Agriculture Reference
In-Depth Information
rule
(Richards and Jia
2006
). According to this rule, the
i
-th pixel is classified with
the label
c
if
Another commonly used method for supervised classification is Bayes
'
Pr
c
x
i
jðÞ>
Pr
l
x
i
jðÞ 8
l
6¼
c
;
ð
4
:
24
Þ
where Pr(
c
|x
i
) and Pr(
l
|x
i
) are the posterior probabilities of different classes, and x
i
is the brightness vector for each multispectral band of pixel
i
. According to Bayes
'
Theorem, Eq. (
4.24
) can be written as
p
x
i
c
>
p
x
i
l
8
Pr
c
ðÞ
Pr
l
ðÞ
l
6¼
c
;
ð
4
:
25
Þ
where Pr(
c
) and Pr(
l
) are the prior probabilities of the classes obtained using some a
priori knowledge, and
p
x
i
c
and
p
x
i
l
are the likelihoods. The function
p
x
i
c
g
c
x
ðÞ¼
Pr
c
ðÞ
ð
4
:
26
Þ
is the discriminant function. If the different classes have the same prior probabil-
ities, Eq. (
4.25
) reduces to
p
x
i
c
>
p
x
i
l
.
One possible alternative for supervised classification is the parallelepiped tech-
nique. This method is a widely used decision rule that is based on simple Boolean
and/or logical operators. Using the statistics in Eqs. (
4.20
) and (
4.21
), the pixel
i
is
classified as belonging to class
c
if and only if
ʼ
cm
s
cm
x
im
ʼ
cm
þ
s
cm
;
ð
4
:
27
Þ
p
Var
cm
where
s
cm
¼
,
M
are the spectral
bands. If a pixel value is between the minimum and maximum thresholds for all the
bands being investigated, it is assigned to that class. If the pixel is assigned to
multiple classes, it can be assigned to the last matched class. Areas that do not fall
within any of the parallelepipeds are designated as unclassified. This method differs
from MLC because it uses only maximum and minimum pixel values.
,
c
¼
1,
,
C
are the classes, and
m
¼
1,
...
...
4.6.3 The Contextual Approach to the Thematic Extraction
of Information
However, traditional techniques for the thematic extraction of information have a
serious drawback; each pixel is classified individually, independently to its neigh-
borhood. Using this approach, a large amount of additional information may be lost.
For example, in a Landsat image, it is more likely that a region classified as forest is
surrounded by other forest pixels when compared with a region labeled as urban.
For this reason, statisticians have developed some procedures that explicitly con-
sider the role of contextual information.
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