Agriculture Reference
In-Depth Information
In the presence of radiometric errors, we can proceed as follows. First, we
assume that different sensors detect the same phenomenon in the same manner.
This is equivalent to assuming that the sensors record images that are statistically
similar. In other words, the means (
) of the brightness
of the images recorded by different sensors in each spectral band should be equal. If
there are differences between these statistics, we can reasonably assume that there
has been a measurement error introduced during the data acquisition process. A
correction can be made by considering the gray levels associated with the pixels
detected by one sensor as a baseline, and using it to transform the brightness
measured by the other sensors. Therefore, we can define (Richards and Jia
2006
)
ʼ
) and standard deviations (
˃
x
i
¼ ˃
m
=˃
t
ð
Þ
t
y
i
þ ʼ
m
˃
m
=˃
t
ð
Þ ʼ
t
;
ð
:
Þ
4
5
where
x
i
is the newly restored brightness value of the
i
-
th
pixel,
t
y
i
is the
old
value
recorded by the sensor
t
,
˃
m
are the mean and standard deviation of the
brightness in each spectral band of the baseline sensor
m
, and
ʼ
m
and
ʼ
t
and
˃
t
are the mean
and standard deviation of the sensor under investigation,
t
.
Furthermore, the image may be further restored by considering the characteris-
tics of observed random phenomena. The aim of this strategy is to remove the error
components of the RS images, and the methods are mainly developed by statisti-
cians (Besag
1986
; Geman et al.
1990
; Cressie
1993
). In this approach, an RS image
represents a deformation of the true scene, which, in all its complexity, can be
defined in terms of a set of phenomena that evolve in a continuous space. Formally
speaking, we can define the real scene using
M
maps expressed as continuous
variables
m
X
(
α
,
ʲ
), where (
α
,
ʲ
) are the geographical coordinates, and
m
¼
1,
...
,
M
represents the number of observed spectral bands. Obviously a higher spectral
resolution results in a more accurate representation of reality. We can define the
discrete counterpart of these continuous variables as
ð
j
þʴ
ð
iþʴ
m
X
ij
¼
m
X
α; ðÞ
d
α
d
ʲ:
ð
4
:
6
Þ
i
j
This image depends on the chosen interval
, which is the spatial resolution or
accuracy of the observation window. In essence, the continuous variable
m
X
(
ʴ
α
,
ʲ
)is
N
+
, and
transformed to the discrete variable
m
X
ij
, where 0
m
X
ij
R
,
m
X
ij
2
0
255.
The observed image, Y, can be defined as (Ripley
1988
)
R
Y
¼
f
X
ð
; ε
Þ;
ð
4
:
7
Þ
where the function
f
incorporates the effects of the pixel dislocations caused by the
imperfections of the platform and the dispersion of the energy by the atmosphere,
X is the discrete representation of the true scene, and
ε
is an error with
ε
~
N
(0,
ʣ
).
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