Image Processing Reference
In-Depth Information
Methods other than normalization have been suggested for eliminating the mass
assigned to the empty set. For example, this mass is assigned to
D
in [YAG 87],
in other words assigned to ignorance. In [DUB 88], a more subtle method is sug-
gested: for example, if the focal elements
A
1
and
A
2
of two sources are in conflict
(
A
1
∩
A
2
). This
means we are assuming that at least one of the two sources is reliable without speci-
fying which and the disjunctive form of the result is the most cautious attitude.
A
2
=
∅
), then the product
m
1
(
A
1
)
m
2
(
A
2
) is assigned to
m
(
A
1
∪
7.4.3.
Properties
Let us now examine the properties of the combination rule. It is commutative and
associative. The mass function defined by:
m
0
(
D
)=1and
∀
A
⊆
D, A
=
D, m
0
(
A
)=0
[7.29]
is the neutral element for the combination. This mass represents a completely uninfor-
mative source, which is unable to distinguish any element of
D
. In fact, this is what
our intuition tells us, that the mass function plays no part in the combination. The def-
inition of this mass function replaces the indifference principle used in probabilities
(equal distribution of the probabilities over all of the elements) and better represents
the absence of information.
is not idempotent. Consider again the previous example, but this time
with the following mass functions:
The law
⊕
C
1
C
2
C
3
m
1
0.7
0.2
0.1
m
2
0.7
0.2
0.1
Their non-normalized and normalized fusions lead us to:
C
1
C
2
C
3
∅
m
1
⊕
m
2
non-normalized
0.49
0.04
0.01
0.46
m
1
⊕
m
2
normalized
0.91
0.07
0.02
0.0
This example illustrates the non-idempotence of the combination rule. The
strongest values are reinforced and the smaller ones weakened. It is also important to
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