Agriculture Reference
In-Depth Information
to regions in an image. The supervised classification algorithm depends on the
nature of the available data and the desired output (Jensen
2004
).
The first step of a supervised classification method is the definition of the
training areas for each spectral band. The known pixels for each of
the
pre-decided classes (
c
¼
,
C
) and each spectral band (
m
¼
,
M
) form the
1,
...
1,
...
corresponding sample sets
S
1
,
S
2
,
,
n
K
pixels,
respectively. The brightness values for each band and each training class can be
statistically analyzed using a mean vector and covariance matrix defined as
,
S
K
, which contain
n
1
,
n
2
,
...
...
0
1
ʼ
c
1
ʼ
c
2
...
ʼ
cM
@
A
;
ʼ
c
¼
ð
4
:
20
Þ
and
0
@
1
A
:
Var
c
1
Cov
c
12
Cov
c
1
M
...
Cov
c
21
Var
c
2
Cov
c
2
M
...
V
c
¼
ð
4
:
21
Þ
...
...
...
...
Cov
cM
1
Cov
cM
2
Var
cM
...
The most commonly used supervised method is maximum likelihood classification
(MLC). From a statistical point of view, the MLC method is considered to be
robust, and it produces estimators with good statistical properties. In other words,
MLC methods are versatile, and can be applied to most models and types of data.
Additionally, they provide efficient methods for quantifying uncertainty using
confidence bounds. Although the methodology for maximum likelihood estimation
is simple, the implementation is sometimes mathematically intensive.
The MLC procedure assumes that each training class in each band is normally
distributed. Using Eqs. (
4.20
) and (
4.21
), under Normality assumption, it is possible
to define the likelihood of the pixel
i
, with brightness value x
i
, being in class
c
as
1
1
2
x
i
ʼ
c
t
V
1
c
p
x
i
c
ðÞ¼
2
exp
ð
Þ
ð
x
i
ʼ
c
Þ
:
ð
4
:
22
Þ
M
=
2
V
c
1
=
ðÞ
2
j
j
where |V
c
| is the determinant of the covariance matrix. These likelihoods are
calculated, and each pixel is then assigned to the most likely class, i.e.,
p
x
i
c
>
p
x
i
l
8
l
6¼
c
ð
4
:
23
Þ
The idea behind MLC parameter estimation is to determine the parameters that
maximize the likelihoods of the sample data. Note that it is the most powerful
classification method, if the training data is accurate. Therefore, this method
requires excellent training data.
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