Graphics Reference
In-Depth Information
w
(
m
,
n
)
where
is a two-dimensional separable Gaussian window function.
The Gaussian pyramid is a set of low-pass filtered images. In order to obtain the
band-pass images required for the multi-resolution spline it is necessary to subtract
each level of the pyramid from the next lowest level. Let
G
'
be the image obtained
+
1
G
G
'
G
by expanding
, and
has the same size as
. Then the EXPAND operator
+
1
+
1
can be defined as:
'
G
=
EXPAND
G
(
)
(3)
l
+
1
l
+
1
2
2
i
+
m
j
+
n
−
'
G
=
4
mn
w
(
m
,
n
)
G
(
,
)
(4)
l
+
1
l
+
1
2
2
=
2
=
−
2
Therefore, the Laplacian pyramid can be defined as:
L
G
G
'
,
0
l
N
=
−
≤
<
l
l
l
+
1
(5)
L
G
,
l
N
=
=
N
N
N
where
is the number of Laplacian pyramid levels.
An important property of the Laplacian pyramid is that it is a complete image re-
presentation. The steps used to construct the pyramid may be reversed to recover the
original image exactly. Therefore, the reconstruction of original image from the Lap-
lacian pyramid can be expressed as:
G
=
L
+
EXPAND
G
=
L
+
EXPAND
L
+
EXPAND
G
(
)
(
(
))
0
0
1
0
1
2
(6)
=
L
+
EXPAND
L
+
EXPAND
L
+
+
EXPAND
L
(
(
(
)))
0
1
2
First each image is converted to grayscale. Then each grayscale image is processed
by a Laplacian filter. The absolute value of the filter response is calculated. The me-
thod then computes a weighted average along each pixel, using weights computed
from the quality measure. To obtain a consistent result, it is needed to normalize the
values of the
(
i
,
j
)
N
weight maps such that they sum to one at each pixel
:
−
1
N
ˆ
W
=
W
W
(7)
ij
,
k
ij
,
k
'
ij
,
k
k
'
=
1
ij
k
(
i
,
j
)
k
th
,
where subscript
refers to pixel
in the
image.
R
The resulting image
can then be obtained by a weighted blending of the input
images:
Search WWH ::
Custom Search