COMPLEX NUMBERS AS A COMPACT WAY TO REPRESENT SCORES AND THEIR RELIABILITY IN RECOGNITION BY MULTI-BIOMETRIC FUSION

Multi-biometric systems are a powerful solution to deal with limitations of single classifiers, therefore improving the final recognition accuracy. The sub-systems composing the final architecture often return supplementary indices of input quality and/or of response reliability, which further qualify each recognition score. These indices can enter different information fusion policies. First, they can be used as weights for the fusion of the corresponding scores, in such a way that less trustworthy responses have a lower influence. Alternatively, they can be used to drive the selection of a subset of systems actually enabled for each fusion operation. The present work discusses their appropriate combination with respective scores, to obtain single values which are easier to handle and compare. It is worth underlining the different nature of quality and reliability measures. The quality estimation of input samples requires a complex analysis of environmental conditions, including capture sensors, besides computations over acquired data. Reliability of a system estimates its ability to return a correct response. As an alternative to combination, some solutions rather estimate the joint distributions of conditional probabilities of the scores from the single subsystems. These solutions require training through a huge number of samples. Furthermore, they assume stable score distributions. Our unified representation of the recognition score and of the corresponding quality/reliability value into a single complex number provides simplification and speed up of fusion of multi-classifier results. It also allows to devise procedures to readily compare the performance of different modules in a multi-biometric system, given that there is no natural ordering of these pairs of values of different nature. Moreover our method achieves performance comparable to top performing schemes, yet does not require a prior estimation of (joint) score distributions. As a matter of fact, though representing an upper bound to the obtainable performance, Likelihood ratio has the limit to require an accurate estimation of score distributions, while our approach relies on the reliability of each single response. This feature is very interesting when the set of relevant subjects may present significant variations over time.