FUZZY FUSION OF BIOMETRIC INFORMATION

              In the previous chapter, different methodologies for rank level fusion were obtainable. These methods included plurality voting method, highest rank method, Borda count method; logistic weakening method and quality based rank fusion method for multimodal biometric system. Among those methods, the logistic weakening method constantly provides high Performance, however it still has some drawbacks. The results obtained through this method can be varied considerably for different datasets due to their miscellaneous qualities. Logistic deterioration method for a multimodal dataset with the same image quality will produce results similar to Borda count method, as the assigned weights to different biometric matchers’ outputs will be the same.

MARKOV CHAIN

A Markov chain is named for the Russian mathematician Andrei Andreyevich Markov. It is a mathematical model that can be thought of a being in exactly one of a number of states at any time (Markov, 1906). A Markov chain has a set of states, S = {s₁; s₂;:::; s_r}. The process starts in one of these states and moves successively from one state to another (Kemeny, Snell, & Thompson, 1974). Each move is referred to as a step. If the chain is currently in state s_i, then it can move to state s_j with a probability p_ij. This probability is preset at the beginning of the process and does not depend on how the state was reached. The probability p_ij is referred to as transition probabilities. The process can remain in the same state with probability pii. The starting state is given by an initial probability distribution (Kemeny, Snell, & Thompson, 1974).

Markov chains are applied in a number of ways to many different fields. They can be either used as mathematical model equivalent to some random physical process, or to reproduce an abstract theoretical thought. Application areas of Markov chain include physics (thermodynamics, statistical mechanics), chemistry (enzyme activity), the expansion of copolymers, statistics (statistical testing, Bayesian inference, etc.), Internet applications (page rank, analyzing Web navigation behavior of users, etc.), economics, finance, information sciences (Hidden Markov Model for pattern acknowledgment, Viterbi algorithm for error correction), bioinformatics, social sciences education, stock market predictions, music, and sports (Grin stead & Snell, 1997).

In 2011, Monwar and Gavril ova (2011) utilized Markov chain as a method for biometric rank combination. This approach brought a new dimension to the current ways of biometric rank aggregation and can be effectively used by the homeland and border security forces and by other cleverness services.

They considered the biometric rank aggregation similar to a voting mechanism. In the multimodal biometric rank fusion process, the classifiers are considered as voters. So, if there are three biometric traits used in a multimodal biometric system, the number of voters in the system would be three. Those three voters or classifiers manufacture three ranking list based on the comparison or distance scores of test and template biometric data. The final process is to combine the ranking lists obtained from three classifiers or voters to make a consensus ranking lists to find out the preferred identity or alternative from the system.

The same two datasets which were used in the experiments involving Markov chain-based rank fusion are used. Here, comparison has been made on fuzzy fusion approach with unimodal matchers, with the rank fusion approaches and with Match score and decision fusion approaches which is shown in through Figures 6-11.

The fuzzy logic based fusion approach for multimodal biometric system has been described. It is a powerful intelligent tool used in many cognitive and decision-making systems. After discussing the basics of fuzzy logic, the fuzzy fusion mechanism in the context of a multimodal biometric system has been illustrated. A brief discussion on the research conducted for fuzzy logic based fusion in different application domains has also been presented. The system overview and the choice of fuzzy rules to govern the system have been presented. The biggest advantage of the system is that instead of binary Yes/No decision, the probability of a match and confidence level can now be obtained.