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Mapping without the sun
Zhang, Jixian

in which
expands [G*+,] (i,j)
= X ( 3 >
m=-L e n=-L e
(j+n) mod2=0
(i+m) mod2=0
The attribute enhanced depends on the expansion filter being
forced to be half-band, i.e. an interpolator by 2, and chosen
independently of the reduction filter, which may be half-band as
well or not. The ELP outperforms the standard LP for image
compression, thanks to the fact that its layers are uncorrelated
with one another. The filter choice stems from a trade-off
between selectivity (sharp cut-off) and computational cost. In
particular, the absence of ripple is the most favourable feature.
The ELP can be easily generalized to deal with scales whose
ratios are integer or even fractional numbers.
As an intermediate step from pixel-based to region-based fusion
schemes, a region-based fusion approach has the additional
advantage that the fusion process become more robust and
avoid some of the problem in pixel-level fusion, such as high
sensitivity to noise and blurring effects [Piella, 2002].So a
region-based Laplacian fusion scheme in place of a pixel-based
Laplacian fusion scheme is used (figure 1).
segmentation based on the linked pyramid [Burt, 1981] to
partition the image domain at these scales is introduced. The
activity level and match measures are computed for every
region in the decomposed input images. All this information is
integrated to yield a decision map which governs the
combination of the coefficients of the transformed sources
[Blum, 2005]. This combination results in a multiresolution
decomposition is used to obtain a fused image by
multiresolution synthesis. The parameters and functions
comprised by the various blocks can be chosen in a variety of
ways. Since different combinations will lead to different
performances, it is important to study the effect of these choices
on the final fusion process.
2.2 Morphological pyramid (MP) fusion
A morphological pyramid can be constructed by the successive
filtering of the original image with a sequence of morphological
operators [Toet, 1989]. These operators transform the image
representation using predefined shapes, called structuring
elements. Structuring element is a matrix used to define a
neighbour hood shape and size for morphological operations.
Approaching image processing from the vantage point of
human perception, morphological operators simplify image data
preserving essential shape characteristics, and eliminate
irrelevancies. Morphological filters also remove noise without
adding greyscale bias, making them well suited for shape
Image A
Image B
Reconst met ion
All morphological filters are based on two fundamental
operators: erosion and dilation. These two transforms can be
defined in terms of the binary image B and a structuring
element S. However, for generality, let B and S be sets in N-
dimensional space (E N ) with b and s being N-tuples of element
coordinates; then, the dilation of B by S is denoted by B® S
and is defined by
B ® S = (ce E n |c= b +s for some b ©B and sGS} (4)
Erosion is the morphological dual of dilation, that is, the
dilation of a set B is equivalent to the erosion of the
complement set B*. The erosion of B by S is denoted by B® S
and is defined by
B 0 S= {xe E n |x +^g b for every xe S} (5)
Using these morphological building blocks, two higher order
operations, opening and closing, can be defined. The opening of
image B by structuring element S is denoted and defined as
BoS = (B0S)®S (6)
While the closing of image B by structuring element S is
denoted and defined as
B • S = (B © S) 0 S (7)
Figure 1. A region-based LP fusion scheme with two input
image A and B.
The region-based fusion scheme extends the pixel-based fusion
approach. In the scheme, multiresolution decompositions
represent the input images at different scales. A multiresolution
Finally, filters can be constructed from the opening and closing
operations. To create an open-close filter, closing is followed
by opening. The reverse is true for the close-open operation.
Binary morphology can be extended to non-binary sets though
the use of the min and max operations. A function, f(x), dilated
by a structuring element, S, is defined by
(f® S)(
where x £ D in
Z 2 . Effectively,
while erosion is
(f0 s;
For a MP constr
the image I L by
Il= [(Ii
where L is the p;
[• ]isasubsamp
Replacing the
pyramids, the M
Image A
3. EXPE1
As mentioned a
fusion are used t
on the left (Figur
(Figure 3b) are tv
the two pyramid
3d. To compare
are evaluated in \