Image Processing Reference
In-Depth Information
constituent bands. To answer question such as- Do all input images participate
well in the process?, a measure called fusion symmetry FS has been defined in
[147] for two input images as-
50
.
MI
(
I
1
,
F
)
FS
=
)
−
0
.
(9.13)
MI
(
I
1
,
F
)
+
MI
(
I
2
,
F
A lower value of FS is desired, indicating information from both images is sym-
metrically captured. In order to extend the definition to deal with a large number
of images (typically multispectral and hyperspectral), we employ the modified
version of the fusion symmetry measure proposed in [92]. The modified fusion
symmetry measure quantifies the symmetry in participation of image bands from
the entropy weighted standard deviation in the mutual information between the
final and the constituent images. Bands with higher information content typically
have more features, and hence, are expected to contribute more towards fusion.
On the other hand, if a band contains very less features as indicated by a low
value of the entropy, we would naturally expect lesser contribution from the same
towards the final result of fusion. Therefore, the symmetry in the fusion process
must be considered in accordance to the intrinsic information contents of con-
stituent bands. The corresponding definition of fusion symmetry
FSin the context
of hyperspectral image fusion is given by Eq. (
9.14
).
k
=
1
(
2
MI
(
I
k
,
F
)
−
FF
)
H
(
I
k
)
FS
=
.
(9.14)
k
=
1
H
(
I
k
)
A lower value of this measure is desired, which indicates a uniformity in the fusion
process with respect to its constituent images. This definition can be particularly
effective in case of remote sensing hyperspectral images where the distribution
of information among the bands is usually uneven.
While we have discussed several measures for performance assessment of a fusion
technique, it is important to understand their susceptibility to the noise in the data.
One is able to quantify the performance of a particular fusion technique with respect
to the consistency, sharpness, contrast, etc., using these measures. However, none of
these measures can evaluate the robustness of the fusion scheme against noise in the
data. If any of the constituent bands is badly corrupted by noise, all measures such
as variance, entropy, and average gradient will wrongly indicate a very sharply fused
image. A very high value of FFmay indicate the presence of possible data corruption
in certain image bands, but it is unable to relate the measure to the accuracy of the
fusion process.
