65 
Burt, 1981] to 
ntroduced. The 
uted for every 
> information is 
1 governs the 
'ormed sources 
multiresolution 
;d image by 
and functions 
in a variety of 
id to different 
of these choices 
t the successive 
f morphological 
orm the image 
led structuring 
ed to define a 
ical operations, 
atage point of 
ilify image data, 
and eliminate 
2 noise without 
lited for shape 
0 fundamental 
isforms can be 
1 a structuring 
S be sets in N- 
ples of element 
îoted by B ® S 
idseS} (4) 
>n, that is, the 
erosion of the 
noted by B ® S 
(5) 
/o higher order 
The opening of 
defined as 
(6) 
l element S is 
(7) 
ing and closing 
ing is followed 
open operation, 
ary sets though 
on, f(x), dilated 
(f© s)(x) = max № -y)} ( g ) 
,yeS 
where x £ D in Z 2 , Z is the set of integers and S is a subset of 
Z 2 . Effectively, dilation is a moving local maximum operator 
while erosion is a moving local minimum operator defined by 
(f0 S)(x) = maX № + y)} (9) 
jyeS 
For a MP constructed with an open-close filter, we can describe 
the image I L by 
Il= [(Il-i • S) ° S] 
(10) 
where L is the pyramid level, S is the structuring element, and 
[• ]is a subsampling. 
Replacing the Laplacian pyramids with the morphological 
pyramids, the MP fusion scheme is shown in figure 2. 3 
Image A 
Image B 
Fused 
Ia&ce 
Figure 2. The MP fusions scheme 
3. EXPERIMENTAL STUDY AND ANALYSIS 
As mentioned above, the two pyramid techniques of image 
fusion are used to fuse multi-focus images. An image focusing 
on the left (Figure 3a) and the other image focusing on the right 
(Figure 3b) are two co-registered. The fused images obtained by 
t e two pyramid techniques are shown in Figure 3c and Figure 
• To compare the two pyramid techniques, the fused images 
are evaluated in visual examination and quantitative analysis. 
Figure 3a. Focus on the left 
ES Magnifier Qutóty 
Figure 3b. Focus on the right 
ES Magnifier ! 
Figure3c. Fused image by the Laplacian pyramid