Probabilistic and Statistical Methods - Information Fusion in Signal and Image Processing - page 89

estimation are quite close to those of centralized estimation. The advantage of this
approach, in this context, is therefore quite obvious.
6.10. Discussion
The widespread progress of probabilistic methods, particularly of Bayesian meth-
ods, is the result of the knowledge acquired through numerous experiments that helped
guide the modeling and learning phases, rather than of Cox's justification [COX 46]
(see Appendix A).
The major advantage of probabilistic methods comes from the fact that they rely
on a solid mathematical background, and have been the subject of many studies. As
a result, they offer a wide selection of tools that can be used both for modeling (for
example, using parametric laws with well-studied properties) and model learning (for
parametric or non-parametric laws) (see, for example, [CHA 95, LEE 87, LUO 89]).
They also suggest usage rules that are either theoretical (bounds, asymptotic values)
or heuristic (hypothesis tests, validity criteria, confidence tables). Finally, probabilis-
tic modeling, supported by the frequentist interpretation, which is widespread in the
world of physics and signal processing, is a concept currently shared universally, serv-
ing as basis for comparison with other models.
Another advantage of probabilistic and statistical methods, this time from the com-
bination perspective, is again that they rely on solid mathematical background and can
be used for updating complex knowledge networks [PEA 86a, PEA 86b]. They allow
the introduction of information that can easily be expressed in probability form, such
as spatial context in the framework of Markov fields (see Chapter 9) or information
quality expressed as the probability for a measurement to be reliable [GRA 00].
However, and despite their solid mathematical background, these methods are also
criticized and suffer several drawbacks. We will discuss them all in this section, but
we should point out that some of them are disputed by unconditional probabilities.
First of all, even though they lead to a good representation of the uncertain nature
of information, they cannot easily be used to represent its imprecision and often cause
confusion between these two concepts. Furthermore, during the learning phase, they
require that very stringent constraints are met by the measurements (imposed by the
basic probability axioms) and by the set of considered classes (comprehensiveness).
The constraints can make learning very difficult (how is it possible to characterize ar-
eas that are not wheat fields in aerial imaging 4 ?), or, if the problem to solve is complex,
4. This problem is an example of the more general problem encountered in shape classification
and recognition: generally, the complement of a class is not a class.