7.3.1 Sample Selection

In this step, a distinct sample has been chosen for each subject for a biometric trait which gives high variance in scores compared to other samples for that biometric trait of that subject. Let , the r^th sample of the p^th subject for a biometric trait B, gives the maximum variance among all samples of the p^th subject for the biometric B. To select , first, scores of the i^th sample () of the p^th subject with all other samples ( and j = 1, 2, ... , Q) of the p^th subject are calculated for the biometric trait B and the variance v_p,i(B) of the scores is computed for the i^th sample. The scores for the i^th sample with all other samples for the p^th subject is represented in Eq. (7.4) and the score variance for the i^th sample of the p^th subject is calculated in Eq. (7.5).

(7.4)

(7.5)

In Eq. (7.4), S_p,i(B) denotes the score vector of length Q − 1 and denotes the score between the i and j samples of the p subject for B. In Eq. (7.5), µ_p,i(B) represents the mean of all scores for the i^th sample of the p^th subject for biometric trait B and calculated using Eq. (7.6).

(7.6)

The variance for the all samples () of the p^th subject is calculated using Eq. (7.4), (7.5) and (7.6) and a variance vector v_p(B) is created for the p^th subject (see Eq. (7.7)).

(7.7)

The maximum variance from v_p(B) is determined and the corresponding sample are selected as a distinct sample of the p^th subject for the biometric trait B. Let v_p,r(B) be the maximum variance in V_p(B). The r sample (B_r ) is selected as a distinct sample for the p subject for B and represented as . In this way, the distinct samples () are selected for all P subjects of biometric trait B.

7.3.2 Subject Selection

Now, there are all subjects with one distinct sample () for a biometric trait. In this step, M subjects will be selected as reference subjects from these subjects which yield the high diversity in scores with respect to other subjects. In other words, are to be selected as reference subjects which give top M variances among all P subjects. It may be noted that a reference subject contains single biometric template from each trait. To choose the reference subjects, the same maximum variation finding strategy is followed as in sample selection. Here, the main difference is that the variation among all subjects are computed rather than all samples of a subject. First, a score vector S_p,r(B) is calculated for the p^th subject (see Eq. (7.8)) with all other subjects for a biometric trait B and the score variance is computed for the p^th subject in Eq. (7.9).

(7.8)

(7.9)

In Eq. (7.8), r^p and r^q are the selected samples for the p^th and q^th subject, respectively and is the score between the selected samples of the p^th and q^th subjects for the biometric trait B. The length of the score vector S_p,r (B) is P − 1. In Eq. (7.9), µ_p(B) is the mean of all scores between the p^th subject and all other subjects for the biometric trait B. The value of µ_p(B) is calculated using Eq. (7.10).

(7.10)

A variance vector of all subjects is calculated for the biometric trait B using Eq. (7.9) and the vector is represented with v(B) (see Eq. (7.11)).

(7.11)

The top M variances can be found from v(B) and M subjects are selected corresponding to the top variances as a reference subjects for each biometric trait. Let (m = 1, 2, . . . , M ) be the subject with top m^th variances. are selected as reference subjects for the biometric trait B and represent as R¹(B), R²(B), . . . , R^M (B). The reference subjects contain single template for each biometric trait. In this way, reference subjects can be selected for all other biometric traits. The extracted features of three biometric traits (B1, B2 and B3) of reference subjects are defined in Eq. (7.12). The feature vector of the m^th (m = 1, 2, . . . , M ) reference subject for biometric trait B is represented in Eq. (7.13). In Eq. (7.13), K_B and L_B denote the number of feature vectors extracted from the biometric trait B and the length of a feature vector, respectively.

(7.12)

(7.13)

7.5.1 Score Normalization

Several score normalization techniques (min-max, z-score, tanh, sigmoid, reduction of high-scores effect (RHE), etc.) exist in literature [15, 33, 12, 31]. Table 7.2 shows the effectiveness of the different score normalization methods with respect to robustness, scalability, efficiency and ease of use. From Table 7.2, it can be seen that RHE method [12] is more robust and efficient among all other normalization techniques. Hence, RHE normalization technique has been applied in this work. All scores of each biometric trait are normalized using

Table 7.2: Characteristics of the different score normalization methods

Eq. (7.16).

(7.16)

I_n E_q. (_7.16), is the normalized score of for the biometric B. S(B) denotes the distribution of all scores and S^∗(B) denotes the genuine score distribution [12] for the biometric B.

7.5.2 Score Fusion

The normalized scores are used to calculate the multimodal score for a sample. There exist several score fusion methods (maximum rule, minimum rule, sum rule, product rule, weighted sum rule, likelihood ratio, SVM and etc.) [15, 12, 24, 30, 31, 29]. The characteristics of the different fusion methods are shown in Table 7.3. From Table 7.3, it can be seen that the SVM based score fusion is the most efficient with respect to the different parameters like accuracy, robustness and scalability. Hence, SVM classifier is preferable to classify the genuine and imposter subjects using the normalized scores [25, 13, 9, 26, 12, 32]. In this work, SVM classifier [19, 22] is used to calculate the multimodal score because SVM-based classification performs better for biometric data classification [9, 12, 32].

Let the normalized score vector of the q^th sample of the p^th subject with respect to the m^th reference subject. Then, the SVM classification function for is represented using kernel trick [19, 34] (see Eq (7.17)).

(7.17)

In Eq. (7.17), N_s is the number of support vectors, S_i denotes the i^th support vector, y_i is the class associated with S_i, K(·, ·) represents a non-linear kernel function and α_i represents Lagrange multiplier associated with _Si. The sign of represents the class of the and the absolute value of indicates the confidence of being in that class. In this approach, the confidence value is considered as a combined score. The combination of all biometric traits is considered as multimodal biometric trait and denoted it as B4. The multimodal score of the q^th sample of the p^th subject with respect to the m^th reference subject is represented by that is,

Table 7.3: Characteristics of the different score fusion methods

To decide the support vectors (S_i), classes (y_i) of each support vector and Lagrange multipliers (α_i) associated with each support vector, the SVM classifier is trained with a set of training samples. 280134 training data are used to train the SVM classifier. These data are created from 100 users of the Gallery set. Detail description of the training procedure is given in Section 7.10.3.

Note that the multimodal scores for all samples (q = 1, 2, . . . , Q) of all subjects (p = 1, 2, . . . , P ) against all reference subjects (m = 1, 2, . . . , M ) calculated as mentioned above (also see Eq. (7.17)) are in different scales than the unimodal biometric traits. Hence, the multimodal scores are normalized using RHE normalization technique (see Eq. (7.16)) and the normalized multimodal score of the q^th sample of the p^th subject against the m^th reference subject is represented with .

Now, there are four normalized score values for a sample with respect to a reference subject. Four normalized score values of the q^th sample of the p^th subject against the m^th reference subject is denoted with a vector . The normalized score vector for all samples of all subjects against all reference subjects are generated and represented in Eq. (7.18) where p = 1, 2, . . . , P and q = 1, 2, ... , Q. These score vectors are used to generate index key for a sample. Index key generation technique is discussed in the next section.

(7.18)

7.7.1 Index Space Creation

An index space into the database corresponding to each reference subject is created. If there are M reference subjects then M index spaces are created. Figure 7.3 shows an overview of the m^th index space which is corresponding to the m^th reference subject. Each index space contains one table for each biometric trait. There are four biometric traits B1, B2, B3 and B4 where B4 represents multimodal trait in this approach. Four tables in each index space are created. In Fig. 7.3, table for a biometric trait B is denoted with (in the m^th index space) and the length of the table is denoted with L_B. The length of each table depends on the enrollments of subjects into the database and is decided experimentally (see Section 7.10.5.2). The index values of the cells for the table are represented with 1, 2, . . . , L_B . Each cell of the table contains a list called IDL which stores a set of identities of subjects (see Fig. 7.3).

Figure 7.3: Index space for the m^th reference subject.

7.7.2 Storing Multimodal Biometric Data

The identity of each sample is stored into the database based on the generated index keys which is stated as follows. For the key value of the index key , the m index space and table are selected. The unique identity of the q^th sample of the p^th subject is represented as where p and q represent the subject number and sample number of the subject, respectively. The identity are stored into the identity list IDL corresponding to a cell of the table . The cell position in the table is calculated based on the index key value. The cell position (t_B ) in the for the key value is found using Eq. (7.22) and Eq. (7.23). In Eq. (7.22) and Eq. (7.23), L_B denotes the length of the table, and min_ƒm(B) and max_f m_(B) represent the minimum and maximum values of all key values of all samples of all subjects against the m^th reference subject for the biometric B, respectively and calculated using Eq. (7.24).

(7.22)

where,

(7.23)

(7.24)

Note that if there are P number of subjects with Q number of samples each, M number of reference subjects and each subject has B biometric traits then there are M index spaces and each index space has B number of tables. N = P × Q number of identities are stored in each table.

Illustration: The storing technique is illustrated with an example. Let there be five subjects (P = 5) and each subject has four samples (Q = 4) to be enrolled into the database. Also assume that there are three reference subjects (R¹, R² and R³). The four dimensional index keys are generated for the third sample (q = 3) of the fifth subject (p = 5) with respect to all three reference subjects which is shown in Fig. 7.4(a). Three index spaces are created corresponding to each reference subject in the database and each index space contains four tables. Figure 7.4(b) shows all tables of the first index space. Let assume that the length of each table is 5, and the range of key values for B1, B2, B3 and B4 with respect to the first reference subject are 0 to 0.8, 0 to 0.7, 0 to 0.5, and 0 to 1, respectively. Now, it is shown how to store the identity of a subject for the first index key (highlighted row in Fig. 7.4(a)). The first index space is selected to store identity corresponding to the first index key .The identity will be stored into all tables of the first index space. The cell positions t_B1, t_B2, t_B3 and t_B4 of the for the are calculated using Eq. (7.22), respectively. The calculated cell positions for four tables are 4, 3, 2 and 4, respectively. The sample identity is stored into the identity list (IDL) at the 4^th 3^rd 2^nd and 4^th cell positions of and respectively. The highlighted cells in Fig. 7.4(b) show the positions for storing the identity .

Figure 7.4: Example of storing the 3^rd sample of the 5^th subject into the 1 ^st index space of the database.

7.9.1 Creating Feature Vector for Ranking

In Section 7.8, four candidate sets (CSET(B1), CSET(B2), CSET(B3) and CSET(B4)) have been retrieved. From these candidate sets, a set of feature vectors are created for ranking. Let consider a total of N subject identities are retrieved in all four candidate sets for a query. Each subject identity has own vote in each candidate set. The votes of the retrieved subjects is represented in each candidate set as shown in Table 7.4. In Table 7.4, Idⁱ denotes the identity of the i^th retrieved subject and v_i(B) denotes the vote for that subject identity in the candidate set CSET(B). For each retrieved subject, a feature vector is created from the number of votes of that subject in each candidate set. The feature vector for the subject identity Idⁱ is represented in Eq (7.26).

(7.26)

7.9.2 SVM Ranking

In this step, each feature vector is ranked using SVM ranking method [20, 34]. Unlike SVM classification function, which outputs a distinct class for a feature vector, the ranking function gives an ordering of feature vectors. The ranking function outputs a score for each feature vector, from which a global ordering of feature vectors is constructed [20, 34]. Let vⁱ feature vector is preferred to v^j feature vector and specified as vⁱ ≻ v^j. The objective is to find a global function F(·) which outputs a score such that F(vⁱ) > F(v^j) for any vⁱ ≻ v^j. The global ranking function F (·) on a feature vector vⁱ can be computed using SVM [20, 34] and represented in Eq. (7.27). In Eq. (7.27), K(·,·) is kernel function, N_s is the number of support vectors, (V_k − V_l) is the pair wise difference support vector and α_k,l is the Lagrange multiplier associated with the (V_k − V_l).

Table 7.4: Retrieved subjects and their votes in each candidate set

(7.27)

The pair wise difference support vector (V_k − V_l ) and the Lagrange multiplier α_k,l for the global ranking function F (·) are computed from a set of labeled training data. The detail method to train the SVM for ranking can be found in [20, 22]. To generate the set of training data, T number of queries are randomly selected from the gallery set and a set of feature vectors is created for each query using the method discussed in Section 7.9.1. Let R_t be the training data generated from the t^th query (t = 1, 2, . . . , T ) and is represented in Eq. (7.28).

(7.28)

In Eq. (7.28), denotes the i^th feature vector for the t^th query and the rank of Note that the training data R_t follows strict ordering [20], that is, .The ranks of the feature vectors in the training data are given by manually or any automatic ranking method [20, 22]. In this approach, a rank is assigned to each feature vector of a training data by an automatic method which is discussed in the following.

The ranking method for training data is based on a weighted feature vector. Let be the weighted value of the i^th feature vector for the t^th training data. The weighted value is computed by Eq. (7.29).

(7.29)

In Eq. (7.29), represents the weight of the i^th feature vector for the t^th training data. The weight is assigned to each feature vector of a training data in such a way that if the identity related to the feature vector is present in all candidate sets then it gets higher preference than the other feature vector. The weight is computed using Eq. (7.30).

(7.30)

The weighted values are calculated for all feature vectors of a training data using Eq. (7.29) and rank the feature vector based on the weighted values. The rank one is given to the feature vector with the highest weighted value, rank two to the feature vector with the second highest weighted value and so on. In this way, the rank is assigned to each feature vector of all training sets.

Illustration: The SVM-based ranking of each retrieved subject is illustrated with an example. Figure 7.6(a) shows the retrieved candidate sets for a query. There are 5 unique subjects among all candidate sets. A feature vector is generated for each subject identity. For the subject identity Id¹, there are 10, 6, 3 and 5 votes in CSET(B1), CSET(B2), CSET(B3) and CSET(B4). Hence, the feature vector v¹ corresponding to Id¹ is < 10 6 3 5 >. The feature vectors for all retrieved subjects are shown in Figure 7.6(b). The value of SVM ranking function is computed for each feature vector which is shown in Figure 7.6(c). In Figure 7.6(c), it can be seen that the feature vector v¹ related to Id¹ gives the maximum value for SVM-ranking function. The rank 1 is assigned to the subject identity Id¹.

Figure 7.6: An example of SVM-based rank to each retrieved subject for a query.

7.10.1 Database

There are few publicly available multimodal databases with iris, fingerprint and face biometric traits. Out of which, WVU [5, 4] and BioSecure [1] are the two multimodal database which contain three biometric traits, namely iris, fingerprint and face. But the authority of the WVU database does not disclose the privacy of the users. Hence, WVU face database is also not available to the research community. On the other hand, BioSecure [1] database contains less number of users and this database is not freely available to the research community. As a way out, a set of virtual users are created from three publicly available large unimodal databases and the experiments are performed on these virtual user dataset. CASIAV3I [2], WVU [5, 4] and FRGC Still version 2.0 [27, 28, 3] unimodal biometric databases are used for iris, fingerprint and face biometric traits, respectively. The description of these databases are given in the following.

Iris Database: The CASIAV3I database [2] contains 2639 eye images from 395 eyes of 249 persons. One to twenty six images are captured from each eye. It may be noted that the iris data of left and right eyes of a person are different. Hence, each eye is treated as a unique subject. The summary of CASIAV3I iris database is given in Table 7.5. Figure 7.7(a) shows two sample eye images of CASIA database. At least two samples from each subject are considered so that use can be at least one sample for enrollment into the database and one sample for probing. There are 372 subjects which have at least two samples for each subject. These subjects are used to create virtual users in this experiments.

Fingerprint Database: The WVU fingerprint database [5, 4] contains 7136 images of 270 persons. The images are captured from 4 different fingers (left index, left thumb, right index, right thumb). Three to twenty images are captured from each finger. As each finger of a person is different, the each finger is considered as unique subject. Hence, there are 1080 unique subjects in the WVU fingerprint database. The features can not be extracted from the fingerprint images of 320 subject. So, 750 subjects are used to create virtual users in this experiment. The summary of WVU fingerprint database is given in Table 7.5. Two Sample fingerprint images selected randomly from WVU database are shown in Fig. 7.7(b).

Table 7.5: Summary of biometric databases and virtual users

Face Database: FRGC Still version 2.0 database [27, 28, 3] contains 16028 frontal face images of 466 subjects. The images from each subject are captured in indoor environment with two different protocols (FERET and Mugshot) and two different facial expressions (Neutral and Smiley) [27]. In this experiment, a subset of 4007 face images of 466 persons has been taken with neutral expression captured with FERET protocol (FERET-Neutral). These images are captured in Fall 2003 and Spring 2004 semester of 2003-2004 academic year. The images from each subject are captured in indoor environment. A brief summary of the FRGC database is given in Table 7.5. All these images are used for virtual user creation. Figure 7.7(c) shows two face images of two different subjects.

Virtual Users: A sample (instance) of a virtual user consists of three images from three biometric traits, namely iris, fingerprint and face. The virtual users are created from the above mentioned databases. Those subjects from the databases are considered which have at least two samples because at least one sample is needed for enrollment and one sample for probe. Note that there are 372, 1080 and 466 subjects have at least two samples for iris, fingerprint and face biometric databases, respectively. From these three databases 372 virtual users (subjects) can be created with three biometric traits. To create virtual user (subject), first, all samples of a subject are selected from the database of each biometric trait. The subject is selected randomly. Then, a sample image from each biometric trait of the subject is taken and used as a sample image of virtual user. It may be noted that each subject has some uniqueness with respect to each biometric trait. Hence, the subjects or samples are not used to create a virtual user which are already selected for a virtual user. This helps to create virtual users with unique multi biometric traits. In this procedure, 372 virtual users are created and each virtual user has 2 to 20 samples, resulting in a total of 2625 samples. The summary of virtual users is given in Table 7.5.

Figure 7.7: Sample images of CASIAV3I iris, WVU fingerprint and FRGC face databases.

7.10.2 Evaluation Setup

To evaluate the performance of the proposed approach, all samples of all virtual users are divided into two sets: Gallery and Probe. The samples in the Gallery set are enrolled into the index database and samples in the Probe set are used as query to search the index database. 80% samples of each subject are used to create the Gallery set and other 20% to create the Probe set. The samples of the Gallery set are selected randomly from each subject.

The experiments have been done with an Intel Core2Duo processor (2.00 GHz) and 2.0-GB memory. The developed programs are executed with GCC 4.3 compiler.

7.10.3 Training of SVM-based Score Fusion Module

SVM-based score fusion technique is used to combine the scores of different traits and the SVM needs to train before using it in score fusion. The model [22, 21, 14] is trained with known training samples. The training samples contain the scores of all traits and their classes. The class of the training sample is genuine if the score is calculated from the samples of the same subject and imposter if the samples are from different subjects. To create training samples, first, 100 subjects with 2 to 10 samples per subject are selected form the Gallery set. From these selected samples, 2,498 genuine and 2,77,636 imposter pairs are created. Then, the scores between each pair of sample for each biometric trait are calculated using Eq. (7.3) given in Section 7.2 and the scores are normalized using the RHE score normalization method described in Section 7.5.1. Thus, a total of 2,80,134 training data have been created. Each training data has been assigned either genuine or imposter class based on pairs (genuine or imposter). The SVM is trained with these training data and perform 5-fold Cross validation [22, 14] to measure the performance with training data. 96.75% cross validation accuracy has been observed, that is, the SVM training is of good classification accuracy. SVM^ligtht tool [22, 21] is used for training and testing the SVM model.

7.10.4 Training of SVM-based Ranking Module

To train the SVM in rank level fusion, an enrolled database, a set of query samples and the retrieved candidate sets for each query with their ranking are required. For this purpose, 1 sample from 100 subjects is randomly selected as query from the gallery set and the rest of the samples of Gallery set are enrolled into the database. For each query sample, four candidate sets are retrieved corresponding to four biometric traits using the proposed retrieving technique (see Section 7.8). To create training data for SVM ranking, it has to be assigned a rank to each candidates retrieved in the candidate set. To do this, a feature vector is created corresponding to each candidate retrieved candidate set using the proposed method described in Section 7.9.2. An initial rank is given to each training data using Eq. (7.29) as mentioned in Section 7.8. In this way, 100 training sets are created from the 100 query samples. 5-fold cross validation [14, 23] is performed with these training data and observe 92.46% cross validation accuracy. The SVM^Rank tool [23, 20] is used to train and test the SVM in ranking module.

7.10.5 Validation of the Parameter Values

Three parameters are used in this proposed indexing approach. The first parameter is the number of reference subjects (M) which is used in index key generation. The second parameter is the size of the table (L_B) in index space which is used in storing the biometric data into the index space. The third parameter is the number of neighbor cells (δ) of a table. The values of these three parameters are validated experimentally. The experimental validations are given in the following.

7.10.5.2 Size of Table (L_B)

The HR and PR of the proposed indexing technique depend on the number of entries into a cell of the index table. If number of entries into the cell are more then the chances of finding a query subject within the cell increase; as a result HR increases and vice-versa. At the same time, the PR also increases as more number of samples in the cell which need to be retrieved at the time of querying. The number of entries depends on the number of cells of a table which is referred as table size. The number of entries into a cell decreases when table size increases and vice versa. Hence, the HR and PR of different number of enrolled samples are measured with different table sizes. In this experiment, sizes of the table is calculated by taking different percentages of the total number of enrolled samples. The table size is considered 10% to 100% of enrolled samples with step of 10% increment. The experiments have been done with 500, 1000, 1500 and 2000 enrolled samples and results are presented in Fig. 7.9. From Fig. 7.9(a), it is observed that HR decreases rapidly beyond the table size as 30% of the total enrolled samples for different number of enrollments. Whereas in Fig. 7.9(b), it can be seen that PR decreases when the table size is less than 20% of the total enrolled samples for different number of enrollments. Hence, the size of the table is chosen as 20% of the total number of enrolled samples.

Figure 7.8: HR and PR with different number of reference subjects.

7.10.5.3 Number of Neighbor Cells (δ)

For an index key, a set of stored identities are retrieved from a cell and its neighborhood cells of a table. If more number of cells are considered then the HR will be increased but the PR will be also increased. Hence, there should be a choice for selecting the number of neighborhood cells (δ). For this purpose, an experiment is conducted with different values of δ. The values of δ are chosen from 1 to 10 and the HR and PR are measured at each δ value. The result is presented in Fig. 7.10. From Fig. 7.10, it can be seen that by incrementing the value of δ from 1 to 5 the HR is increased from 95.81% to 99.55% with the increase of PR 2.57%. However, incrementing the value of δ from 5 to 10, the HR increases only 0.30% with the increase of PR 4.93%. The value of δ = 5 gives 99.55% HR at 13.86% PR. The value of δ = 5 is selected in the experiment.

Figure 7.9: HR and PR with different number of enrolled samples and different table sizes.

7.10.6 Evaluation

The efficiency of the proposed indexing technique is judged with respect to accuracy, searching time and memory requirement. After selecting the 10 reference subjects, the Gallery set contains 1957 samples and Probe set contains 668 samples from 372 subjects with iris, fingerprint and face biometric traits. Experiments are evaluated with these Gallery and Probe sets. In experiment, the indexing is performed using iris, fingerprint and face trait separately, and different combinations of these three traits (multimodal) also.

7.10.6.1 Accuracy

To analyze the accuracy of the proposed approach, HR and PR are measured. The HR and PR achieved by indexing with iris, fingerprint, face and different combinations of these three traits are reported in Table 7.6. From Table 7.6, it can be seen that the indexing with three traits gives 99.55% HR which is higher than the indexing with uninodal or combination of any two traits. However, the PR is little higher than the unimodal or combination of any two traits.

The result is also substantiated in terms of CMS which gives the probability of at least one correct identity present within a top rank. How CMS varies with rank is shown in Fig. 7.11 as CMC curve for indexing with each unimodal traits as well as for the multimodal indexing. From Fig. 7.11, it is observed that 91.62%, 92.96% and 86.98% CMSs are possible at the top 30 ranks for indexing with iris, fingerprint and face, respectively. On the other hand, indexing with the combination of three traits gives 99.25% CMS at the 30^th rank.

Figure 7.10: HR and PR for different values of δ with the proposed indexing technique.

Further, the performance of the proposed method is analyzed with respect to FPIR and FNIR. To do this, first FMR and FNMR are calculated as follows. Each query template of the Probe set is

Table 7.6: HR and PR of the proposed indexing technique with unimodal and multimodal traits

Biometric trait	HR	PR
Iris	93.56	14.63
Fingerprint	95.96	12.98
Face	90.27	15.86
Iris+Fingerprint	97.75	17.62
Fingerprint+Face	97.21	16.44
Iris+Face	93.86	17.18
Iris+Fingerprint+Face	99.55	17.77

matched with each template in the Gallery set using SVM classification. 3738 genuine pairs and 13,03,538 imposter pairs are chosen from the Gallery and Probe, and the genuine score and imposter scores are calculated for each genuine and imposter pairs, respectively. Finally, FNIR and FPIR are calculated for the identification system without indexing and with indexing using Eq. (4.20) and (4.21), respectively. The trade-off between FPIR and FNIR for the identification system without indexing is shown in Fig. 7.12. Figure 7.12 also shows the trade-off between FPIR and FNIR for indexing with iris, fingerprint, face and combining of three traits. From the experimental results, it may be interpreted that 5.22% FNIR can be achieved at 1% FPIR without indexing where as 2.72%, 2.43%, 3.04% and 2.42% FNIR can be achieved at 1% FPIR for iris, fingerprint, face and multimodal (combination of iris, fingerprint and face) indexing. From Fig. 7.12, also it can be observed that using the proposed indexing approach a lower FPIR can be achieved for an FNMR.

Figure 7.11: CMC curves of the proposed indexing technique with different combination of biometric traits.

Figure 7.12: FPIR versus FNIR curves of the proposed identification system without any indexing and with iris, fingerprint, face and multimodal based indexing.

7.10.6.3 Memory Requirement

Table 7.7: Average retrieving time for a query with different database sizes.

The memory requirement is calculated to store the identities into the database. In this approach, four tables are considered corresponding to each reference subject in an index space and ten reference subjects in the database. Hence, there are 40 tables in the database. Each table stores the identities of all samples. Let 4 bytes memory is required to store the subject identity of a sample and 1 byte is required to store the sample identity of the subject. 2³² subjects and 256 samples per subject can be stored using 5 bytes memory. Suppose, each cell requires 4 bytes memory to store the reference of the identity list (IDL). The table size (L_B) depends on the number of enrollments. In this approach, the table size is considered as 20% of the number of enrollments. If there are N samples need to be enrolled, then the memory requirement (Memory_N ) can be calculated using Eq. (7.31).

(7.31)

The memory requirement is calculated for different number of enrollments and result is shown in Fig. 7.13. It is observed that the memory requirement increases linearly with the database size.