Instrumentation & Measurement Magazine 24-4 - 39

1 N



i 1
N 
xi 
2
where xi represents the value of pixel and μ signifies the avFig.
4. Laplacian Pyramid-Method1.
erage value of the image. A larger value indicates a superior
quality of image [29].
Mutual Information (MI): is a quantifiable measure of the
mutual dependence of two variables and illustrates the quantity
of the data shared by two images:
MI U V p u v log2
u Uv V
,
 ,

   
  
p uv
,
pu p v
Fig. 5. Discrete Wavelet Transform-Method2.
whereas p(u,v) represents the joint probability distribution
function of U and V,and p(u),p(v) represents the marginal
probability distribution function of U and V, respectively [30].
Fusion Factor (FF) is defined by:
FF I AF BF
  I
where IAF and IBF depicts the mutual information quantity.
Fig. 6. Stationary Wavelet Transform-Method3.
Higher estimations of fusion factor portray enormous measure
of data present in image [31].
Fusion Symmetry (FS): means the symmetric measure of
fused image with respect to input image. The fusion procedure
is better if the value of FS is less [30].


0.5
FS abs
AF BF
IAF

II
Structural Similarity (SSIM): represents the similarity in
structural content of two images for the measurement of quality
of image:
SI   cc 22 

SM ,xy 
Fig. 7. 2D-DDWT PCA Image Fusion-Proposed method.
a single input image. The proposed method is being shift invariant
and hence preserves the edge and phase content of the
source image. The information measurements are analyzed
with multimodal medical images and subjective examination
was performed dependent on different factors.
Performance Metrics
The fused images are evaluated quantitatively using the following
fusion metrics, namely entropy, standard deviation,
mutual information, fusion factor, fusion symmetry and structural
similarity.
Entropy (EN): portrays the measure of data content in a certain
picture. The bigger the worth is, the better combination
results are acquired:
EN pi log pi

L 1
  
i 0
where pF is the standardized histogram of the merged image to
be assessed. Here, L is the supreme gray level for a pixel in the
image. L is set to 255 [28].
Standard Deviation is defined by:
June 2021
FF
2

MIA
MIB
FF
FS
SSIM

  

xy
 
12


y
xy xcc
22 2
x y 12
2
where μ, σ, c represents the mean, standard deviation and
covariance respectively. Higher similarity represents better
quality image [33].
Tables 1-5 give the objective evaluation of five sets of images
compared with the different methods. As listed in the tables,
the entropy is higher for the proposed strategy, demonstrating
more measure of data content in the merged image. The standard
deviation measured is higher for the proposed technique
Table 1 - Performance measurements of
different methods for Set1 image
Set 1
EN
D
Method1 Method2 Method 3 Proposed
4.9134
3.9775
64.9116
4.6384
5.4173
10.0557
0.0387
0.7174
IEEE Instrumentation & Measurement Magazine
65.6119
4.5598
5.3040
9.8638
0.0377
0.7618
4.9031
65.738
4.5022
5.5416
10.0438
0.0517
0.7591
5.4271
69.7347
4.8938
5.4756
10.3693
0.0281
0.7794
39
Instrumentation & Measurement Magazine 24-4

Table of Contents for the Digital Edition of Instrumentation & Measurement Magazine 24-4
