The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
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spatial domain, while the gray level and multi-spectral 
information are represented in the color domain. When the 
location and color vectors are concatenated in the joint spatial- 
SSIM = ^Ma ' Mb + Cl X^&ab + Q ) 
(Ma + Mb +C i )( a A + + Q ) 
(7) 
color domain of dimension d=p+2, thus, the multivariate kernel 
is defined as: 
K 
h s ,h r 
(x) = -y - k 
h]h p _ 
(2) 
Where X s is the spatial part and X r the color part of the 
feature vector; k(x) is the common profile used in both of the 
two domains; h s and h r are the kernel bandwidths; and C is 
the corresponding normalization constant. The quality of 
segmentation is controlled by the spatial domain h s and color 
domain h r . 
where fi A , /U B are the mean values of regions in images A and 
B; and <J A , <J B are the variances of images A and B. <T AB is 
the covariance of A and B. C,, C-, are two constants. 
The SSIM index may be illustrated geometrically in a vector 
space of image components. These image components can be 
either pixel intensities or other extracted features. It is more 
meaningful to compare the similarity of two regions than to 
compare region match measures. 
Another parameter — the region activity level — is defined as 
follows (Piella, 2003): 
c(i,j)er 
(8) 
4. STRUCTURE SIMILARITY INDEX METRIC (SSIM) 
FOR FUSION DECISION MAKING 
When the regions are obtained by the overlaying process, the 
regions’ structure similarity index metrics are computed to 
guide the wavelet coefficient fusion. Wang,(2002) firstly 
proposed a Universal Image Quality Index (UIQI) which 
achieves satisfactory result for assessing compressed image 
quality. Afterward, Wang,(2004) improved on it and named it 
Structure Similarity Index Metric (SSIM) which is a global 
metric to measure the similarity of two images. In this paper, we 
use the SSIM to calculate the similarity of corresponding 
regions in two input images. It is defined as follows: 
SSIM(x, y) = [l(x,y)] a • [c(x,y)Y ■ [s(x,j>)] r (3) 
Where N denotes the pixel number in region r and c(i,j) 
denotes the corresponding wavelet coefficient at location (/, j) . 
For each region, the coefficients are fused according to the 
SSIM. If SSIM is less than a threshold CC , we will perform 
selection; and otherwise we will perform averaging. 
c F (r) = 
c A( r )> 'f a A (r)> a B (r),SSIM(r) < a 
c„ (O, tf a A (r) < a B (r), SSIM(r) < a (9) 
c A +c, 
-,SSlM(r) > a 
For each edge, the fusion rule is as follows: 
The luminance, contrast and structure comparison measures 
were given as follows: 
l(x,y) 
bI+mI+c, 
c(x,y) 
2 + C-i 
a 2 + a 2 + C, 
x y 2 
(4) 
(5) 
B cr + C 3 
y > («) 
ZT (7 + Ci 
x y 3 
Cj, C 2 , C 3 are constants. When CC = j3 = y = \in formula 
(3), the SSIM index is given by 
C F 0 > j) — 
c A (A j\ only if c A (i, j) is at an edge 
c B (i, j), only if c B (/, j) is at an edge (10) 
c A (i,j) + c B (i,j) 
both are at edges 
Once the composite coefficients are obtained, the fused image 
can be produced by inverse wavelet procedure. 
5. EVALUATION OF PROPOSED METHODS 
To evaluate the proposed method, two sets of images are used. 
One is the built-up area and the other is rural area. Both are 
from IKONOS-2 sensors. The dimensions of Panchromatic (Pan) 
and Multi-Spectral (MS) images are 512*512 and 128* 128, 
respectively. The proposed fusion result is compared with the