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Top1. Introduction
Multimodal biometrics (MMB) has gained popularity among researchers as they provide more information for processing purpose of an individual rather than a unimodal biometric system. Secured MMB systems (MMBS) should be capable of authenticating a person's identity based on his biometric traits like faces (Bourlai, Kittler, & Messer, 2009; Geng & Jiang, 2013), fingerprints (Mehtre, 1993; Hiew, Teoh, & Yin, 2010), iris (Wildes et al., 1996)etc. In MMBS, at least two different biometrics need to be fused. Levels of fusion (Ross & Govindarajan, September 2004) can be raw level, feature level, match score level or decision level. Fusion at feature level, though difficult and understudied (Ross & Govindarajan, March 2005), possesses more importance than the other levels, because extracted feature set from raw data holds most significant and rich information. Several evaluation protocols (P. Grother & Bone, 2003; A. K. Jain & Prabhakar, January, 2004; Blackburn, 2004), on closed test set identification, have been designed for measuring the performance of different existing algorithms. In open test identification, the challenge is to reject the imposters. Selection of proper intra-class threshold is a way of accepting genuine users or rejecting fraudulent attempts as imposters. However, selection mechanism of proper threshold is an open research area as it is hurdled by different levels of security.
In several articles (Manseld & Wayman, 2002), Equal Error Rate (EER), the point where False Acceptance Rate (FAR) and False Rejection Rate (FRR) intersects, in a Receiver Operating Characteristics (ROC) curve, had been selected as decision threshold. Martin et al. (A. Martin, 1997) proposed the use of detection error trade-off (DET) curve, a non-linear transformation of ROC curve, as a threshold selection tool. In principle, both curves for threshold determination is useful, provided the threshold value is computed over large numbers of test images and hence is computationally expensive.
To design MMBS, ROC curve based method is not a stable solution due to the following reasons. (a) A good estimate of FAR cannot be determined as it is impossible to include even a single representative of all possible imposter instances. (b) In reality, a system can have extremely few genuine accesses and also relatively few imposter accesses because there exist infinitely many imposters in the universal set. (c)The common practice is to use a global threshold for a system rather than user specific version of ROC.
In MMB the submitted query image, Q, can be categorized to the following types. (a) Q is not a valid MMB image under consideration (P). For example, if the MMB dataset consists of face and fingerprint biometrics, the submitted Q could be a non biometric image, like an image of a car or an animal. (b) Q is mimicking the original P. For example, consider a verification system that authenticates a user by inputting his face image and fingerprints. Now, Mr. Y maliciously could place a minutely designed 3D mask of Mr. X, in front of camera and Mr. X's false fingerprint impression on the input sensor and claim himself to be Mr. X, in order to break the security of the system. (c) Q is a valid P, but Q is an outlier of the P training set. That is, no instance of Q exists in the P training dataset. (d) At least one instance of Q does belong to P training dataset. Note that, cases (a), (b) and (c) do fall under fraudulent attempts and a robust and secured MMBS should be capable of rejecting such deceiving attempts. However, in these three cases, no sample instance of Q is present in the P datasets and hence it is virtually impossible for the system to generate a good (very low) estimate of FAR.