Image Processing Reference
In-Depth Information
a class. This point of view amounts to considering that fusion is an estimation prob-
lem and is a way of using combination operators other than the product. In particular,
the mean, weighted mean and consensus methods are often used [COO 88, COO 91,
FRE 85]. Robust estimators can also be used, in order to reduce or eliminate the influ-
ence of outliers. Finally, methods provided by regionalized variable theory [MAT 70],
such as kriging or universal kriging, can also be used in this context.
6.6. Decision
The last step involves the decision, for example, choosing which class a point
belongs to. This binary decision can be paired up with a measurement of the quality
of this decision, which can possibly lead to its rejection. The most commonly used
rule in probabilistic and Bayesian decision is the
a posteriori
maximum:
if
p
x
I
1
,...,I
l
=max
p
x
I
1
,...,I
l
,
1
n
,
x
∈
C
i
∈
C
i
|
∈
C
k
|
≤
k
≤
but many other criteria have been developed by probabilists and statisticians, in order
for them to find the best way to adapt to the user and to the context of his decision:
maximum likelihood, maximum entropy, maximum marginal probability, maximum
expected value, minimum risk, etc. However, the large diversity of these criteria leaves
the user hard-pressed to justify a choice and brings him further away from the objec-
tivity initially sought by these methods.
6.7. Other methods in detection
The field of detection by multi-sensor fusion has been studied at length and has led
to several methods. A distinction is made between centralized detection, in which mea-
surements made by different sensors are considered as a vector on which the decision
is made, and decentralized detection, in which each sensor yields a binary response
(detection or not), and these answers are then combined by a fusion operator.
In the first case [VAR 97], the decision rules often rely on average risk, maximum
profit, minimum risk, all taken from the Bayesian approach, but also on criteria such as
the Neyman-Pearson criterion, which consists of maximizing the detection probability
for a given probability of having a false alarm. This implicitly assumes that the false
alarm is considered as the worst error, which is not always the case depending on the
applications (for example, in the case of humanitarian demining, non-detection is the
worst error).
In the second case, if we have
l
sensors, each one producing a binary response,
the fusion operator is considered as a logical function of these
l
responses (which
constitute the operator's input). The number of possible operators is very high, (2
2
l
),
Search WWH ::
Custom Search