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A Novel Technique of Fingerprint Identification Based on Sectorization of Complex Walsh Plane Dr. H. B. Kekre, Dr. Tanuja K. Sarode and Rekha Vig Abstract— In this paper a new method for fingerprint identification has been described. This method treats the digitized fingerprint images in transform domain using well known Walsh transform.To map these coefficients onto two dimentional plane, we have proposed complex Walsh Transform. A sectorization algorithm, which creates sectors of the complex Walsh plane, is applied to the image transforms, which helps in generating the feature vectors of the images. The feature vector (set of features) of a test image is compared with those stored in the database and a match is solicited. This algorithm has been implemented on a database of 168 fingerprint images and the measures GAR(Genuine Acceptance Rate), FRR(False Reject Rate) and average number of matches calculated show that this algorithm though simple can be effectively used in Automated Fingerprint Identification Systems. Index Terms—Fingerprint identification, Walsh transform, complex plane, security, biometrics, sectorization.

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1 INTRODUCTION

I

dentification of a person has become an important issue and is also a major concern in security related areas like airports etc. An individual can be uniquely identified with the help of his biometric features, which may involve his physical or behavioural traits[1][2][13]. These biometrics may include fingerprints, iris, voice etc. which are being most commonly used. A complte list of biometrics is shown in figure 1. Though fingerprint as biometric trait is more prevalent, other biometrics like face, iris etc are becoming increasingly popular[4][5]. Any biometric system works in two phases, 1) Enroll-

trics is generated which generally stores certain features of the biometrics of those individuals, rather than the complete biometric as image or signal. These features are extracted using certain algorithm and are called templates. In the identification phase, when the identity of an individual is sought, he offers his same biometric and using same algorithm the template is generated and compared with those in the databse[1][2]. An imposter will not be identified as his template will not be present in the database[9]. The heart of any biometric system is the method or the algorithm which has been used to extract the features of biometrics[14]. Other than this, the method of generating digitized biometric, measures used to match the features with those in database etc are to be considered. The most

Fig. 1. Different types of biometrics

ment phase 2) Identification Phase as shown in figure 2. In the enrollment phase, all individuals enroll themselves with the biometrics system by offering a digitized version of their respective biometric. A database of these biome-

Fig. 2. Two stage biometric system

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• Dr. H. B. Kekre is with Department of Computer Science, MPSTME, NMIMS University, Mumbai India. • Dr. Tanuja K. Sarode is with the Department of Computer Science, TSEC, Mumbai, Indis. • Rekha Vig is with the Electronics and Telecommunication Engineering Department, MPSTME, NMIMS University, Mumbai India.

important paramaters for the evaluation of a biometric system are accuracy in terms of Genuine Acceptance Rate (GAR) and False Acceptance Rate (FAR) Genuine Acceptance Ratio (GAR): Depending on the choice of threshold, the legitimate users’ biometric that

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are genuinely accepted by the system can be from none to all images. A legitimate user is an individual that is verified against the givendatabase. The threshold of the genuinely accepted data divided by the number of all legitimate user data is called Genuine Acceptance Ratio (GAR). Its value is one, then all legitimate users are accepted, and zero if no legitimate user is accepted.[10] False Acceptance Ratio (FAR): Depending on the choice of threshold, the impostor’s biometric that are falsely accepted by the system can be from none to all images. Impostor is an individual that is verified against a different stored database. The threshold of the falsely accepted data divided by the number of all impostor data is called False Acceptance Ratio (FAR). Its value is one, if all impostor data are falsely accepted, and zero if none of the impostor data is accepted[10]. Fingerprint as biometrics have gained enormous popularity due to the following reasons[15]. • Easy to use • Cheap • Small size • Low power • Non-intrusive • Large database already available Though many automated fingerprint identification systems are in use throughout the world, certain issues like accuracy, ease of implementation etc. leave a gap for research. There are various methods of extracting the features of fingerprint images.They are basically categorized into two types: 1) Image-based (Spatial domain)[[4][5] , 2) Transform-based (Transform domain)[6][16]. In image based methods the fingerprint image is processed in spatial domain to generate the features, whereas in transform domain[3] the fingerprint image is transformed using any orthogonal transform and the feature vector is then generated[7][8]. In this paper a transform domain method to identify fingerprints has been used. Walsh transform[11][17], an orthogonal transform is used to generate the Walsh coefficients of the fingerprint, which are projected on a complex plane. This plane is subjected to sectorization[16], and the features are then generated by taking the mean of coefficients of each sector. The sections followed are organized in the following manner. Section 2 explains the generation of Walsh coefficients and the subsequent sectorization method. Further, section 3 discusses the implementation and result and section 4 concludes the paper.

2 WALSH COEFFICIENT GENERATION AND SECTORIZATION 2.1 Walsh Transform The fingerprint image, 256 X 256 pixels is subjected to Walsh matrix (256 X 256) and a 2-D Walsh transform is generated. The coefficients of this 2-D Walsh transformed image are such that the top left pixel is the DC component and the sequency component increases as we move towards right or down. The basic set of eight Walsh functions is shown in figure 3. They are generated from

square functions and are named as cal or sal functions (analogous to cos and sin functions). The corresponding cal and sal coefficients for the 2-D Walsh transform are as shown in figure 4.

C0 =W0 S1 =W1 C1 =W2 S2 =W3 C2 =W4 S3 =W5 C3 =W6 S4 =W7 Fig. 3. Set of eight Walsh functions The cal and sal components are paired together as explained further to form complex values and these are then transformed onto two separate complex 2-D planes, one for cal components called the even pairs and the other for sal components called the odd pairs. These planes are then subjected to sectorization to generate feature vector.

2.2 Pairing of Walsh components The cal and the sal components of Walsh transform matrix except the first and last row and first and last column are paired together to form complex values Ck and Sk such that Ck = Cm,n + i*Cm+1,n+1 for m,n = 1,3,5……n-1 and Sk = Sm,n+1 + i*Sm+1,n for m,n = 1,3,5……n-1 These complex values Ck and Sk are then projected onto two separate complex planes as shown in figure 5.

TABLE 1 WALSH TRANSFORM COEFFICIENTS C00

S01

C02

S03

C04

…

C0n-1

S0n

S10

C11

S12

C13

S14

…

S1n-1

C1n

C20

S21

C22

S23

C24

…

C2n-1

S2n

S30

C31

S32

C33

S34

…

S3n-1

C3n

C40

S41

C42

S43

C44

…

C6n-1

S4n

S50

C51

S52

C53

S54

…

S5n-1

C5n

.

.

.

.

.

…

.

.

Sn0

Cm1

Sm2

Cm3

Sm4

…

Smn-1

Cmn

2.2 Sectorization of Complex planes

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The processing speed of an automated fingerprint identification system largely depends on the size of the feature vector. The smaller the size, the faster is the system. If all the coefficients of the transformed Image are taken as

Sectors

Criteria

I, IV, VI and VII

If imag < real

II, III, V and VIII

If imag >= real

TABLE 3 CRITERIA FOR TWELVE SECTORS Sectors

Criteria

I, VI, VII and XII

If imag < real*tan(I/6)

II, V, VIII and XI

If imag >= real*tan(I /6) and imag < real*tan(I /3)

Fig. 4. Complex plane showing cal paired coefficients

III, IV, IX and X

If imag >= real*tan(I /3)

The features obtained from the test image are compared with those obtained from the stored fingerprint in the database. This comparison is done separately for each complex plane and the results for both are fused together to get the final matching results

Fig. 5. Complex plane showing Sal paired coefficients

feature vector, the size of feature vector would be 256X256. Hence in order to reduce the size of feature vector method of sectorization is used here. The complex planes are divided into 4, 8 and 12 sectors as shown in figure. Here first the complex plane is divided into 4 sectors, the division being same as those of the quadrants of a plane as shown in figure 2.For more number of sectors i.e. 8 and 12 sectors as shown in Figure 6, the 4-sector plane is considered as the basic entity and the criteria shown in the tables 2 and 3 are applied for division. The sectors generated are radial and the mean values of the transform coefficients in each sector are calculated as in equation (4), where Mk is the mean and N is the number of coefficients in a sector, which form the features. The feature vector consists of the DC component, mean of absolute values of first row, mean of absolute values of last row, mean of absolute values of first column, mean of absolute values of last column and all Mk , mean value of each sector, and hence the number of features is S+5 for each complex plane, where S is the number of sectors. (1)

TABLE 2 CRITERIA FOR EIGHT SECTORS

a)

b)

Fig. 6. . Sectorization of complex plane of Walsh transform coefficients a) 8-sectors b) 12-sectors

3 EXPERIMENTAL RESULTS AND DISCUSSION In this section, the details of the database of fingerprint images and the results obtained from the approaches described above for fingerprint have been explained. In this experiment, we have used the fingerprint image database containing 168 fingerprint images of size 256×256 pixels including 8 images per finger from 21 individuals. The set of fingerprints are obtained with rotational ( +/- 15o ) and shift (horizontal and vertical) variations. Testing was performed using MATLAB 9 on Intel Core 2 Duo 2.10 GHz processor with 2 GB RAM. To test the performance of proposed fingerprint identifi-

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cation techniques, total 168 queries are fired on the databases to compute GAR values per query. The similarity measure which is used for matching of query with database images used here is Euclidian distance. Tables 4 and 5 summarize the results obtained for the algorithm mentioned above. Second column of each table TABLE 4 VALUES OF GAR Sectors 4 8 12

For CalCoefficients 74.2 84.3 89.4

For SalCoefficients 75.7 84.23 88.56

Fused Results 88.82 90.82 92.65

TABLE 5 AVERAGE NUMBER OF MATCHED FINGERPRINTS Sectors

For CalCoefficients

For SalCoefficients

Fused Results

4 8 12

3.28 3.61 3.74

3.33 3.56 3.86

3.43 3.76 3.93

show the GAR and the average number of matches for a fingerprint out of 7 samples of that fingerprint in the database and the third column for that of sal-coefficients. The values in the final column show the fused results of column 2 and 3, which have been generated by choosing the best (OR) of the cal and sal coefficient methods. The GAR obtained is 0.9265 for 12 sectors and hence the FRR is 0.0735 as shown in figures 7 and 8. The second measure i.e. average number of matches depicts that more than half the number of images in database (7 samples per fingerprint) are being obtained as matches.

4 CONCLUSION A fingerprint identification method has been discussed in this paper which deals with the Walsh transform of the fingerprint images. Though Walsh transform is not complex in nature, it has been converted into complex values to project it onto a complex four-quadrant plane, for the purpose of sectorization. Sectorization of a four-quadrant plane into 4, 8 and 12 sectors has been done in order to generate features which are the mean values of coefficients of various sectors. The Euclidean distance between the features of a test image and those of stored (database) images has been calculated and the matched results shown and discussed. The GAR achieved with this method is as high as 92.65% and the maximum value of average number of matches of a fingerprint is 3.93 out of 7 sample database images of the same fingerprint. These results demonstrate that this technique can be successfully used in Automated Fingerprint Identification Systems.

REFERENCES [1] [2] [3] Fig. 7. Comparison of average number of matches obtained out of 7 samples of the same fingerprint in the database

[4]

[5]

[6]

[7]

Fig. 8. Comparison of GAR obtained

L. Jain et al., Intelligent Biometric Techniques in Fingerprint and Face Recognition, CRC Press, 1999. D. Maltoni, D. Maio, A. Jain, and S. Prabhakar, Handbook of Fingerprint Recognition. New York: Springer, 2003. Gonzalez Rafael C., Woods Richard E., “Digital Image Processing,” 3rd edition. Prentice Hall, 2008. Anil Jain, Arun Ross, Salil Prabhakar, “Fingerprint matching using minutiae and texture features,”Proc. Int’l conference on Image Processing (ICIP), pp. 282-285, Oct. 2001. . (Conference proceedings) L. Hong, Y. Wan, and A.K. Jain, "Fingerprint Image Enhancement: Algorithms and Performance Evaluation", IEEE Trans. on Pattern and Machine intell, Vol. 20, No. 8, pp. 777-789, August 1998. H. B. Kekre, Tanuja K. Sarode, Vinaya M. Rawool, “Finger Print Identification using Discrete Sine Transform (DST)” International Conference on Advanced Computing & Communication Technology (ICACCT-2008) Asia Pacific Institute of Information Technology, Panipat India 8-9 Nov 2008 H. B. Kekre, Tanuja K. Sarode, Vinaya M. Rawool, “Fingerprint Identification using Principle Component Analysis (PCA)” International Conference on Computer Networks and Security (ICCNS08) held at VIT Pune, 27-28,September 2008

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[8]

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H. B. Kekre, Tanuja K. Sarode , Sudeep D. Thepade, “DCT Applied to Column Mean and Row Mean Vectors of Image for Fingerprint Identification” Proc. Int. Conf. on Computer Networks and Security (ICCNS08) ,Sept. 2008. (Conference proceedings) John Berry and David A. Stoney “The history and development of fingerprinting,” in Advances in Fingerprint Technology, Henry C. Lee and R. E. Gaensslen, Eds., pp. 1-40. CRC Press Florida, 2nd edition, 2001. Arun Ross, Anil Jain, James Reisman, “A hybrid fingerprint matcher,” Int’l conference on Pattern Recognition (ICPR), Aug 2002. . (Conference proceedings) H.B.Kekre, Dhirendra Mishra, “Four Walsh Transform Sectors Feature Vectors for Image Retrieval from Image Databases” Int. Journal of Computer Science and Information Technology (IJCSIT) Vol. 01, No. 02, 2010 D. Maio and D. Maltoni, “Direct gray-scale minutiae detection in fingerprints,” IEEE Tran. On Pattern Anal. Machine Intell.,vol. 19 no. 1 , pp. 27-40, 1997. John Berry and David A. Stoney ―”The history and development of fingerprinting”, in Advances in Fingerprint Technology, Henry C. Lee and R. E. Gaensslen, Eds., pp. 1-40. CRC Press Florida, 2nd edition, 2001. Emma Newham, ―The biometric report, SJB Services, 1995. A. K. Jain, L. Hong, Y. Kulkarni ―”A Multimodel Biometric System using Fingerprint, Face, and Speech” Proc.2nd Int’l Conference on Audio- and Video-based Biometric Person Auhentification, Washington D.C., pp. 182-187, 1999. Federal Bureau of investigation, “The Science of Fingerprints: Classification and Uses”, Washington, D.C., 1984, U.S. Government Printing office. H.B.Kekre, Tanuja K. Sarode, Rekha Vig, “Fingerprint Identification using Sectorized Cepstrum Complex Plane”. International Journal of Computer Applications (IJCA) Volume 8– No.1, October 2010 H.B.Kekre, Tanuja K. Sarode, Rekha Vig, “Sectorized Row and Column Walsh Transform based Fingerprint Identification”. International Journal of Computer Applications (IJCA) ICWET/Number 2, June 2011

Dr. H. B. Kekre has received B.E. (Hons.) in Telecomm. Engg. from Jabalpur University in 1958, M.Tech (Industrial Electronics) from IIT Bombay in 1960, M.S.Engg. (Electrical Engg.) from University of Ottawa in 1965 and Ph.D. (System Identification) from IIT Bombay in 1970. He has worked Over 35 years as Faculty of Electrical Engineering and then HOD Computer Science and Engg. at IIT Bombay. For last 13 years worked as a Professor in Department of Computer Engg. at Thadomal Shahani Engineering College, Mumbai. He is currently Senior Professor working with Mukesh Patel School of Technology Management and Engineering, SVKM’s NMIMS University, Vile Parle(w), Mumbai, INDIA. He has guided 17 Ph.D.s, 150 M.E./M.Tech Projects and several B.E./B.Tech Projects. His areas of interest are Digital Signal processing, Image Processing and Computer Networks. He has more than 350 papers in National / International Conferences / Journals to his credit. Recently thirteen students working under his guidance have received best paper awards. Four of his students have been awarded Ph. D. of NMIMS University. Currently he is guiding eight Ph.D. students. He is fellow of IETE and life member of ISTE.

Dr. Tanuja K.Sarode has received M.E.(Computer Engineering) degree from Mumbai University in 2004, Ph.D. from Mukesh Patel School of Technology, Management and Engg., SVKM’s NMIMS University, Vile-Parle (W), Mumbai, INDIA. She has more than 11 years of experience in teaching. Currently working as Assistant Professor in Dept. of Computer Engineering at Thadomal Shahani Engineering College, Mumbai. She is member of International Association of Engineers (IAENG) and International Association of Computer Science and Information Technology (IACSIT). Her areas of interest are Image Processing, Signal Processing and Computer Graphics. She has 90 papers in National /International Conferences/journal to her credit Rekha Vig has received B.E. (Hons.) in Telecomm. Engg. from Jabalpur University in 1994 and M.Tech (Telecom) from MPSTME, NMIMS University in 2010. She is working as Assisstant Professor in the Department of Electronics and Telecommunications in Mukesh Patel School of Technology Management and Engineering, NMIMS University, Mumbai. She has more than 12 years of teaching and approximately 2 years of industry experience. She is currently pursuing her Ph.D. from NMIMS University, Mumbai. Her areas of specialization are image processing, digital signal processing and wireless communication. Her publications include more than 15 papers in IEEE international conferences, international journals and in national conferences and journal.

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