Digital Signal Processing Reference
In-Depth Information
fusion, i.e. when the modalities are uncorrelated, a critical issue is that
individual class-conditional probabilities, and the log-likelihood ratios as
well, usually results in values with different ranges, with different means and
variances. Thus prior to the fusion process, a common practice is to apply
normalization on resulting likelihoods, such as sigmoid normalization.
Another issue is varying reliability of each likelihood contributing to the
final decision. Thus commonly, a weighted sum of normalized likelihoods is
used:
where values are weighting coefficients to be determined. Most of the
decision fusion schemes existing in the literature [15, 17] vary actually in the
way they interpret Equation (6). In one extreme, there are techniques that try
to estimate these coefficients, which are ideally feature and class dependent.
Coefficients can be set to some fixed values using some a priori knowledge
or can be estimated adaptively via various methods such as noise estimation
or measuring the experimental or statistical dispersion of each decision [11].
The problem of this approach is that, estimation of the reliability parameters
itself is not in general very reliable and moreover unimodal misclassification
may occur even with high likelihood ratios. Erroneous decisions keep
contributing to the final decision likelihood, hence scarifying from correct
unimodal decisions. In the other extreme, there are techniques based on the
well-known
max
rule [15]. In regard to Equation (6), this strategy uses the
following rule to set the coefficients
When seen as a binary mechanism as above, the max rule may filter out most
of the erroneous contributions in the final decision. But the fact that
unimodal misclassification may occur even with high likelihood ratios is still
not taken into account. In the next subsection, we propose a decision scheme
that compromises these two extreme approaches.
