Image Processing Reference

In-Depth Information

to yield the magnitude and orientation of edges at every pixel. The relative values of

the edge magnitude and orientation for every pixel are then calculated by comparing

those with the same for the corresponding pixel of the fused image. The relative edge

magnitude is calculated through the division of the edgemagnitude of the input image

pixel and the fused image pixel, while the difference between the edge orientation

of the image pixel and the fused image pixel has been used to obtain the relative

edge orientation. These values are then used to derive the quantities referred to as

the edge strength and preservation. The actual expression for these values includes

additional constants that determine the exact shape of sigmoid functions which are

used to describe the edge strength preservation. The final measures for the magnitude

and the orientation model the loss of information in the fused image
F
, and quantify

how well the strength and orientation values of pixels in input images are being

represented in the fused image
F
. The product of these two final quantities is used

to evaluate the fused image, and thus, the corresponding fusion technique. When

this measure equals one, it indicates fusion with no loss of information from the

corresponding input image, while the value of zero refers to the complete loss of

edge information. However, this measure can quantify only the loss related to the

edge detection.

Wang and Bovik have proposed a universal image quality index (UIQI)forthe

assessment of several image processing applications [183]. This measure is primarily

meant to evaluate the quality with respect to a standard or reference image. This

measure can be decomposed into three components—(
i
) correlation, (
ii
) luminance,

and (
iii
) contrast. The mathematical expression for UIQI is given by combining the

second order statistical measures for the above three parameters. The UIQI between

images
I
1
and
I
2
is calculated as:

σ
I
1
I
2

2
m

(

I
1
)

m

(

I
2
)

2

σ
I
1
σ
I
2

UIQI

=

σ
I
1
σ
I
2
·

2
·

I
2
,

(2.5)

||

I
1
||

2

+||

I
2
||

2

2

σ

I
1
+
σ

where

σ
I
1
represents the standard deviation,
m

(
·
)

represents the mean, and

σ
I
1
I
2
is the

correlation between two images. The

operator is used to represent the dot product

between two lexicographically ordered images in the form of column vectors. It may

be seen that the final expression for the UIQI can be simplified by canceling some

of the variance terms from Eq. (
2.5
). The dynamic range of UIQI is [

·

1, 1] where

the highest value of 1 indicates that the two images are exactly the same. Piella and

Heijmans have developed a metric for fusion evaluation based on the UIQI [138].

They have proposed the use of a local window to calculate the UIQI due to non-

stationary nature of an image signal. A weighted linear combination of these values

provides the required quality measure for the fused image. The weights are based on

some saliency measure in the local window.

When the pixel intensity can be treated as a discrete random variable, one can

effectively use some of the information theoretic measures to assess different image

processing operations. The entropy of a discrete random variable (image in our case)

refers to its information content. Themutual information (MI) represents the common

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