3D Face --> Combining Systems

In this section we describe how the analysis methods discussed in section 4 are used to combine multiple face recognition systems. Firstly, we need to address the problem of prioritising surface space dimensions. Because the average magnitude and deviation of face-key vectors from a range of systems are likely to differ by some orders of magnitude, certain dimensions will have a greater influence than others will, even if the discriminating abilities are evenly matched. To compensate for this effect, we normalize moments by dividing each face-key element by its within-class standard deviation (calculated from test set A face-keys). However, in normalising these dimensions we have also removed any prioritisation, such that all surface space components are considered equal. Although not a problem when applied to a single surface space, when combining multiple dimensions we would ideally wish to give greater precedence to the more reliable components. Otherwise the situation is likely to arise when a large number of less discriminating dimensions begin to outweigh the fewer more discriminating dimensions, diminishing their influence on the verification operation and hence increasing error rates.

In section 4 we showed how FLD could be used to measure the discriminating ability of a single dimension from any given face space. We now apply this discriminant value dn as weighting for each surface space dimension n, prioritising those dimensions with the highest discriminating ability.
With this weighting scheme applied to all face-keys, we now require some criterion to decide which dimensions to combine. It is not enough to rely purely on the discriminant value itself, as this only provides an indication of the discriminating ability of that dimension alone, without any indication of whether the inclusion of this dimension would benefit the existing set of dimensions. If an existing surface space already provides a certain amount of feature specific discrimination, it would be of little
benefit (or could even be detrimental) if we were to introduce an additional dimension describing a feature already present within the existing set.

Previous investigations have used FLD, applied to a combined subspace in order to predict effectiveness when used for recognition. Additional dimensions are introduced if they result in an increase in discriminant value. This method has been shown to produce face space combinations achieving significantly lower error rates than individual two-dimensional systems, although Heseltine et al do note that an EER-based criterion is likely to produce a better combination, at the expense of greatly increased training time. However, with a more efficient program and greater computational resources, we now take that approach: the criterion required for introduction of a new dimension to an existing surface space is a resultant decrease in EER (computed using test set A).


Combined surface space = first dimension of current optimum system
Compute EER of combined surface space
For each surface representation system:
For each dimension of surface space:
Concatenate dimension onto combined surface space
Compute EER of combined surface space
If EER has not decreased:
Remove dimension from combined surface space
Save combined surface space ready for evaluation


Figure 5: Fishersurface combination algorithm