A novel hybrid score level and decision level fusion scheme for cancelable multi-biometric verification

Abstract

In spite of the benefits of biometric-based authentication systems, there are few concerns raised because of the sensitivity of biometric data to outliers, low performance caused due to intra-class variations, and privacy invasion caused by information leakage. To address these issues, we propose a hybrid fusion framework where only the protected modalities are combined to fulfill the requirement of secrecy and performance improvement. This paper presents a method to integrate cancelable modalities utilizing Mean-Closure Weighting (MCW) score level and Dempster-Shafer (DS) theory based decision level fusion for iris and fingerprint to mitigate the limitations in the individual score or decision fusion mechanisms. The proposed hybrid fusion scheme incorporates the similarity scores from different matchers corresponding to each protected modality. The individual scores obtained from different matchers for each modality are combined using MCW score fusion method. The MCW technique achieves the optimal weight for each matcher involved in the score computation. Further, DS theory is applied to the induced scores to output the final decision. The rigorous experimental evaluations on three virtual databases indicate that the proposed hybrid fusion framework outperforms over the component level or individual fusion methods (score level and decision level fusion). As a result, we achieve (48%, 66%), (72%, 86%) and (49%, 38%) of performance improvement over unimodal cancelable iris and unimodal cancelable fingerprint verification systems for Virtual_A, Virtual_B, and Virtual_C databases, respectively. Also, the proposed method is robust enough to the variability of scores and outliers satisfying the requirement of secure authentication.

Appendices

Appendix A: Preliminaries on Dempster-Shafer theory of evidence

In Bayesian theory, the probabilities are assigned to each individual proposition from a set of mutually exclusive propositions. Alternatively, DS theory assigns masses to each combination of events. Unlike DS theory, the probability theory is unable to discriminate between ignorance and uncertainty due to sketchy information. Fundamentally, the Bayesian theory departs DS theory in the aspect of handling ignorance. DS theory does not assign belief to ignorance or to a falsified hypothesis. The mass is assigned particularly to the subsets for which we seek to assign belief. This implies neither belief nor disbelief for the evidence to a certain value. Hence we have utilized DS theory in our work.

Consider, 𝜃 be a finite set of all possible hypotheses known as a frame of discernment. The power set 2^𝜃 contains all subsets of 𝜃 including a null set (ϕ) and itself. Each subset in the power set is referred as a focal element and assigned a value in between [0, 1] on the basis of their evidence. A value of 1 corresponds to total belief and 0 for no belief. In general, the assigned value is named as basic belief assignment (BBA). In DS theory [33], BBA is assigned to each subset i.e. hypothesis also known as the mass of the individual proposition,

$$ m : 2^{\theta}\rightarrow \left[ 0,1 \right]. $$

(12)

If $\theta =\left \{ A,B \right \} \ \text {then} \ 2^{\theta }=\left \{\varnothing ,A,B,\theta \right \}$. The mass function fulfills the following criteria:

$$ \sum\limits_{a_{i}\in 2^{\theta}}m\left( A_{i} \right)= 1 , \ \ \ m\left( \varnothing \right)= 0 $$

(13)

where $\varnothing$ represents the empty set. The measure of belief is defined by the function bel : 2^𝜃 → [0, 1],

$$ bel\left( A \right)=\sum\limits_{B\subseteq A, B\neq \varnothing } m\left( B \right). $$

(14)

The bel can also be formally defined as:

$$ bel_{Y,t}^{\theta,\Re}\left[ E_{Y,t} \right]\left( w_{0}\in A \right)=x $$

(15)

This means the degree of belief x for the classifier Y at time t when w₀ ∈ A. Here, E_Y,t represents the evidential information known to classifier Y at time t. For ease in representation, we use bel(A) instead of $bel_{Y,t}^{\theta ,\Re }\left [ E_{Y,t} \right ]\left (w_{0}\in A \right )$. Next, plausibility (pl) is measured as:

$$ pl:2^{\theta} \rightarrow \left[ 0,1 \right], \ \ \ \ pl\left( A \right)= 1-bel(\neg A)={\sum}_{B\cap A \neq \varnothing } m\left( B \right) $$

(16)

If 𝜃 defines the set of all possible hypotheses, then the level of uncertainty is denoted by m (𝜃). In a hypothesis, beliefs and disbeliefs may not sum to 1 and may attain 0 value. A value of 0 signifies no evidence present for the hypothesis. The DS theory based aggregation involves the following steps:

• The measure of belief is evaluated based on the facts from the different sources of information. As compared to Bayesian theory, the masses are not distributed among classes.

• Dempster rule of combination is applied to aggregate belief measure obtained from the available information and facts.

For different sources, (1, 2,⋯ ,N), Dempster’s rule of combination is described in (16):

$$ m_{1,2, \cdots, N}\left( A \right)=\frac{{\sum}_{B_{i}\cap {\cdots} \cap B_{k}=A} m_{1}\left( B_{i} \right) \cdot {\dots} \cdot m_{N}\left( B_{k} \right)}{1-K} $$

(17)

where A,B₁,…,B_N ⊆ 𝜃, and

$$ K= \sum\limits_{B_{i} \cap {\dots} \cap B_{k}=\varnothing} m_{1}\left( B_{i} \right) \cdot m_{2} \left( B_{j} \right) {\dots} m_{N} \left( B_{k} \right) $$

(18)

where K denotes the conflict present between evidences; 1-K is the normalization factor.

A.1 Updation of masses

In a majority of the scenarios, mass updating is required if any new evidence or belief is encountered. Suppose, E ⊂ 𝜃 and E_d be the evidence not present in E. If this new evidence provides the exact value of E_d, then bel(A) is updated based on the following condition rule:

$$ bel[E_{d}](A)=bel(A \cup \neg E)- bel(\neg E) $$

(19)

After the computation of the masses, the classification is performed onto the training set. One of the aggregation rules is applied to evaluate total conflicting mass. Next, the winner-take-all assignment is utilized to compute A(k), which is defined in (19):

$$ m\left( A_{k} \right)= \max_{A_{j}} m\left( A_{j} \right), \ \ \ j = 1,{\dots} M + 1 $$

(20)

where M + 1 represents is the total number of classes including the class of rejection and A_M+ 1 = 𝜃.