Image Processing Reference
9.3. The combination level
The inclusion of spatial information on the combination is less common and more
In probabilistic fusion, Markov fields offer a natural framework for this purpose.
In the expression of Bayes' rule, the Markovian hypothesis is involved in the a pri-
ori probability. This probability is combined with the probabilities conditional to the
classes by way of a product. This comment leads us to consider that spatial informa-
tion, in this model, constitutes a source of data like any other.
This is the most common approach and it has been applied on several levels of
representation. On the local, pixel level, many examples can be found in other works
(for example, [AUR 97b, DES 96]). On a more structural level, Markov fields are
defined on graphs that are more general than the pixel graphs (the nodes are primi-
tives or even objects) and examples can be found for road detection in SAR images
[TUP 98], for the segmentation of MRI images of the brain [GER 95], for recognizing
structures of the cerebral cortex [MAN 95, MAN 96], for the interpretation of aerial
images [MOI 95], etc.
With other theories, it would also be possible to develop similar approaches, with
spatial information still considered as an additional source of data.
This is, for example, the case of spatial relations mentioned above considered as
an additional source of information: recognizing an object can be the result of the
fusion of information regarding that object and of information regarding the relations
it has to have with respect to other objects. The fuzzy set framework allows both the
representation and the fusion of such information [BLO 00c].
We should mention another example: in [HEG 98], a mass function is defined for
representing the spatial context and combined with mass functions representing the
information extracted from the images according to Dempster's rule. However, there
are still few studies in this field, which certainly deserves to be developed further.
9.4. Application examples
9.4.1. The combination level: multi-source Markovian classification
Let us consider the same example of the fusion of MRI images of the brain from
Chapters 7 and 8, with the objective of segmenting the healthy brain, the pathology
and the ventricles, this time using a Markovian approach. This method was developed
in [AUR 95, AUR 97a, AUR 97b].