Image Processing Reference
In-Depth Information
Choosing and evaluating methods is as crucial as it is difficult. Again, there is no
general solution for choosing methods that are adapted to the different types of infor-
mation and knowledge handled, or to the applications we may have in mind. Evaluat-
ing methods can be more or less easy depending on whether the truth is accessible or
not. Attempts to compare numerical fusion methods, when applied to the same prob-
lems, have given contradicting results and therefore have failed. We think the main
reason for this is that each problem is expressed more easily in one theory than in
another, so solving them with the wrong tools requires these techniques to become
distorted, and does not make much sense.
Finally, in the case of image processing applications, and also for certain appli-
cations in robotics, the introduction of spatial information in fusion is an important
point, for which the set of existing methods could benefit from further development.
Particularly, the recent successes achieved by taking into account structural informa-
tion shows the advantage of combining spatial information from different levels.
We have noticed in the previous chapters that each approach is adapted to a lim-
ited set of imperfections in the information to fuse. It is rare for all of the imperfec-
tions to be modeled simultaneously and in a simple way in a unique theory. Thus, a
field of investigation that remains open involves the fusion of methods or the com-
bined use of different complementary formalisms. These studies on method com-
bination are promising, because their goal is to use the advantages of the different
theories in order to make them cooperate with each other. This combination can
rely on relations that exist between the different methods. For example, a probabil-
ity can be interpreted as a particular mass function, a belief function whose focal
elements are such that each one is included in the next can be interpreted as a pos-
sibility distribution, a possibility distribution can be interpreted as confidence inter-
vals or as a family of probabilities (see, for example, [DUB 99] for details on the
connections between possibilities and probabilities), etc. Thus, studies have already
been conducted to combine the imprecision represented by fuzzy sets with probabilis-
tic uncertainty (for example, [CAI 93, PIE 94, SAL 95] in a Markovian classification
method where the classes are fuzzy), to combine Markov fields with belief functions
[BEN 97, HEG 98], or to work with belief functions whose focal elements are fuzzy
[SME 81, YAG 82, YEN 90, ZAD 79].
12.3. Bibliography
[BEN 97] B ENDJEBBOUR A., P IECZYNSKI W., “Segmentation d'images multisenseur par
fusion évidentielle dans un contexte markovien”, Traitement du Signal , vol. 14, no. 5,
p. 453-464, 1997.
[CAI 93] C AILLOL H., H ILLION A., P IECZYNSKI W., “Fuzzy Random Fields and Unsuper-
vised Image Segmentation”, IEEE Trans. on Geoscience and Remote Sensing , vol. 31, no. 4,
p. 801-810, 1993.
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