideally
0
in the best case and
1
in the worst case. Once
D
λ
and
D
s
have been defined (Alparone
et al
., 2008), QNR is given by
(1
TABLE 10.2
Spatial distortion
D
s
, spectral distortion
D
λ
and
quality with no reference (QNR) index are reported for the selected
algorithms for the IKONOS test image. The best results are shown
in bold.
Metric
EXP
GS
GSA-CA
GLP-CA
GMMSE
D
s
0.1454
0.1146
0.0685
0.0782
0.0723
D
s
)
β
. QNR should be ideally 1 and 0 in the
best andworst case, respectively.
α
and
β
are factors chosen to give
a different weight to spatial or spectral distortion. In the reported
D
λ
)
α
...
(1
−
−
D
λ
0.0222
0.0704
0.0684
0.0754
0.0657
QNR
0.8356
0.8231
0.8678
0.8523
0.8668
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