Image Processing Reference

In-Depth Information

Fig. 2.3
Illustration of the

notations for a hyperspectral

image

This image can be considered as a set of
K
two-dimensional spectral bands. We

shall denote the
k
-th band by
I
k
,

K
. Each
I
k
, therefore, refers to a 2-D

spatial plane. The gray value of the pixel at the location (
x

k

=

1

,

2

,...,

,

y
) in this band is given

by
I
k
(

.

The hyperspectral image
I
contains spectral signatures of the pixels covered by the

spatial extent of the imaging sensor. The image, therefore, is a collection of spectral

signatures across locations

x

,

y

)

(

x

,

y

),

x

=

1

,

2

,...,

X

;

y

=

1

,

2

,...,

Y
. Each of the

spectral signature is a vector of dimensions

. A pixel in the fused image is

primarily generated by processing the spectral signature of the pixel that represents

an array of observations across all spectral bands for the given spatial location.

We shall often work with this 1-D spectral array at a given location. Therefore,

we shall introduce a different notation to refer to the spectral arrays (or vectors)

in the hyperspectral image
I
. We shall denote the array of observations (i.e., the

spectral signature) at location

(

K

×

1

)

. It may be noted that this

notational change is purely meant for the ease of understanding as the same data will

be referred from different dimensions. Figure
2.3
illustrates the relationship between

the two aforementioned notations. A hyperspectral image
I
, thus, can be considered

as a set of bands
I
k
where the set contains
K
elements. The same image can also be

considered to be a set of spectral arrays
s

(

x

,

y

)

by
s

(

x

,

y

)
∀
(

x

,

y

)

(

x

,

y

)

where the set contains
XY
elements.