Image Processing Reference
In-Depth Information
(
)
2. Entropy: The entropy of an image, H
gives an indication of the information
content in the image. Thus, images with a higher entropy are richer in information
content. For an image with gray levels [ 0
I
,
L
1 ] , the entropy H k of the image
F k is given as:
L
1
H k
H
(
F k ) =−
0 P F k (
i
)
log
P F k (
i
),
(9.3)
i
=
where
P F k represents the probability density function of the given image F k ,
represented by its gray-level histogram. As more and more images are being
fused, we would naturally expect an increase in the information content in the
fused image. Thus, an addition of constituent images during the process of fusion
should result in an increase in the entropy H k . Similar to the variance measure,
image entropy is also susceptible to the presence of noise in constituent images.
Also, the entropy does not provide any information about the spatial details. Its
usefulness lies in providing the average information content in the image as a
whole.
3. Average Gradient: Sharply fused images enhance details in the scene such as
edges, boundaries, and various objects. It helps human observers to identify vari-
ous features, and also improves the performance of various machine vision algo-
rithms such as image segmentation and object recognition. The average gradient
of an image
is a simple but efficient measure of its sharpness in terms of
gradient values. The average gradient is defined [24] by:
g
¯
(
I
)
x F k 2
y F k 2
X
Y
1
XY
g k ≡¯
¯
g
(
F k ) =
+
.
(9.4)
x
=
1
y
=
1
¯
The average gradient
g k should increase monotonically as k increases. A good
fusion technique should ensure that addition of a new band to fusion leads to
an increase in sharpness of the fused image. As the isolated noisy pixels tend to
increase the spatial gradient, this measure is also susceptible to the presence of
noise in the data.
9.3.2 Performance Measures with an Asymptotic Reference
This set of measures is used for the consistency assessment of the fusion technique
considering the final fused image F
F K , as the reference. The idea is somewhat
different from the conventional ways of fusion evaluation. Also, generalized image
fusion typically combines very few images, say 2-3. Not much study has been carried
out towards extension of these techniques for larger data sets. We need to analyze
the behavior and performance of existing techniques for fusion of large data sets
 
 
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