Image Processing Reference
InDepth Information
By the change of sign, we formulate the MAP estimation as the minimization prob
lem, i.e.,
dx dy
F
2
=
argmin
F

s
−
β
F

+
λ
F
∇
F

.
(5.15)
x
y
Equation (
5.15
) represents the final solution for the estimation of the fused image.
An iterative solution to Eq. (
5.15
) can be derived from the approach proposed by
Rudin et al. [155] using the evolution parameter
∇
F
(
m
)
∇
F
(
m
)

F
(
m
+
1
)
=
F
(
m
)
−
τ
T
(β
F
(
m
)
−
β
s
)
+
λ
F
∇•
,
(5.16)
where
(
m
)
indicates the iteration number, and
τ
refers to the step size per iteration.
•
indicates the dot product operator. The iterations can be stopped when the process
converges, i.e., when the difference in the fused images obtained over successive
iterations (

F
(
m
+
1
)
−
F
(
m
)

) is smaller than a predefined threshold. The TV prior
based estimators typically converge within a very few iterations. The intensity values
of estimated fused image are then linearly scaled into [0, 1] to use the complete
dynamic range of the display device.
5.6 Implementation
Selection of the parameters of the algorithm is an important factor for its performance.
The above discussed technique is a twostep procedure involving the computation
of the sensor selectivity factor (
β
), and the estimation of the fused image (
F
). The
computation of
requires evaluation of two quality measures at every pixel in the
data. The first quality measure is related to the wellexposedness of the pixel which
is measured through a Gaussian function. The value of variance
β
2
β
in Eq. (
5.6
)
is essential for a proper evaluation of the measure
Q
1
. This variance parameter
σ
2
β
defines the spread of the bellshaped Gaussian curve. A very small value of the spread
parameter results in a narrowwidth Gaussian curve around the midintensity level.
Thus, a large number of pixels that are away from the middle gray level get assigned
to a very small quality values. Although we want to exclude the gray values on either
extrema (by assigning them smaller possible quality values), in this scheme, one may
lose the information provided by pixels that are slightly away from the midintensity
value. On the other hand, a too high value of
σ
2
β
results in a Gaussian curve with a
very slow falloff. Thus, most of the pixels, including the ones close to either extrema
will also get significant weightage which is not desired. We have selected the value
of this parameter to be 0.20 which gives a desirable balance. The constant
C
in the
measure
Q
2
in Eq. (
5.7
) is the second parameter we need to set before we proceed to
actual fusion. This constant determines the selection of pixels contributing towards
fusion on the basis of amount of the local sharpness. As
C
increases, the value of
σ