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 
identification. 
Image A 
Image B 
Segmentation 
LP 
Match 
Activity 
LP 
Activity 
Decision 
l 
-> 
Combination 
1 
Reconst met ion 
Fused 
Iaace 
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 
KP 
Acti 
Fi 
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 \