Performance of Fingernail Plates in Identification Systems
For identification systems, the performance may be evaluated using the parameter True Positive Identification Rate (TPIR). TPIR is the proportion of times the identity determined by the system is actually the true identity of the person who is providing the biometric sample [37]. If the biometric system provides the identities of the top x matches, the Ranka TPIR, R_{x},is the proportion of times the true identity of the individual is contained in the top x matching identities. For performance analysis of an identification system, the TPIR at various ranks may be depicted in the Cumulative Match Characteristics (CMC) curve where TPIR, R_{x}, are plotted against Rank x = 1,2 ,...N where N is the total number of people enrolled in the database.
Performance of Fingernail Plates in Unimodal Identification Systems
In this section, performances of the three fingernail plates in unimodal identification systems have been analysed for each of the three deep learning models  TLA, TLR, and TLD. Figure 9.13 makes a comparison of the performance of the index, middle, and ring fingernail plate using the TLA featureset. Similar comparative performance portrayal of the three fingernail plates are depicted in Figures 9.14 and 9.15 for the TLR and TLD featuresets, respectively.
It is observed from Figures 9.139.15 that identification systems built from either the index or the middle fingernail plate shall provide good performance. The ring fingernail plate also fares well, but lags in performance behind the other two nail plates. Analysing the results depicted in these three figures also shows that for all the three nail plates, the best identification accuracy is given by TLD, followed by TLR and TLA, in that sequence. This, of course, is because of the depth of the respective models. Also, for all the three nail plates, TLD provides a high identification accuracy of above 93%. The other two models, TLA and TLD, also fare reasonably well.
FIGURE 9.13 CMCs comparing the Performance of Index, Middle, and Ring Fingernail Plates in Unimodal Identification Systems using TLA as the feature extraction technique.
FIGURE 9.14 CMCs comparing the Performance of Index, Middle, and Ring Fingernail
Plates in Unimodal Identification Systems using TLR as the feature extraction technique.
FIGURE 9.15 CMCs comparing the Performance of Index, Middle, and Ring Fingernail Plates in Unimodal Identification Systems using TLD as the feature extraction technique.
Table 9.4 tabulates the values of Rankl TPIRs obtained from all the three nail plates from the three deep learning models considered.
The lowest Rank1 TPIR is obtained from the index nail plate when the TLA featureset is used; and that is as high as 85.39%. Table 9.4 also demonstrates that the best Rank1 identification performance is provided by the middle fingernail plate for TLA, by the index and the middle fingernail plates for TLR, and by index fingernail plate for TLD.
Э.6.2.2 Performance of Fingernail Plates in Multimodal Identification Systems
In this section, the index, middle, and ring fingernail plates have been subjected to different frameworks of ranklevel fusion. For all the experiments conducted, the performance of ranklevel fusion of these three nail plates has been analysed for all the three deep learning models: TLA, TLR, and TLD.
TABLE 9.4
Rank1 TPIR (in %) for Various Unimodal Identification Biometric Systems built using Index, Middle, and Ring Fingernail Plates^{1}
Model 
Trait 

Index 
Middle 
Ring 

TLA 
85.39 
90.45 
85.95 
TLR 
91.01 
91.01 
90.45 
TLD 
93.82 
93.26 
93.26 
^{a} Numbers in bold and italics signify the best performance across one or the other parameter.
9.6.2.2.1 Experiment A
For the first set of experiments under this section, the three ranking lists of all the three fingernail plates have been fused separately for the three models: TLA, TLR, and TLD. In this experiment, fusion has been performed using two different linear, weighted fusion methods, namely the Logistic Regression and the Mixed Group Rank. Here, the weights have been chosen via empirical computation. Figure 9.16 compares the performance of the nail plates after ranklevel fusion through Logistic Regression and Mixed Group Rank, where the TLA featureset is used. Similar comparative performances of ranklevel fusion for the TLR and TLD models are shown in Figures 9.17 and 9.18, respectively.
FIGURE 9.16 CMCs after RankLevel Fusion of all three Fingernail Plates for TLA featureset using Logistic Regression and Mixed Group Rank, where all weights have been computed empirically.
FIGURE 9.17 CMCs after RankLevel Fusion of all three Fingernail Plates for TLR feature set using Logistic Regression and Mixed Group Rank, where all weights have been computed empirically.
FIGURE 9.18 CMCs after RankLevel Fusion of all three Fingernail Plates for TLD featureset using Logistic Regression and Mixed Group Rank, where all weights have been computed empirically.
Figures 9.169.18 establish that an identification system built from the index, middle, and ring fingernail plates gives good performance accuracy, where the TLD based results are better than those based on TLR and TLA. Analyses of the results depicted in Figures 9.169.18 also bring out an interesting point. The corresponding Rank1 TPIR values are the same for all three models, when Logistic Regression and Mixed Group Rank are the chosen fusion rules. However, with increasing ranks, the TPIR values increase in two different trends for the two fusion methods. While for all three deep learning models, 100% TPIR is achieved at Rank12 for the Mixed Group Rank rule, the same is achieved by using the Logistic Regression method only at the final rank, i.e., Rank 178.
A tabular depiction of the TPIR values at a few' selected ranks is given in Table 9.5 to illustrate the aforementioned trend of results.
9.6.2.2.2 Experiment В
The weights for the three different fingernail plates in Experiment A have been assigned through empirical computation. With an aim to further improve accuracy, the exact experiments under Experiment A have been repeated by computing weights using PSO. This has been done to ensure optimal weight assignment to the three nail plates, and thus to provide better results. In Figure 9.19 the performance of the nail plates is depicted when their corresponding TLA featuresets are subjected to rank level fusion using Logistic Regression and Mixed Group Rank methods. Similar performances are depicted in Figures 9.20 and 9.21 w'hen TLR and TLD feature sets are used. All the three aforementioned figures show that w'hen PSO is used for the computation of weights, the results improve for each of the cases, wuth the best Rank1 accuracy being provided by the TLD based ranking lists for the Mixed Group Rank rule.
TABLE 9.5
True Positive Identification Rates (in %) of the Multimodal Systems where Nail Plates of All Three Fingers are fused using Two Linear Weighted Fusion Methods (Weights Computed Empirically)
Logistic Regression Method 

Rank Model Ф 
1 
2 
3 
8 
178 
TLA 
94.38 
96.63 
98.88 
99.44 
100 
TLR 
96.07 
97.75 
99.44 
99.44 
100 
TLD 
97.19 
98.32 
99.44 
99.44 
100 
Mixed Group Rank Method 

Rank Model Ф 
1 
2 
3 
8 
12 
TLA 
94.38 
95.51 
96.63 
98.88 
100 
TLR 
96.07 
97.75 
98.88 
100 
100 
TLD 
97.19 
98.32 
98.88 
100 
100 
FIGURE 9.19 CMCs after RankLevel Fusion of all three Fingernail Plates for TLA featureset using Logistic Regression and Mixed Group Rank, where all weights have been computed using PSO.
Figures 9.199.21 show' that the three fingernail plates can be combined to build a reliable identification system. Systems where the fusion is performed using Logistic Regression give appreciable performance. However, the systems w'hich employ Mixed Group Rank outdo the former.
Table 9.6 portrays the improvement in Rank1 TPIR values obtained in this set of experiments when the weights are optimised using PSO.
FIGURE 9.20 CMCs after RankLevel Fusion of all three Fingernail Plates for TLR featureset using Logistic Regression and Mixed Group Rank, where all weights have been computed using PSO.
FIGURE 9.21 CMCs after RankLevel Fusion of all three Fingernail Plates for TLD featureset using Logistic Regression and Mixed Group Rank, where all «'eights have been computed using PSO.
9.6.2.2.3 Experiment C
To check the efficacy of the proposed system further, the next experiment has implemented ranklevel fusion of the three nail plates using another fusion rule: the Inverse Rank Position method. Figure 9.22 shows the results obtained after carrying out this experiment. It is seen that fusion of the TLR featurebased scores through this method gives the highest Rank1 identification accuracy (98.88%). Table 9.7 illustrates the Rank1 TPIRs for the three models.
TABLE 9.6
Rank1 Identification Rates (in %) of the Multimodal Systems where Nail Plates of All Three Fingers are fused using Two Different Linear Weighted Fusion Methods^{a}
Model 
Fusion Method 

Logistic Regression 
Mixed Group Rank 

Weights computed Empirically 

TLA 
94.38 
94.38 
TLR 
96.07 
96.07 
TLD 
97.19 
97.19 
Weights determined using PSO 

TLA 
96.07 
96.63 
TLR 
97.75 
98.32 
TLD 
98.32 
98.88 
^{a} Number in bold and italics signify the best performance obtained.
9.6.2.2.4 Experiment D
Appreciable identification accuracy obtained from experiments AC performed under the current section motivated authors to explore the fingernail plate multimodal identification system further. With the same intent, multimodal systems have been designed where all three fingernail plates have been fused using two different nonlinear weighted fusion rules.
FIGURE 9.22 CMCs after RankLevel Fusion of all three Fingernail Plates for TLA. TLR, and TLR using Inverse Rank method.
TABLE 9.7
Rank1 Identification Rates (in %) of the Multimodal Systems where Nail Plates of All Three Fingers are fused using the Inverse Rank Position method^{a}
TLA 
TLR 
TLD 
97.75 
98.88 
98.32 
^{a} Number in bold and italics signify the best performance obtained.
The experiment carried out under this section builds a multimodal system where the index, middle, and ring fingernail plates have been fused using Weighted Exponential and Hyperbolic Tangent: two different nonlinear, weighted fusion rules. Figure 9.23 gives the comparative depiction of the performance of the index, middle, and ring fingernail plates when their corresponding TLA based scores are fused at the rank level using Weighted Exponential and Hyperbolic Tangent, while the same finding for TLR featureset is shown in Figure 9.24, and that for TLD featureset is given in Figure 9.25. For this experiment, all weights have been determined via empirical computation.
Figures 9.239.25 demonstrate that while the identification performance might be considered to be satisfactory, the results obtained in this experiment, especially the Rank1 TPIRs are lower than that obtained through the Inverse Rank Position method, or those obtained through the Linear Weighted methods even when respective weights are computed empirically. Also, the Rank1 TPIRs obtained using TLD model is less than that obtained using both TLR and TLA when Hyperbolic Tangent is used as the fusion rule. This is highly unlikely as TLD is much deeper than TLA, and this may have been caused because of possible inappropriate weight attribution to the three nail plates considered. Table 9.8 enlists the Rank1 TPIRs obtained under this experiment.
FIGURE 9.23 CMCs after RankLevel Fusion of all three Fingernail Plates for TLA featureset using Weighted Exponential and Hyperbolic Tangent, where all weights have been computed empirically.
FIGURE 9.24 CMCs after RankLevel Fusion of all three Fingernail Plates for TLR featureset using Weighted Exponential and Hyperbolic Tangent, where all weights have been computed empirically.
FIGURE 9.25 CMCs after RankLevel Fusion of all three Fingernail Plates for TLD featureset using Weighted Exponential and Hyperbolic Tangent, where all weights have been computed empirically.
9.6.2.2.5 Experiment E
With an aim to achieve better identification accuracy, and also to check the sort of unlikely results obtained under the previous set of experiments, the same have been repeated after computing weights using PSO. Also, it is important to note that results obtained from Experiment В confirms that optimisation of weights improves identification accuracy considerably. Thus under this experiment, the three nail
TABLE 9.8
Rank1 Identification Rates (in %) of the Multimodal Systems where Nail Plates of All Three Fingers are fused using Two Different Nonlinear Weighted Fusion methods (Weights computed Empirically)
Model 
Fusion Method 

Weighted Exponential 
Hyperbolic Tangent 

TLA 
93.26 
97.19 
TLR 
96.07 
98.32 
TLD 
96.07 
94.38 
plates have been fused using Weighted Exponential and Hyperbolic Tangent rules, where weights have been calculated using PSO.
Figure 9.26 gives the comparative depiction of the performance of fused nail plates using the TLA featureset when the fusion is performed using Weighted Exponential and Hyperbolic Tangent. The same findings for TLR and TLD featuresets are given in Figures 9.27 and 9.28, respectively.
Analysing the CMCs in Figures 9.269.28 reveals that in this experiment, the highest Rank1 TPIR of 99.44% has been provided by both TLR and TLD, when fusion is performed through the Hyperbolic Tangent rule. Comparing these results with those obtained in the previous experiment shows that the performance accuracy has improved significantly when the weight attribution has been performed using PSO.
FIGURE 9.26 CMCs after RankLevel Fusion of all three Fingernail Plates for TLA featureset using Weighted Exponential and Hyperbolic Tangent, where all weights have been computed using PSO.
FIGURE 9.27 CMCs after RankLevel Fusion of all three Fingernail Plates for TLR featureset using Weighted Exponential and Hyperbolic Tangent, where all «'eights have been computed using PSO.
FIGURE 9.28 CMCs after RankLevel Fusion of all three Fingernail Plates for TLD featureset using Weighted Exponential and Hyperbolic Tangent, where all weights have been computed using PSO.
The Rank1 TPIRs of the different systems in this experiment have been given in Table 9.9 to alleviate their comparative representation.
To make a comparison of the methodologies adopted and results obtained in the current work with that of some of the previously reported works which investigated the fingernail, a tabular depiction has been made in Table 9.10.
TABLE 9.9
Rank1 Identification Rates (in %) of the Multimodal Systems where Nail Plates of Three Fingers are fused using Nonlinear Weighted Fusion Methods (Weights computed using PSO)^{1}
Model 
Fusion Method 

Weighted Exponential 
Hyperbolic Tangent 

TLA 
94.94 
98.32 
TLR 
97.75 
99.44 
TLD 
98.88 
99.44 
^{a} Numbers in bold and italics signify the best performance obtained.
TABLE 9.10
Comparison of Proposed Work with Significant Existing Works on Fingernail^{1}
Ref. No. 
Part of Finger Explored 
Feature Extraction Technique 
Database 
Results of Unimodal System 
Results of Fusion 
[15] 
Index Fingernail Bed 
None 
Not reported 
Binary representation of the relative positions of capillary loops is obtained, which is unique to every individual. 
Not explored 
[14] 
Nail Ridges 
None 
Not reported 
Bands of colour obtained. Each represents a single ridge or valley of nail surface. 
Not explored 
[16] 
Nail Surface of Index, Middle, and Ring Fingers 
Handcrafted Approach: Haar Wavelet 
Database of 5 images/180 users = 900 images per modality 
Highest accuracy reported: Verification: GAR = 50% (at FAR = 0.01%) Identification not investigated. 
Fusion of three nail surfaces done. Verification results as high as GAR = 72% (at FAR = 0.01%) for Product Rule. Identification not investigated. 
(Continued)
TABLE 9.10 (Continued)
Comparison of Proposed Work with Significant Existing Works on Fingernail^{1}
Ref. No. 
Part of Finger Explored 
Feature Extraction Technique 
Database 
Results of Unimodal System 
Results of Fusion 
[17] 
Nail Plate of Index, Middle, and Ring Fingers 
Handcrafted Approaches: Haar Wavelet and ICA 
Database of 5 images/180 users = 900 images per modality 
Highest accuracy reported: Verification: GAR = 55% (at FAR = 0.01%) Identification: 81% Rank1 TP1R 
Fusion of three nail plates done. Verification and Identification accuracy as high as GAR = 85% (at FAR = 0.01%) and 96.5% Rank1 TPIR respectively reported 
[8] 
Nail Plate of Index, Middle, and Ring Fingers 
Handcrafted Approaches: Haar Wavelet and ICA 
Database of 5 images/180 users = 900 images per modality 
Highest accuracy reported: Verification: GAR = 60% (at FAR = 0.01%) Identification: 89% Rank1 TPIR 
Fusion of three nail plates done. Verification and Identification accuracy as high as GAR = 80% (at FAR = 0.01%) and 96.5% Rank1 TPIR respectively reported 
[5] 
Knuckle and Nail Plate of Index, Middle and Ring Fingers 
Deep Learning Approach: AlexNet 
Database of 5 images/178 users = 890 images per modality 
Highest accuracy reported from Nail Plates: Verification: GAR = 56.74% (at FAR = 0.01%) Identification: 90.45% Rank1 TPIR 
Fusion of a) three nail plates, b) three knuckles, c) each nail plate with corresponding knuckle done. For fusion of nail plate and knuckle. Verification and Identification accuracy as high as GAR = 96.63% (at FAR = 0.01%) and 98.31% Rank1 TPIR, respectively, reported For fusion of three nail plates, Verification and Identification accuracy as high as GAR = 87.64% (at FAR = 0.01%) and 98.31% Rank1 TPIR, respectively, reported 
(Continued)
TABLE 9.10 (Continued)
Comparison of Proposed Work with Significant Existing Works on Fingernail^{1}
Ref. No. 
Part of Finger Explored 
Feature Extraction Technique 
Database 
Results of Unimodal System 
Results of Fusion 
This Work 
Nail Plate of Index, Middle, and Ring Fingers 
Deep Learning Approaches: AlexNet, ResNet and DenseNet 
Same database as in Ref. [5] 
Highest accuracy Verification: GAR = 74.16% (at FAR = 0.01%) Identification: 93.82% Rank1 TP1R 
Verification and Identification accuracy as high as GAR = 94.94% (at FAR = 0.01%) and 99.44% Rank1 TPIR respectively 
■ Numbers in bold and italics signify the best performance obtained in the current work.