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Intra-Modal Biometric System Using Hand-Geometry and Palmprint Texture Copyrigth Material IEEE Paper No. ICCST-2010-16379-2 Juan Jose Fuertes 1, Carlos M. Travieso 2 , Miguel A. Ferrer 2 , Jesus B. Alonso 2 1 1nstituto Interuniversitario de Investigaci6n en Bioingenieria y Tecnologia Orientada al Ser Humano, Universidad Politecnica de Valencia Camino de Vera sIn, 46022 Valencia, Espana Email: [email protected] 2 0epartamento de Senales y Comunicaciones, Centro Tecnol6gico para la Innovaci6n en Comunicaciones Universidad de Las Palmas de Gran Canaria, Campus de Tafira, Edificio de Telecomunicaci6n, E-35017 Las Palmas de Gran Canaria, SPAIN {ctravieso, mferrer, jalonso}@dsc.ulpgc.es http:www.gpds.ulpgc.es Abstract - This paper presents an identification-verification biometric system based on the combination of geometrical and palm-print hand features. It attempts to improve the performance of existing hand-geometry or palm-print systems which no combine both methods. 1440 hand images of 144 people with 10 samples each one have been acquired by a commercial scanner with 150 dpi resolution. 80 widths of fingers are obtained from binarized images. Wavelet transform, 20 Gabor filter and derivative method are used to extract the texture features from gray-scale images. Support Vector Machine (SVM) is the main classifier used as identifier and verifier. A feature, score and decision level fusion is implemented. An accuracy of 99.97% and an EER=0.0032% (Equal Error Rate) shown the final results of our system. Index Tes - Biometrics, hand identificationlverification system, data fusion, Pattern Recognition and classification. I. INTRODUCTION Nowadays, the security systems are beginning to expand into the society because many studies have been focused on improving them. Most of the techniques used to develop these systems are based on ideas from palm-print image analysis [1]. Although these techniques let us to achieve good results, a highly accurate biometrics system can be built through the combination of palm-print texture and hand-geometry features. Both methods can be studied simultaneously with the extraction of one low-resolution image by means of a simple device which is well accepted by users. Therefore, we are going to review the techniques proposed by other authors in the field of hand-biometric technology, in order to locate our work in the biometric science. Golfarelli et al. [2] proposed a hand biometric system made up of 100 people, 8 samples per person. Using the Bayes classification rule they obtained an EER=0.12%. Jain et al. [3] described a biometric system based on 16 hand-geometry features of 50 individuals, 10 samples per each one. The EER was 7.5%. Sanchez-Reillo et al. [4] presented a biometric system made up of 200 images of 20 people. They used 21 hand geometrical features and the ERR was lower than 5% independently of the classifier. Pavesic et al. [5] showed a finger lengths/widths and palm width system (24 features) using normalized Euclidean distance. With 110 registered and Supported by The Spanish Ministry of Education and Science under the research project with reference "CICYT TEC2006-13141-C033-01ITCM" 978-1-4244-7402-8/10/$26.00 ©2010 IEEE 399 impostors the error rates were FAR=0.01 and FRR= 0.001. YbrOk et al. [6] described a hand-contour coordinates system (2048 points), made up of 458 people, 3 samples per person. The EER was between 0.01 and 0.02 using a modified Hausdof distance. M. Adan et al. [7] proposed a hand biometric system based on 14 geometric features for each hand. Thanks to the normalized sum of feature deviation the FAR was 0.0045 and the FRR was 0.034. Morales et al. [8] showed a geometric-system made up to 20 people, 10 samples per person. The error rate was EER=3.4% using 40 finger widths for three fingers and using SVM (distance to separator hyperplane). Goh et al. [9] presented a palm-print system made up of 75 individuals. It was based on wavelet transform and Gabor filter, with a verification result of 96.7% and an EER close to 4%. Liu et al. [10] showed a research about the use of wavelet transform in the palm-print. Classiing with the ISOOATA algorithm got a 95% of identification accuracy with 180 palm- print of 80 people. Masood et al. [11] developed a palm-print system using wavelet transforms. 50 people took part in the session (10 samples per person), reaching a 97.12% of accuracy with the combination of different wavelet families. Guo et al. [12] described a BOCV system, (Binary Orientation Co-Occurrence Vector) based on the linking of six Gabor features vectors. 7752 samples from 193 people were taken. The error rate was 0.0189%. Zhang et al. [13] presented a novel 20+30 palm-print biometric system made up to 108 individuals. The EER was 0.0022%. Ribaric et al. [14] proposed a multimodal biometric identification system based on geometrical features and palm and finger-print texture. The error rates were FAR=O% and FRR=0.2%. 130 people took part in the test session. Van et al. [15] described a biometric system which combines 1-0 human features. A 97% of accuracy is reached (50 users, 10 samples each one) with the integration of palm-print, finger-print and geometry features. Ferrer et al [16] proposed a multimodal biometric system based on the combination of geometrical, palm and finger features of the human hand. A FAR=O% and FRR=0.15% are obtained when they work with 109 people. Our goal is to improve the performance of existing palm- print or hand-geometry systems, combining both methods, and therefore, reaching an accuracy that may not be possible with single biometric method alone. We propose an identification- verification system using both features of human hand (see
Transcript

Intra-Modal Biometric System Using Hand-Geometry and Palmprint Texture

Copyrigth Material IEEE Paper No. ICCST-2010-16379-2

Juan Jose Fuertes 1, Carlos M. Travieso2, Miguel A. Ferrer2

, Jesus B. Alonso2

11nstituto Interuniversitario de Investigaci6n en Bioingenieria y Tecnologia Orientada al Ser Humano, Universidad Politecnica de Valencia

Camino de Vera sIn, 46022 Valencia, Espana Email: [email protected]

20epartamento de Senales y Comunicaciones, Centro Tecnol6gico para la Innovaci6n en Comunicaciones Universidad de Las Palmas de Gran Canaria,

Campus de Tafira, Edificio de Telecomunicaci6n, E-35017 Las Palmas de Gran Canaria, SPAIN {ctravieso, mferrer, jalonso}@dsc.ulpgc.es http://www.gpds.ulpgc.es

Abstract - This paper presents an identification-verification biometric system based on the combination of geometrical and palm-print hand features. It attempts to improve the performance of existing hand-geometry or palm-print systems which no combine both methods. 1440 hand images of 144 people with 10 samples each one have been acquired by a commercial scanner with 150 dpi resolution. 80 widths of fingers are obtained from binarized images. Wavelet transform, 20 Gabor filter and derivative method are used to extract the texture features from gray-scale images. Support Vector Machine (SVM) is the main classifier used as identifier and verifier. A feature, score and decision level fusion is implemented. An accuracy of 99.97% and an EER=0.0032% (Equal Error Rate) shown the final results of our system.

Index Terms - Biometrics, hand identificationlverification system, data fusion, Pattern Recognition and classification.

I. INTRODUCTION

Nowadays, the security systems are beginning to expand into the society because many studies have been focused on improving them. Most of the techniques used to develop these systems are based on ideas from palm-print image analysis [1]. Although these techniques let us to achieve good results, a highly accurate biometrics system can be built through the combination of palm-print texture and hand-geometry features. Both methods can be studied simultaneously with the extraction of one low-resolution image by means of a simple device which is well accepted by users. Therefore, we are going to review the techniques proposed by other authors in the field of hand-biometric technology, in order to locate our work in the biometric science.

Golfarelli et al. [2] proposed a hand biometric system made up of 100 people, 8 samples per person. Using the Bayes classification rule they obtained an EER=0.12%. Jain et al. [3] described a biometric system based on 16 hand-geometry features of 50 individuals, 10 samples per each one. The EER was 7.5%. Sanchez-Reillo et al. [4] presented a biometric system made up of 200 images of 20 people. They used 21 hand geometrical features and the ERR was lower than 5% independently of the classifier. Pavesic et al. [5] showed a finger lengths/widths and palm width system (24 features) using normalized Euclidean distance. With 110 registered and

Supported by The Spanish Ministry of Education and Science under the research project with reference "CICYT TEC2006-13141-C033-01ITCM"

978-1-4244-7402-8/10/$26.00 ©2010 IEEE

399 impostors the error rates were FAR=0.01 and FRR= 0.001. YbrOk et al. [6] described a hand-contour coordinates system (2048 points), made up of 458 people, 3 samples per person. The EER was between 0.01 and 0.02 using a modified Hausdorff distance. M. Adan et al. [7] proposed a hand biometric system based on 14 geometric features for each hand. Thanks to the normalized sum of feature deviation the FAR was 0.0045 and the FRR was 0.034. Morales et al. [8] showed a geometric-system made up to 20 people, 10 samples per person. The error rate was EER=3.4% using 40 finger widths for three fingers and using SVM (distance to separator hyperplane).

Goh et al. [9] presented a palm-print system made up of 75 individuals. It was based on wavelet transform and Gabor filter, with a verification result of 96.7% and an EER close to 4%. Liu et al. [10] showed a research about the use of wavelet transform in the palm-print. Classifying with the ISOOATA algorithm got a 95% of identification accuracy with 180 palm­print of 80 people. Masood et al. [11] developed a palm-print system using wavelet transforms. 50 people took part in the session (10 samples per person), reaching a 97.12% of accuracy with the combination of different wavelet families.

Guo et al. [12] described a BOCV system, (Binary Orientation Co-Occurrence Vector) based on the linking of six Gabor features vectors. 7752 samples from 193 people were taken. The error rate was 0.0189%. Zhang et al. [13] presented a novel 20+30 palm-print biometric system made up to 108 individuals. The EER was 0.0022%. Ribaric et al. [14] proposed a multimodal biometric identification system based on geometrical features and palm and finger-print texture. The error rates were FAR=O% and FRR=0.2%. 130 people took part in the test session. Van et al. [15] described a biometric system which combines 1-0 human features. A 97% of accuracy is reached (50 users, 10 samples each one) with the integration of palm-print, finger-print and geometry features. Ferrer et al [16] proposed a multimodal biometric system based on the combination of geometrical, palm and finger features of the human hand. A FAR=O% and FRR=0.15% are obtained when they work with 109 people.

Our goal is to improve the performance of existing palm­print or hand-geometry systems, combining both methods, and therefore, reaching an accuracy that may not be possible with single biometric method alone. We propose an identification­verification system using both features of human hand (see

Fig. 1). The hand-images are acquired thanks to a general scanner of 150 dots per inch, and they are stored with 256 gray levels, 8 bits per pixel. The size of these images is set to 1403x1021 pixels after scaling them by a factor of 20% to facilitate later computation. When a hand is detected, it is pre­processed to extract the hand-contour and the region of interest (ROI) of the palm (see Fig 2. (a». The hand-contour images let us to obtain the measurements of the hand and the ROI let us to analyze the palm-print texture. Once we have the evaluated data, they are introduced to the fusion module applying different algorithms to obtain a final score. The results show the effectiveness of our system, getting an identification­accuracy of 99.97% and a verification-EER of 0.0032%.

II. IMAGE PRE PROCESSING

After the images have been acquired we convert each one from 256 gray levels to a binary image, applying the next algorithm, where the threshold is obtained empirically with training samples:

If (originaUmage(i,j) < threshold) Then image(i,j)=O

If (originaUmage(i,j) > threshold) Then image(i,j)=1

To work out the tops and the valleys of the fingers, firstly, we localize the 4 fingers of the hand (through 8 initial points) with the exception of the thumb (see Fig 2. (b». Finding out the maximum of the contour between the 2 points of each finger we obtain the ends. Finding out the minimum between the 2 consecutive points of different fingers we obtain the valleys. Once the most important points of the hand are located, we can begin to work with the contour and the region of interest (see Fig 2. (a». Hand-contour is obtained subtracting the eroded hand-image from the dilated hand-image. The ROI is obtained after lining up the valley of the little finger with the valley of the hearth-index finger, so it no depends with the hand position and it has a vertical size of 300 pixels. The horizontal size can vary some pixels depending on the fingers gap. Once the ROI is obtained, wavelet transform, Gabor 2-D and derivative method will be applied.

Image Acquisition

Image PreProcessing

Fusion Module

Genuine Impostor

Figure 1. Block diagram of the proposed biometric system.

(a) (b)

Figure 2. (a) Hand-Contour and ROI; (b) Detection of the four fingers through 8 initial points.

III. FEATURES EXTRACTION

To extract the geometrical features vector, firstly, we calculate the straight lines which delimit the width of the fingers, so that we can obtain the slope of each finger by means of the average of the straight-lines-slope obtained before, so the slope will be irrespective of the separation between the fingers. Thus, drawing perpendicular lines through the length of the finger we can obtain the points where these lines cross with the contour of the hand, in order to calculate the Euclidean distance. In addition, we also calculate the length of the fingers between the end and the center of the base of the finger.

We have to decide the number of the widths of the fingers. We define "gap": the consecutive distance between two widths. For each finger of one hand, we have determined a specific gap which is calculated dividing the length of the smallest finger of the training database between the number of the wished widths. Low-zones of the fingers are not considered to obtain the widths, because these zones can be affected by the gap between the fingers (see Fig 3. (a».

IV. PALM-PRINT TEXTURE EXTRACTION

To extract texture features from palm-print images (see Fig 3. (b» we have applied 3 different algorithms:

A. Discrete Wavelet Transform (DWT) [17] We have used a successive chain of low filters with

cutoff=TT/2, in order to separate the thin details from the thick details of the palm-print image. It lets to emphasize the difference between the diverse gray levels. The size of the palm-print images is reduced to a different set of values after applying the successive filters. The DWT of a signal f (t) has the form of (1), where lJ1(t) is a family of wavelet functions:

DWT(j,k) = t:: J(t)· l/Jk(t)dt (1) . -j .

l/J�(t) = 22 'l/J(Z-J. t - k) j, k € Z

B. 20 Gabor filter [17] We have also applied a successive chain of Gabor filters,

which let us to know what pixels of the image belong to a specific texture. The image size is also reduced to a different set of values after filtering. The general form of the Gabor filter is:

(2)

where e is the filter orientation, f is the sine wave frequency, and a is the standard deviation. We will take the result from filtering with the odd (sine) Gabor filter.

C. A derivative method (first derivative by rows) It is based on the gray-scale changes which exist on the

palm-print, in order to determinate the changes in the texture. A different set of thresholds are used to binarize the obtained images after applying the derivative in the reduced images:

DCi,j) = ROlCi + 1,j) - ROI(i,j) i = 1, ... , rows j = 1, ... , columns (3)

V. CLASIFICATION SYSTEM

To evaluate the hand features we have used a neuronal network (NN) [18] or a support vector machine (SVM) [19] depending of the number of features. In the first case, multi­layer perceptron is the utilized scheme. Linear and RBF kernel are used in SVM, when it works as identifier (one-vs-all) or verifier (or closed set-verifier).

A. Geometric features We have used both classifiers to evaluate the data. The

number of hidden nerves cell in NN and the variable gamma value of the SVM kernel are optimized experimentally for each test.

B. Palm-Print features To identify/verify that an input hand belongs to a

determinate user/ the claimed identity, we calculate the distance of the input hand features to the separator hyperplane of the SVM that models the hand of the identity claimed. In the first case, the identified user is who has the highest distance to the hyperplane. Referring to verification, if the distance is greater than a threshold, the identity is accepted.

C. Fusion level We have checked the fusion at three levels: at feature,

score and decision level. In the feature level, we have combined geometrical and texture vectors and then, we have applied the most voted rule at decision level.

(a)

Figure 3. (a) Widths of the fingers; (b) Palm-Print.

Two different rules based on likelihood functions of individual verifier have been applied at score level:

(4)

where Ai is the model from SVM of the user i, and P(X'/Ai) is the likelihood function of feature vector from a test sample (X) against the model Ai. We have also applied the rule "the highest distance to the hyperplane" at decision level. On identification applications, if each method identifies a different user, the final identified user will be anyone whose distance to the hyperplane is higher. On verification applications, if at least one method accepts the user, it will be accepted by the final system provided that the distance to the hyperplane of the method which accepts the user was higher than the method which rejects it. If both methods accept the user, it will be verified and if both methods reject the user, it won't be accepted.

VI. EXPERIMENTAL RESULTS

We have collected 1440 samples from 144 users, 10 samples per user. Four images of each user are chosen randomly as training samples and the remaining six images are used to test the system. The results obtained with SVM are much better than those obtained with NN, therefore, we are going to show the SVM ones in average (%) and typical deviation (std). Each test has been done 10 times using lineal and RBF (radial basis functions) SVM kernels, finding the result through a cross-validation strategy.

In the first experiment, a different number of widths per finger and a different number of fingers per hand are used. Also, we have combined the widths with the fingers length (see result in Table I).

TABLE I IDENTIFICATION RESULTS OF GEOMETRICAL FEATURES

Fingers Recognition Recognition RBF

(widths per Lineal Rate (%) ± finger) std

Rate (%) ± std

2 fingers(10) 63.28% ± 4.1 6 98.88% ± 0.07 2 fingers(20) 85.88% ± 0.1 6 98.03% ± 0.01 3 fingers(10) 94.44% ± 0.38 99.77% ± 0.01 3 fingers(20) 97.49% ± 0.33 99.77% ± 0.05

3 fingers(10)+ 97.92% ± 0.01 99.31 % ± 0.1 6

length fingers 4 fingers(10) 99.46% ± 0.06 99.88% ± 0.01

4 fingers(20) 99.38% ± 0.02 99.90% ± 0.01 4 fingers(30) 98.78% ± 0.04 99.46% ± 0.06 4 fingers(40) 96.72% ± 0.03 99.1 5% ± 0.03

4 fingers(10)+ 99.58% ± 0.1 4 99.73% ± 0.06

length fingers

An accuracy of 99.90% is obtained when we acquire 20 widths per each one of the 4 fingers. If we combine widths and lengths the result is worse because the lengths depend on the space between the fingers. The efficiency of our system agrees with the other systems in the state of the art.

The second experiment shows what palm-print algorithm gets better results. It has been used 3 wavelet families: 'haar', 'db5' and 'bior5.5'. The ROI-size in wavelet analysis is obtained after applying 3 successive low filters, reducing it to 37x27 pixels. The size of the ROI used with Gabor algorithm is

reduced to 30x30 pixels after applying 1 Gabor filter, with A = TT/4, 8 = TT/2, ax = TT/2 and Oy = TT. After applying the expression 3 (derivative method) on the gray-scale palm print whose size is 35x35 pixels, a threshold of 3 is used. The result is shown in the Table II.

TABLE I I IDENTIFICATION RESULTS OF PALM-PRINT TEXTURE FEATURES

Recognition Lineal Recognition

Method RBF Rate (%) Rate (%) ± std

± std Haar 99.54% ± 0.01 99.73% ± 0.03

DbS 99.54% ± 0.01 99.31% ± 0.12

BiorS.S 99.76% ± 0.01 99.65% ± 0.02

2D Gabor 99.73% ± 0.03 99.73% ± 0.03 Derivative 99.46% ± 0.09 99.46% ± 0.13

These results agree with other results showed by other authors. The best texture method is the biortogonal (bior5.5), reaching higher accuracy than the obtained with the haar or db5 wavelet families. In the Table III, we show the results of the best methods of geometry and texture in identification and verification form and it combination. The threshold is calculated empirically. The gamma value of the kernel is g = 0.6'10-3 for widths and g = 0.7'10-8 for other situations.

TABLE 11/ IDENTIFICATIONNERIFICATION RESULTS OF THE BEST

GEOMETRICAL AND TEXTURE METHOD AND IT COMBINATION

Recognition Recognition Identification Lineal Rate RBF Rate (%) ±

(%) ± std std Wavelet biorS.S 99.76%±0.01 99.65% ± 0.02

Widths4fingers(20) 99.38%±0.02 99.90% ± 0.01 Feature fusion 99.76%±0.01 99.65% ± 0.02 Verification Threshold EER

Wavelet biorS.S -0.540 0.60% ± 0.02

Widths4fingers(20) -0.252 0.38% ± 0.01

Feature fusion -0.576 0.65% ± 0.01

Score fusion (sum) -0.110 0.028%±S.6e-3 Score fusion

-0.120 0.029%±4.4e-3 (product)

According to Table III we can conclude that the feature fusion is not possible because the size of texture-vector is much higher than the size of widths-vector, and if we use SVM, it is so important that the number of evaluated data of each method was the same to have a fair specific weight. The most voted rule (at decision fusion) does not have sense in this work. A higher accuracy and security system is proved if we implement a score fusion rule.

VII. FINAL SYSTEM RESULTS

Once we have the geometry and texture results, we introduce them to the fusion module to evaluate the decision fusion algorithm ("the highest distance to the hyperplane") and the final system. Table IV shows that one of both hand-features (widths or texture) works at least correctly in many times when a user tries to be identified or verified, getting us a 99.77% of recognition and a 0.0032% of EER.

TABLE IV PERFORMANCE OF THE PROPOSED SYSTEM

VIII. CONCLUSIONS AND FUTURE WORK

This paper presents a biometric identification-verification system based on the fingers-widths and palm-print features of the human hand using Support Vector Machines (SVMs). The results depict the improvement of the widths and Wavelet bior5.5 methods, combining them at score or decision level, getting a safer and higher accuracy system respectively, and the inefficiency of the feature fusion with the feature-vector obtained. We propose the combination of geometrical and palm-print data with other features applying the rules explicated in this work.

IX. REFERENCES

[1) "Palmprint Authentication", International Series on Biometrics, Zhang, D.o., Vol. 3, 256 p., 2004.

(2) M. Golfarelli, D. Maio and D. Maltoni, "On the Error-Reject Trade-Off in Biometric Verification Systems", IEEE Transactions on Pattem Analysis Machine Intelligence, Vol. 19, No. 7, pp.786-796,1997.

(3) A. K. Jain, A. Ross and S. Pankanti, "A Prototype Hand Geometry-based Verification System", 2nd Int. Conference on Audio- and Video-Based Pernal Authentication (AVBPA), Washington, pp. 166-171, March 1999.

(4) R. Sanchez-Reillo, C. Sanchez-Avila and A. Gonzalez Marcos, "Biometric Identification Through Hand Geometry Measurements", IEEE Transactions on Pattern Analysis Machine Intelligence, Vol. 22, No. 10, pp. 1168-1171, 2000.

(5) N. Pavesic, S. Ribaric, D. Ribaric, "Personal authentication using hand-geometry and Palmprint features", Proceedings of the Workshop on Biometrics at ICPR04, Cambridge, UK, 2004.

(6) E. Y6rOk, E. Konukoglu, B. Sankur, J. Darbon, "Shape­based hand recognition", IEEE Transaction on Image Processing, Vol. 15, Issue 7, pp. 1803-1815, July 2006.

(7) M. Adan, A. Adan, A.S. Vazquez, R. Torres, "Biometric verification/identification based on hands natural layout", Image and Vision Computing, Vol. 26, Issue 4, pp. 451-465, April 2008.

(8) A. Morales, M. Ferrer, F. Diaz, J. Alonso, C. Travieso, "Contact-free hand biometric system for real environments", Proceedings of the 16th European Signal ProceSSing Conference (EUSIPCO), Laussane, Switzerland, September 2008.

(9) Michael KO Goh, Tee Connie, Andrew BJ Teoh and David CL Ngo, "A Fast Palm Print Verification System", Proceedings of the International Conference on Computer Graphics, Imaging and Visualization, pp.168-172, July 2006.

(10) Fu Liu, Cai-Xia Lin, Ping-Yuan Cui, Tian Dong, "Palmprint recognition based on ISODATA clustering algorithm", Proceedings of the 2007 International Conference on Wavelet Analysis and Pattern Recognition, Vo1.3, pp. 1129-1133, Beijing, China, 2-4 Nov. 2007

(11) Hassan Masood, Mustafa Mumtaz, M. Asif Afzal Butt, Atif Bin Mansoor, Shoab A Khan, "Wavelet Based Palmprint

Authentication System", Biometrics and Security Technologies, 2008. ISBAST 2008. International Symposium on, pp. 1-7, April 2008.

[12] Zhenhua Guo, David Zhang, Lei Zhang y Wangmeng Zuo, "Palmprint verification using binary orientation co­occurrence vector", Vol. 30, pp. 1219-1227, May 2009.

[l3] David Zhang, Vivek Kanhangad, Nan Luo y Ajay Kumar, "Robust palm print verification using 20 and 3D features", Vol. 43, pp. 358-368, January 2009.

[l4] S. Ribaric, D. Ribaric, N.Pavesic, "Multimodal Biometric user- identification system for network-based applications", lEE Proceedings on Vision, Image and Signal Processing, Vol. 150, No.6, pp. 409-416, December 2003

[15] Hui Yan, Duo Long, "A novel bimodal identification approach based on hand-print", Proceedings of the 2008 Congress on Image and Signal Processing, Vol.4, pp.506-510, 2008.

[l6] Miguel A. Ferrer, Aythami Morales, Carlos M. Travieso, Jesus B. Alonso, "Low Cost Multimodal Biometric identification System Based on Hand Geometry, Palm and Finger Print Texture", 41st Annual IEEE International Carnahan Conference on Security Technology, pp. 52-58, 2007.

[17] R.C. Gonzalez, R.E., Wood, "Digital Image Processing", Ed. Addison-Wesley, 2008.

[l8] Christopher M. Bishop, "Neural Networks for Pattern Recognition", Oxford University Press, 1995.

[l9] Steinwart, I.; Christmann, A.: "Support Vector Machines". Ed. Springer, New York, 2008.


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