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