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

∗