With this chapter, we first present a variety of decision level fusion rules and classifier selection approaches, and then show a case study of face recognition based on decision level fusion, and finally offer a summary of three levels of biometric fusion technologies. In a multi-biometric system, classifier selection techniques may be associated with the decision level fusion as follows: classifier selection is first carried out to select a number of classifiers from all classifier candidates. Then the selected classifiers make their own decisions and the decision level fusion rule is used to integrate the multiple decisions to produce the final decision. As a result, in this chapter, we also introduce classifier selection by showing a classifier selection approach based on correlation analysis. This chapter is organized as follows. Section 15.1 provides an introduction to decision level fusion. Section 15.2 presents several simple and popular decision level fusion rules such as the AND, OR, RANDOM, Voting rules, as well as the weighted majority decision rule. Section 15.3 introduces a classifier selection approach based on correlations between classifiers. Section 15.4 presents a case study of group decision-based face recognition. Finally, Section 15.5 offers some comments on three levels of biometric fusion.
Though the term ‘decision level fusion’ has appeared widely in the biometric literature, it is not used only in the field of biometrics. Indeed, as an information fusion strategy, decision level fusion also has been widely applied in a number of areas such as multisensor data fusion (Hall & Llinas, 1997), multispectral image fusion and geoscience data fusion (Jeon & Landgrebe, 1999; Fauvel, Chanussot, & Benediktsson, 2006). We would like to regard ‘decision level fusion’ as a term of information science rather than a term of biometrics. In some cases on multi-biometrics, the term ‘symbol level fusion’ (Tien, 2003; Gee & Abidi, 2000; Dop, 1999) is also used to represent decision level fusion. The decision level fusion strategy integrates biometric information in a simple and straightforward way in comparison with feature level fusion, which usually directly integrates different biometric traits at the feature level, and matching score level fusion which usually requires that before fusion the matching scores of different biometric subsystems be normalized. A system using the decision level fusion strategy integrates different biometric data at a later stage than the multi-biometric system using feature level fusion or matching score level fusion strategies. The multi-biometric system using the decision level fusion strategy can be described as follows: The system consists of a number of biometric subsystems each of which uses a biometric trait and makes the authentication decision independently. The decision level fusion strategy is then used to combine the decisions of the biometric subsystems to produce the final decision.
Various decision level fusion methods such as Boolean conjunctions, weighted decision methods, classical inference, Bayesian inference, and Dempster–Shafer method (Jain, Lin, Pankanti, & Bolle, 1997), voting (Zuev & Ivanon, 1996) have been proposed. Prabhakar and Jain (2002) combined classifier selection and decision level fusion techniques to perform fingerprint verification. Hong and Jain (1998) integrated faces and fingerprints at the decision level. Chatzis, Bors, and Pitas (1999) used fuzzy clustering algorithms to implement decision level fusion. Osadciw, Varshney and Veeramachaneni (2003) proposed a Bayesian framework to perform decision fusion based on multiple biometric sensors. In addition, modified KNN approach (Teoh, Samad, & Hussain, 2002), decision trees and logistic regression (Verlinde & Cholet, 1999) were also used to fuse multiple biometric traits at the decision level. More studies on decision level fusion such as fusion of iris and face, fusion of 3D data can be found in (Wang, Tan, & Jain, 2003; Gökberk & Akarun, 2006; Li, Zhao, Ao, & Lei, 2005; Gokberk, Salah, & Akarun, 2005; Freedman, 1994; Teoh, Samad, & Hussain, 2004; Niu, Han, Yang, & Tan, 2007). It should be noted that the theoretical framework described by Kittler, Hatef, Duin and Matas (1998) is able to derive a number of real rules for combining classifiers. Roli, Kittler, Fumera, and Muntoni (2002) classified the decision fusion strategies into two main classes: fixed and trained rules. Fusion strategies such as majority voting and the sum rule are recognized as fixed rules. These strategies might allow combination of different systems with similar performance to perform well. Some techniques such as weighted averaging and behavior knowledge space are examples of trained rules, which may allow combination of systems with different performance to improve authentication performance.