Image Processing Reference
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between two classes. Here are a few examples of situations in which fusion based on
belief function theory can be used:
- in extreme cases (which can be considered ideal) where we know all of the infor-
mation regarding the problem at hand;
- when a source only provides information on certain classes: for example, certain
PET 1 images provide information on the limits of the brain but not the head;
- when a source is not capable of telling the difference between two hypotheses:
belief function theory can then be used to consider the disjunction of these two classes,
without adding arbitrary information that would force their separation;
- when attempting to model partial volume effects, typically by representing a
pixel or a voxel belonging to several classes;
- when attempting to represent a source's overall reliability: this can be done by
assigning a non-zero mass to D ;
- in cases where a source's reliability depends on the classes (for example, the
anatomical information provided by functional brain images is not very reliable,
whereas MRI images are very reliable for anatomical classes);
- in cases where we want to add a priori information: even if it is not easy to
use probabilities to represent this information, it can still be added if they lead to a
way of choosing focal elements (particularly hypothesis disjunctions), of defining or
modifying mass functions.
7.3. Estimation of mass functions
Estimation of mass functions is a difficult problem because there is no universal
solution. The difficulty gets worse here if we want to assign masses to the compos-
ite hypotheses [GAR 86, LOW 91]. In image processing, for example, they can be
constructed on three levels: on the highest level (which is often abstract and sym-
bolic), the representation of information is used in a fashion similar to what is done
in artificial intelligence and masses are assigned to propositions, and often provided
by experts [BAL 92, GOR 85, NEA 92]. Most of the time, this information is not
derived directly from data measurements and the corresponding methods are there-
fore not specific to signal and image processing. On an intermediate level, masses are
calculated based on attributes and can rely, for example, on image geometric models
[AND 88, CHE 93, CLE 91, CUC 92]. This level is well-suited for model-based shape
recognition problems, but it is difficult to use for fusion problems on complex struc-
tures without a model. On a low level (the pixel in image processing), many methods
are possible and most rely on statistical shape recognition methods.
1. Positron Emission Tomography, used in particular for functional brain imaging.
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