Image Processing Reference
InDepth Information
The set of participatory performance measures refers to the quality of the final
result of fusion. Therefore, these measures are not useful in studying the progression
of the fusion process. Rather, we are interested in the numerical values of these
measures only, as opposed to the analysis of plots in case of the previous set of
performance measures. The objective of these performance measures is to quantify
the contribution or participation of each of the input bands toward building the final
image. A good fusion technique is expected to extract suitable information from all
the constituent bands during the fusion process. In this section, we explain how this
aspect of a fusion technique can be quantified. The set of measures in Sect.
9.3.1
is
unable to provide this information. The measures defined in Sect.
9.3.2
provide this
information to some extent but do not help in defining the accuracy of the technique.
1.
Relative Bias:
The mean of the fused image
m
, represents the average inten
sity of the entire image. A higher mean value has been used as a performance
indicator in [24, 191]. However, oversaturated images tend to have higher mean
values. In such cases, any fusion technique producing a nearly saturated resultant
image may be incorrectly considered to be better. Therefore, the mean value is not
the correct measure to analyze the performance of the technique. An excessively
high value of the mean of the fused image is not required. However, one may
expect the mean of the fused image to be close to the mean of entire input data. If
we are interested in preserving the radiometric fidelity in the data, we may devise
a technique that generates a fused image with mean close to the input mean, and
preserve the average radiometric mean. The preservation of mean may not be
useful in most of the visual applications, but it does facilitate an easier compar
ison between different regions across the same and different images. Thus, one
should define the deviation of the mean of the resultant image from the mean
values of the constituent bands as a performance measure. We suggest the use of
the relative bias, which can be calculated as the ratio of sum of deviations in the
mean of the constituent bands from the mean of the resultant image to the mean
of the resultant image. A lesser deviation in the relative bias indicates closeness
of the resultant image to its constituent bands in terms of the average intensity.
The relative bias
b
, for fusion of hyperspectral data containing
K
bands can be
defined by Eq. (
9.10
).
(
F
)
K
1
K

m
(
I
k
)
−
m
(
F
)

b
=
.
(9.10)
m
(
F
)
k
=
1
If
m
is the amount of average intensity of the incoming radiation in the
k
th
spectral band, and
m
(
I
k
)
indicates the amount of average intensity of the resultant
fused image, then the relative bias
b
measures the radiometric distortion in terms
of the mean or average intensity of the bands in the data.
As expected, a simple averaging based fusion yields trivially the least bias and,
therefore, this measure alone is not good enough to evaluate the performance
of a fusion scheme. It may be noted here that the relative bias as defined here
does not explicitly relate to the radiometric fidelity of the fusion process. For
such consideration, one may refer to the work by Zhukov et al. which uses the
(
F
)