Image Processing Reference
in image processing [MAI 02], the most frequent of which are the median filter, the
sigma filter, or morphological filtering. Finally, more elaborate techniques use relax-
ation, such as Markov fields, which operate either on the level of the measure (this is
referred to as restoration), or on the level of the classification, as we will see later on.
If we work on the level of primitives (segments, contours, areas) or on the level of
objects or structures in the scene, the local spatial information is implicitly accounted
for in the representation. If the detection of these elements or their localization are
not precise (for example, because of the imperfection of the registration), it is often
advisable to explicitly include this spatial imprecision in the representation, before the
fusion. Fuzzy dilation is an operation well suited for this purpose [BLO 95, BLO 96,
BUS 00]. This allows the conflict to be reduced to the moment when the fusion takes
place and hence to choose a conjunctive combination mode simply and without risk.
In a less local fashion, the spatial relations between primitives constitute impor-
tant information regarding the structure of the scene [BLO 97, BLO 99a, BLO 99b,
BLO 99c, BLO 00b] and they can taken advantage of in fusion, as a source of addi-
tional information [BLO 00a, BLO 00c, GER 99]. In this case, the spatial context
( x ) of an element x is a set of primitives or objects whose spatial relations with
respect to x are known.
9.2. The decision level
The inclusion of spatial information on the decision level is the easiest. The most
common method consists of first establishing a rejection rule (depending on the crisp-
ness and the discriminating nature of the decision) then reclassifying the rejected
elements according to their spatial context. For example, reclassification can be per-
formed according to the following rule (absolute majority):
C i if y
C i ≥ |V|
( x ) ,y
which expresses that at least half of the elements of the neighborhood have to be
in C i in order to put x in C i . This rule does not always allow x to be assigned to a
class. A less severe rule only considers the most represented class in the neighborhood
C i =max
C k .
( x ) ,y
( x ) ,y
These rules apply regardless of the level of representation of the elements consid-
An example of fuzzy classification can be found in [BOU 92], but this is a general
method, which can be applied in a similar fashion to other theories.