Image Processing Reference

In-Depth Information

from a set of pre-defined quality measures of the input data. We calculate the sensor

selectivity factor

β
k
(

,

)

(

,

)

in a particular band
k
as the

product of different individual quality measures of the image. If
Q
1
,

x

y

for a particular pixel

x

y

Q
2
,
···
,

Q
n

are the different quality measures, then the value of

β

is given by Eq. (
5.5
).

n

Q
j
I
k
(

)
,

β
k
(

x

,

y

)
=

x

,

y

(5.5)

j

=

1

where
Q
j
(.)

indicates evaluation of the
j
-th quality measure. These quality mea-

sures, however, should satisfy certain properties. Though we are not dealing with

the conventional fusion weights, the non-negativity of the sensor selectivity is an

essential condition. This factor reflects the fractional component of the true scene

captured by the given sensor element. Intuitively, and by definition, this compo-

nent has to be non-negative. The minimum value of

can be zero, which indicates

pure noisy data without any relation to the true scene. The quality measure should,

therefore, produce a non-negative value, and it should also be confined to a finite

range. If the quality measure produces a negative value due to reasons such as small

magnitude, phase reversal, etc., the multiplicative combination of measures given

in Eq. (
5.5
) may as well turn out to be negative, and change the notion of the cor-

responding measure. Non-negative values enable a direct combination of multiple

quantities without a need for sign change. The value of

β

is calculated as the product

of the local quality measures, and hence, even if a single measure has the value of

zero, the corresponding

β

will be enforced to be zero producing erroneous

results. Secondly, these measures should be confined to a finite range. We do not need

a normalization across all the bands of hyperspectral image, as typically done for the

conventional fusion weights. However, the

β
k
(

x

,

y

)

β

values should be confined to a specific

range. The designated range for

is [0, 1], however the actual value of products of

chosen quality measures may not confine to this range. One has to appropriately scale

the computed product of quality measures to the designated [0, 1] range. We have to

compute these quality measures over each pixel in each spectral band of the hyper-

spectral data. Therefore, it is desirable to select computationally efficient quality

measures
Q
j
's.

Out of the various existing no-reference qualitymeasures, we choose the following

two:

β

•

well-exposedness, and

•

sharpness.

The gain of the hyperspectral sensor array as a function of the wavelength varies

greatly over the entire span of the bandwidth of spectral bands. Pixels with very high

values of intensity appear too bright due to over-saturation. On the other extreme,

poorly-exposed or under-saturated pixels appear too dark, and thus, fail to convey

visually useful information. As these pixels do not provide any significant infor-

mation, one naturally expects lesser contribution from such pixels towards the final

fused image. The sensor selectivity factor for such pixels should obviously be small.