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 )
I 2 )
σ I 1 σ I 2
σ I 1 σ I 2 ·
2 ·
I 2 ,
I 1 ||
I 2 ||
I 1 + σ
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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