The Secure Grip project1 aims to develop a grip-pattern recognition system, as part of a smart gun. Its target users are the police officers. The current authentication algorithm is based on a likelihood-ratio classifier. The grip pattern is acquired by sensors on the grip of the gun. Since in practice various factors can result in missing lines in a grip pattern, restoration of these missing
lines will be useful and practical. We present a restoration algorithm based on null-space error minimization. The simulation results of the restoration and authentication experiments show that this restoration algorithm effectively restores grip patterns,
and is, therefore, capable of improving the system’s authentication performance when missing lines are present

Ganzevoort, W.P.T.

Kooi, K.

Shang, X.

Veldhuis, R.N.J.

English

The Secure Grip project1 aims to develop a grip-pattern recognition system, as part of a smart gun. Its target users are the police officers. The current authentication algorithm is based on a likelihood-ratio classifier. The grip pattern is acquired by sensors on the grip of the gun. Since in practice various factors can result in missing lines in a grip pattern, restoration of these missing lines will be useful and practical. We present a restoration algorithm based on null-space error minimization. The simulation results of the restoration and authentication experiments show that this restoration algorithm effectively restores grip patterns, and is, therefore, capable of improving the system’s authentication performance when missing lines are present

Veldhuis, Raymond N.J.

University of Twente Research Information

RESTORATION OF MISSING LINES IN GRIP PATTERNS FOR BIOMETRICSAUTHENTICATION ON A SMART GUNX. Shang, K. Kooi, R.N.J. Veldhuis and W.P.T. Ganzevoortx.shang@el.utwente.nlUniversity of Twente, EEMCS-SAS, P.O. Box 217, 7500 AE Enschede, the NetherlandsABSTRACTThe Secure Grip project1 aims to develop a grip-pattern recog-nition system, as part of a smart gun. Its target users are thepolice officers. The current authentication algorithm is based ona likelihood-ratio classifier. The grip pattern is acquired by sen-sors on the grip of the gun. Since in practice various factors canresult in missing lines in a grip pattern, restoration of these miss-ing lines will be useful and practical. We present a restoration al-gorithm based on null-space error minimization. The simulationresults of the restoration and authentication experiments showthat this restoration algorithm effectively restores grip patterns,and is, therefore, capable of improving the system’s authentica-tion performance when missing lines are present.1. INTRODUCTIONThe Secure Grip project aims to develop a prototyperecognition system as part of a smart gun, where the grip-pattern recognition ensures that it can only be fired by itsrightful user. This application is intended for use by thepolice officers, since carrying a gun in public brings con-siderable risks [1]. The first prototype of this smart gunsystem (see Figure 1) was described in [2] and [3], interms of its design, implementation and evaluation. Au-thentication simulations were made based on a likelihood-ratio classifier, by using the grip-pattern data collectedfrom a group of police officers (see Figure 2). The simu-lation results indicated that the grip pattern contains suffi-cient information to authenticate the police officers [3].During data collection we observed that sometimes thegrip-pattern images had a couple of lines missing, due tosome damage in the cable of the demonstrator (see Fig-ure 3). This will degrade the authentication performanceof the system. In addition, the registration result of databefore authentication can be affected, which will furtheradd to degradation of the authentication performance. Inpractice there can be various factors resulting in missinglines in a grip-pattern image, while using a smart gun,1This research is supported by the Technology Foundation STW,applied science division of NWO and the technology programme of theMinistry of Economic Affairs.Figure 1:Prototype of a smart gun.Figure 2:An example of the grip-pattern image.such as damages in the cable or in the sensor, or lose con-tacts between electric components. Thus, restoration ofthese missing lines will be useful and practical. In ourwork, we apply a restoration algorithm based on null-space error minimization. We assume that the missinglines are only present in grip patterns of the test set, whilein those of the training set complete data are available.This paper presents the restoration algorithm and analyzesits effect on the authentication performance of the smartgun system. Section 2 reviews the authentication algo-rithm. The restoration algorithm is described in Section 3.Subsequently, Section 4 presents and analyzes the simu-lation results of the restoration and authentication experi-ments. Finally, the conclusions are given in Section 5.Figure 3:Grip-pattern image with missing lines.2. AUTHENTICATION ALGORITHMThe authentication algorithm is based on a likelihood-ratio classifier for Gaussian probability densities. Thelikelihood-ratio classifier has been proved to be optimal,in terms of the average overall error rates if the data hasa known probability density function [4], [5]. We assumethat both the overall data, and that of each individual sub-ject, are Gaussian distributed. The pixel values of eachgrip-pattern image are aligned into a column vector, andare used as the features in the algorithm. In our system,the feature space has the dimension of 1936, since eachgrip pattern was recorded as a 44 by 44 image.In practice, the exact probability density function of nei-ther the overall data, nor the data of each individual sub-ject is known, and therefore needs to be estimated fromthe training data. In total, four parameters need to be es-timated. They are the mean vector of the overall data, themean vector and the covariance matrix of each individualsubject’s data, and the transformation matrix. In our case,the number of training samples from each subject shouldbe much more than 1936. This is to prevent the estimatedcovariance matrices from being singular, and to preventthe classifier suffering from overtraining. Otherwise, thealgorithm would suffer from the so-called small-sample-size problem. However, we cannot make this large num-ber of measurements, since it would be rather impracticalfor the user enrollment.To solve the small-sample-size problem, we assume thateach subject has the same within-class covariance matrix.Thus, this common covariance matrix can be estimatedmore accurately, by using data from all the subjects. As afurther step to relieve the effect of the small-sample-sizeproblem, we reduce the dimension of the feature space.Firstly, we apply a PCA (Principal Component Analysis)to project the overall data to a subspace with the biggestvariances. In this new space, the directions contributing tothe authentication, are not more than the number of sub-jects minus one. Also, these directions have the smallestvariances of each individual subject’s data [2]. According-ly, a further dimension reduction is achieved, by applyinga PCA to each individual subject’s data, and discardingall the directions, except only the 40 (41 subjects in total)with the smallest variances.3. RESTORATION ALGORITHMWe assume that the covariance matrix of the feature vec-tors has a null space of a dimensionality that is at leastthe number of unknown features. Let the column vectorxdenote a feature vector withN elements. Furthermore, letx =(uv), (1)with u containing them unknown features andv contain-ing theN −m known ones. We assume thatx has a zeromean. Let̂u denote the estimate foru:û = HT v. (2)Let the feature space be anM -dimensional subspace ofRN described byO = {x|x = Fφ,F ∈ RN × RM ,M ≤ N −m,φ ∈ RM ,FT F = I}. (3)The columns ofF compose anM -dimensional orthonor-mal basis of the feature subspace. Note thatM is assumedto be much smaller thanN . We look for û, such that thenorm of the signal component in the null space, the null-space error, after restorationE0 = ‖(I− FFT )(ûv)‖2 (4)is minimized [6]. The matrix(I−FFT ) projects onto thenull-space ofF, therefore(I− FFT )2 = (I− FFT ). (5)We partitionF in two sub-matrices:F =(F1F2), (6)with F1 anm × m matrix andF2 an(N − m) × m ma-trix. By using (5) and (6), the null-space error (4) can berewritten asE0 = (ûT vT )(I− FFT )(ûv)= ‖û‖2 + ‖v‖2 − ‖FT1 û + FT2 v‖2. (7)Setting the derivative with respect tôu equal to zero yieldsthe following equation(I− F1FT1 )û = F1FT2 v, (8)from whichû can be solved.We briefly look at the sensitivity of this restoration algo-rithm to model errors, which occur when the observeddeviates from the assumptions. We assume thatx = x′ + g (9)=(u′v′)+(g1g2), (10)with g an error component in the null space ofF. Thismeans thatFT1 g1 + FT2 g2 = 0. The error component inthe restoration is now given byε =(I− F1FT1)−1F1FT2 g2= −(I− F1FT1)−1F1FT1 g1= g1 −(I− F1FT1)−1g1. (11)The first term reflects the presence of model errors in thepart that is to be restored. The second term reflects theerror due to the compensation for model errors in the givendata. The compensation error grows strongly when theeigenvalues ofF1FT1 approach 1.Note that this restoration algorithm works only in thecase that the missing lines are present in grip patterns ofthe test set, while in those of the training set completedata are available. If there are also missing lines in dataof the training set, some other type of restoration algo-rithm should be applied. Linear interpolation, for exam-ple, could be a choice.4. EXPERIMENT, RESULTS AND DISCUSSIONIn this section simulation results of the restoration and au-thentication experiments are presented and analyzed, interms of the average restoration error per pixel of the miss-ing lines and the overall Equal-Error Rate (EER), respec-tively.4.1. Experiment set-up and resultsWe collected data from a group of 41 police officers, with25 grip-pattern images recorded from each. We assumedthat the missing lines were only present in data of the testset, while in that of the training set, no lines were miss-ing. We made simulations of restoration in different cases,where the number of missing lines increased from one tillten in each sample of the test set. In all cases 75% of thedata was randomly chosen for training, and the rest 25%Number of Average restorationmissing lines error per pixel1 105.012 119.273 118.044 117.845 114.116 117.897 118.738 118.629 117.2710 114.92σ2W 239.62Table 1:Restoration error per pixel.for testing. The missing lines in each sample were ran-domly chosen as well. To evaluate the restoration qual-ity we calculated the average restoration error per pixel.The simulation results are shown in Table 1. As a refer-ence, the average within-class variance per pixelσ2W ofthe training set is also presented.To evaluate the effect of the restoration of missing lineson the authentication performance, we did two experi-ments. In the first experiment, the test set consisted ofsamples where a certain number of lines were missing ineach sample. That is, pixel values in those lines were allset to zero. While in the second experiment, the test setwas composed of samples, where the missing lines wererestored with our restoration algorithm. The authentica-tion performance was assessed by the overall Equal-ErrorRate (EER). This was calculated by taking into account allthe likelihood-ratios of both the genuine subjects and theimposters. We averaged the overall EERs obtained from20 runs of simulation as the final result. In each singlerun, we randomly chose 75% of the data for training, andused the rest 25% for testing. This whole procedure wasrepeated, with the number of missing lines in each sampleof the test set increasing from one till ten. The simula-tion results are shown in Table 2. For easy comparison,the simulation result when the test set is without missinglines is also presented.MLs and RLs represent missinglines and restored lines, respectively, andσEER representsthe standard deviation of the EERs in all 20 runs. The au-thentication results are further shown in Figure 4, as thenumber of missing lines increases.4.2. DiscussionOne can see from Table 1 that the average restoration er-ror per pixel is fairly constant, when different numbers ofmissing lines in the data are present. That is, the restora-tion error per pixel seems to be robust against the increaseComplete test set EER (%) = 0.55Number EER (%) EER (%) σEERof MLs with MLs with RLs (%)1 0.65 0.59 0.192 0.70 0.67 0.273 0.65 0.62 0.204 0.81 0.66 0.215 1.03 0.65 0.216 1.06 0.70 0.287 1.20 0.79 0.338 1.20 0.81 0.259 1.52 0.85 0.2610 1.50 0.93 0.31Table 2:EERs obtained in authentication experiment.Figure 4:EERs obtained by using data with missing andrestored lines as function of the number of missing lines.in the number of missing lines. Also, the average restora-tion error per pixel is much smaller, compared to the av-erage within-class variance per pixel of the training set.This indicates that the restoration algorithm restores dataeffectively.In addition, Table 2 shows that up to three missing lines,the authentication results are not affected very much incomparison with that by using a complete data set. Thissuggests that the current authentication algorithm is robustagainst the presence of a small number of missing lines.However, as the number of missing lines in the test setbecomes higher, the authentication performance degradesmore. Thus, restoration of missing lines in the grip pat-terns is useful, especially when the number of missinglines is relatively high.Finally, the presented restoration algorithm effectively re-stores the missing lines, and therefore improves the sys-tem’s authentication performance. On the other hand, asshown in Figure 4, the authentication result by using therestored data becomes worse as the number of missinglines in each sample increases. This is because that themore missing lines are present, the higher restoration errorresults in a grip-pattern image. However, on the whole thisrestoration algorithm works well to improve the authenti-cation performance of the system when missing lines arepresent.5. CONCLUSIONSIn the smart gun system the current authentication algo-rithm seems to be robust against the presence of a smallnumber of missing lines. However, restoration of miss-ing lines in the grip patterns is necessary and practical,when the number of missing lines becomes higher, saymore than five in the case of a grip pattern of44 × 44pixels.The presented restoration algorithm has been proved to beable to effectively restore the missing lines in grip-patterndata. In addition, the average restoration error per pixelseems to be robust against the increase in the number ofmissing lines. On the other hand, the authentication resultby using the restored data becomes worse as the number ofmissing lines increases, due to the accordingly increasedrestoration error. Yet, on the whole this restoration al-gorithm works well to improve the authentication perfor-mance of the system when missing lines are present.6. REFERENCES[1] The national Uniform Crime Reporting Program,“Law Enforcement Officers Killed and Assaulted”,tech. rep., Federal Bureau of Investigation, 2001.[2] Raymond Veldhuis, Asker Bazen and Joost Kauff-man, “Biometric verification based on grip-patternrecognition”, presended atSPIE, 2004.[3] X. Shang, R.N.J. Veldhuis, A.M. Bazen andW.P.T. Ganzevoort, “Algorithm Design for Grip-Pattern Verification in Smart Gun”, accepted forProRISC, 2005.[4] Asker Bazen and Raymond N.J. Veldhuis,“Likelihood-Ratio-Based Biometric Verificaton”,IEEE Transactions on circuits and systems for videotechnology, vol. 14, no. 1, January, 2004.[5] H.L. Van Trees,Detection, Estimation, and Modula-tion Theory, New York: Wiley, 1968.[6] R.N.J. Veldhuis,Restoration of Lost Samples in Digi-tal Signals, New York: Prentice Hall, 1990.

Restoration of missing lines in grip patterns for biometrics authentication on a smart gun

NARCIS 

Algorithm Design for GripPattern Veriﬁcation in Smart Gun”, accepted for ProRISC,

Asker Bazen and Joost Kauffman, “Biometric veriﬁcation based on grip-pattern recognition”, presended at SPIE,

Likelihood-Ratio-Based Biometric Veriﬁcaton”, IEEE Transactions on circuits and systems for video technology,

Restoration of Lost Samples in Digital Signals,

The national Uniform Crime Reporting Program, “Law Enforcement Ofﬁcers Killed and Assaulted”, tech. rep., Federal Bureau of Investigation,

Trees, Detection, Estimation, and Modulation Theory,

Restoration of missing lines in grip patterns for biometrics authentication on a smart gun

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