Image Processing Reference
InDepth Information
associated with a source is calculated by combining the mass functions associated
with each singleton, defined in the first model by:
m
i
C
i
(
x
)=
α
i
Rp
x
C
i

1+
Rp
x
C
i
,
[7.15]

m
i
D
\
C
i
(
x
)=
α
i
1+
Rp
x
C
i
,
[7.16]

m
i
(
D
)(
x
)=1
−
α
i
,
[7.17]
where
α
i
is a discounting coefficient related to the class
C
i
, which makes it possible
to take into account the source's reliability for this particular class (and not its overall
reliability, unlike the previous model) and
R
is a probability weighting coefficient. If
R
=0, only the reliability of the source is taken into account, otherwise the data is
also taken into account.
In the second model, the masses associated with each singleton are defined by:
m
i
C
i
(
x
)=0
,
[7.18]
m
i
D
C
i
(
x
)=
α
i
1
Rp
x
C
i
,
\
−

[7.19]
α
i
+
α
i
Rp
x
C
i
.
m
i
(
D
)(
x
)=1
−

[7.20]
This model corresponds to the case where
p
(
x

C
i
) gives us information essentially
on what
C
i
is not.
⊕
i
m
i
, where
is Demp
ster's orthogonal sum (see section 7.4). This model is wellsuited for cases where one
class is easily learned compared to all of the others, which is common in shape recog
nition in images, or in the case when each class is determined based on an adequate
sensor (for example, a road sensor in an aerial image can be used to define the proba
bility of belonging to the road, as opposed to belonging to all of the other classes, but
is not capable of telling these other classes apart).
The mass associated with the source is then calculated as
⊕
In [DRO 97], disjunctions are defined based on a significance criterion for the
conditional probabilities. If only one probability
p
(
x
C
i
) is significant (thus creating
the need to define thresholds), then a simple mass model involving the singletons
is used. If several probabilities are significant, the disjunctions of the corresponding
hypotheses are also taken into account. For example, if three values are significant and
are such that
p
(
x


C
i
)
>p
(
x
C
k
), the mass function is defined by:
m
C
i
(
x
)=
p
x

C
j
)
>p
(
x

C
i
−
p
c
C
j
,


[7.21]
m
C
i
∪
C
j
(
x
)=
p
x
C
j
−
p
x
C
k
,


[7.22]
m
C
i
∪
C
k
(
x
)=
p
x
C
k
,
C
j
∪

[7.23]
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