Image Processing Reference
In-Depth Information
image, if
c
1
(
),
c
2
(
),
and
c
3
(
)
represent the weights for the
k
-th spectral band
related to the red, green and blue channels, respectively, then the fusion procedure to
obtain the resultant RGB image
F
k
k
k
(
x
,
y
)
≡{
F
r
(
x
,
y
),
F
g
(
x
,
y
),
F
b
(
x
,
y
)
}
is given
by Eq. (
2.3
).
K
F
r
(
x
,
y
)
=
c
1
(
k
)
I
k
(
x
,
y
)
k
=
1
K
F
g
(
,
)
=
c
2
(
)
I
k
(
,
)
x
y
k
x
y
k
=
1
K
F
b
(
x
,
y
)
=
c
3
(
k
)
I
k
(
x
,
y
),
(2.3)
k
=
1
where
I
k
(
in the
k
-th hyperspectral band. These
weights are subjected to the constraint—
k
=
1
c
1
(
x
,
y
)
is the pixel at location
(
x
,
y
)
)
=
k
=
1
c
2
(
)
=
k
=
1
c
3
(
)
in order to satisfy the requirement of the equal energy white point [78]. The color
matching functions have been derived from the CIE 1964 tristimulus functions, which
are stretched across the wavelength axis so that the entire range of the hyperspectral
image can be covered. For this stretching, only the first and the last bands of the
hyperspectral image are equated with those of sRGB transformed envelopes, while
the remaining values have been obtained via a linear interpolation [79]. The same
authors have also introduced a set of fixed basis functions based on certain optimiza-
tion criteria for display on the standard color space (sRGB), and the perceptual color
space (CIELAB) [79]. These fixed basis functions are piecewise linear functions
that provide a uniform variation in hue across the spectral response of the scene.
The authors claim that the results produced using these functions are superior to the
former case of the color matching functions in terms of providing a more uniform
hue variation over the spectrum.
The problem of visualization of hyperspectral image has been formulated into an
optimization framework in [44]. This work considers the goal of preservation of spec-
tral distances. The process of fusion maps a hyperspectral image containing
K
bands
into a color image of 3-bands. A pixel in the original data has been considered to be a
K
-dimensional quantity, while in the output, the same pixel has been represented as
a 3-dimensional quantity. Here, the goal is to preserve the Euclidean norm of these
distances from the input spectral space (
k
k
k
3
)
in order to provide a perceptual interpretation of the scene. This method allows an
interactive visualization where the user can modify the color representation of the
resultant image. It uses an HSV color space which facilitates a faster remapping of
the tone during interactive visualization. However, it is not as good as other color
spaces such as
L
K
) into the output spectral space (
∈ R
∈ R
b
color space towards the preservation of spectral distances [44].
A spatial lens and a spectral lens have been provided as a part of interactive visu-
alization, which allow users to enhance the contrast in a particular region, and to
highlight pixels with a particular spectral response, respectively. Mignotte has also
∗
a
∗
