Environmental Engineering Reference
In-Depth Information
MS
Upsampling
to Pan scale
Band-dependent
MTF filtering
Pan
−+
d
MS
F
g
k
Computation
of N gains
FIGURE 10.1
Multiresolution fusion scheme: spatial details
d
are extracted from the Pan image and injected in the expanded
MS images. Images
g
k
rule the injection gain.
obtained from spatially degradedMS and Pan images. The degra-
dation factor equals the spatial resolution ratio between original
MS and Pan data. This evaluation protocol is used, among others,
by the ERGAS (Ranchin and Wald, 2000) and the Q4 indexes
(Alparone
et al
., 2004b). More recently, it has been shown that
quality may be assessed without a reference image, i.e., directly
at the spatial resolution of Pan, by evaluating the QNR index
(Alparone
et al
., 2008). QNR is based on the invariance of the Q
index defined by (Wang and Bovik 2002) and measures the qual-
ity 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. QNR,
D
λ
and
D
s
are the indices that
are adopted in this work to assess the quality of the fused products.
Fig. 10.1. The scheme evidences the characteristic by which an
algorithm is classified asMRA: details are extracted by subtracting
a low-pass filtered version of the Pan image to the Pan image
itself.
According to this scheme, and by simplifying the notation
here and in the following by avoiding to explicitly indicate the
spatial indices for all the images, the MRA fusion algorithm is
expressed by
MS
k
MS
k
P
k
)
g
k
+
=
(
P
−
k
=
1,
···
,
N
(10.1)
Where
MS
k
is the fused multispectral image,
k
denotes the
k
-th
band and
N
indicates the number of MS bands; the low-pass
filtered Pan version
P
k
is obtained by convolving
P
by means
of the MTF of each MS band and
MS
k
represents the
k
-th MS
component expanded to the scale of the Pan image. The injection
model is accomplished by the weight image
g
k
that modulates,
through an element-by-element multiplication, the image of the
high spatial details. If
g
k
is constant for each band, the injection
model is defined as
global
;inthiscase
g
k
is usually derived by
computing global statistical parameters on the whole MS and
P
images. Otherwise,
g
k
is related on the local context measured on
a sliding window of the current pixel, can be computed by taking
local statistics of the MS and
P
images and the model is denoted
as
local
. The choice adopted in (Aiazzi
et al
., 2009) is to take
g
k
as the regression coefficients
β
(
P
k
,
MS
k
), relating the MS bands
MS
k
and the Pan MTF filtered version
P
k
.
β
(
P
k
,
MS
k
)isgiven
by the covariance of
P
k
and
MS
k
, normalized by the variance of
P
k
. The scheme is denoted with GLP when the
global
model is
adopted. Conversely, GLP-CA denotes the scheme when the
local
model is adopted.
10.2
Multiresolution fusion
scheme
One of the most powerful and efficient framework for MRA
algorithms is represented by the generalized Laplacian pyramid
(GLP) decomposition. Its performances are practically the same
as those of the ''
`atrous
'' wavelet transform (Aiazzi
et al
., 2002).
The method can take into account the MTF of each MS channel,
thus fitting the detail extraction from the Pan image to each
MS band (Aiazzi
et al
., 2006). In addition, local CA models can
be adopted in the injection process, with the aim to preserve
and sometimes increase the spectral information of the fused
products, by unmixing the coarse MS pixels through the sharp
Pan image. Anoticeable example is givenby theGLPwith context-
based decision (GLP-CBD) algorithm (Aiazzi
et al
., 2002) that
employs a CA model aimed at inserting or not the spatial
details for each pixel. Although the GLP-CBD model is very
efficient when computing evaluation scores, its fused images can
sometimes suffer from a poor contrast in some localized areas. In
order to prevent this effect, the decision rule can be modified as
described in (Aiazzi
et al
., 2009) by avoiding the on-off decision
in the CA model.
A simplified scheme for MRA fusion that holds once the MS
images have been registered with the PAN image is reported in
10.3
Component
substitution fusion scheme
Let us consider the general CS fusion scheme in Fig. 10.2.
An algorithm is classified as CS when details are extracted by
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