International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
referred to the related problems and insufficiency of mentioned
methods as the formal methods of decision fusion. It was also
showed that it is the main problem in voting methods that they
use only the local classification results for local winner class in
only one defined pixel. This causes an intensive increasing in
commission and omission errors of decision fusion results for
correlated data, and also for class correlated classifiers errors.
Also, the rank based methods, which use the local classification
results in the order of the rank of all classes in a defined pixel,
the volumes of transferred data and data, which should be
processed, will be intensively increased. Improvements in
performances for voting and rank based methods are related to
the degree of error diversity among combined classifiers.
Unfortunately, in classification applications, it may be difficult
to design an ensemble to exhibit a high degree of error
diversity. The Bayesian method does not consider uncertainty
and may have error and complexity in the posterior
probabilities measurements. We explain that the Dempster-
Shafer method, which is an extension of Bayesian inference,
overcomes some of the difficulties. This method can be used
without prior probability distributions and is able to deal with
uncertainty. The main and common problem in suggested
fusion methods is the ignorance of nature of local data
classifiers and similarity of classes. Also, these methods use
only the local classification results in one point (pixel), without
attention on result distribution for all classes and other different
pixels. For solving these problems and accessing desirable
results, by using the mathematical features and distribution of
multi-sensor local classifications results, we introduced
commission and omission errors functions. Formulation the
similarity and correlation of local classification results and
errors for different classes and need to hard decision, can be
considered as the main features of these new tools. Finally, by
using the common features of the mentioned tools, we
presented the dual measure decision fusion (DMDF) method.
The assumption of uncorrelated errors is not necessary for
DMDF because an optimal class selector always selects the
most appropriate class for each pixel. In previous section, we
deployed these methods for fusion of three local classifier
results. After comparing the results, we showed that the DMDF,
which uses the special features of multi-sensor local decisions,
has lower commission and omission errors and higher reliability
than other methods. Of course, the DMDF method is a flexible
method that can use for any decision fusion problem and any
application. Although we obtained desirable results through
developing the DMDF, extraction the new measures and
distribution, and applying of some tools such as: fuzzy
measures and methods, and neural network for accession the
better reliability are considered as the next interest research of
the writer.
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