Definitions - Information Fusion in Signal and Image Processing - page 8

Symbolic processes include formal calculation on propositions (for example,
logic-type methods or grammars, more details of which can be found in [BLO 01]),
possibly taking into account numerical knowledge. Structural methods, such as graph-
based methods, which are widely used in structural shape recognition (particularly
for fusion), can be included in the same category.
We use the phrase hybrid process for methods where prior knowledge is used in
a symbolic way to control the numerical processes, for example, by declaring propo-
sitional rules that suggest, enable or on the contrary prohibit certain numerical opera-
tions. Typically, a proposition that defines in which cases two sources are independent
can be used to choose how probabilities are combined.
1.4.3. Representations
As shown in the two previous sections, representations and their types can play
very different roles. Numerical representations can be used for intrinsically numerical
data but also for evaluating and quantizing symbolic data. Numerical representations
in information fusion are often used for quantifying the imprecision, uncertainty or
unreliability of the information (this information can be either numerical or symbolic
in nature) and therefore to represent information on the data we wish to combine
rather than the data itself. These representations are discussed in greater detail in the
chapters on numerical fusion methods. Numerical representations are also often used
for degrees of belief related to numerical or symbolic knowledge and for degrees of
consistency or inconsistency (or conflict) between the elements of information (the
most common case is probably the fusion of databases or regulations). Let us note
that the same numerical formalism can be used to represent different types of data or
knowledge [BLO 96]: the most obvious example is the use of probabilities to represent
data as different as frequencies or subjective degrees of belief [COX 46].
Symbolic representations can be used in logical systems, or rule-based systems,
but also as a priori knowledge or contextual or generic knowledge used to guide a
numerical process, as a structural medium, for example, in image fusion, and of course
as semantics attached to the objects handled.
In many examples, a strong duality can be observed between the roles of numerical
and symbolic representations, which can be used when fusing heterogenous sources.
Examples will be given in different fields in the following chapters.
1.5. Fusion systems
Fusion generally is not an easy task. If we simplify, it can be divided into sev-
eral tasks. We will briefly describe them here because they will serve as a guide to
describing theoretical tools in the following chapters. Let us consider a general fusion
problem with m sources S 1 ,S 2 ,...,S m , and where the objective is to make a decision