Biometric identification is an emerging subject in applications like high-security wireless access and secure transactions across computer networks. Fingerprints are easy to use and provide relatively good performance. Furthermore, fingerprint sensors are cheap and can be integrated easily in wireless hardware. In this paper, methods are presented for the estimation of a high resolution directional field from fingerprints. It is shown how, from the directional field, very accurate detection of the singular points and the orientations of those points can be obtained. These estimates can for instance be used for accurate registration (alignment) of two fingerprints in a fingerprint verification system

Bazen, A.M.

Gerez, S.H.

Gerez, Sabih H.

University of Twente Research Information

Mobile Communications in Perspective, Annual CTIT Workshop, Enschede, The Netherlands,University of Twente, Center for Telematics and Information Technology, February 2001.Extraction of Singular Points from Directional Fields ofFingerprintsAsker M. Bazen and Sabih H. GerezUniversity of Twente, Department of Electrical Engineering,Laboratory of Signals and Systems,P.O. box 217 - 7500 AE Enschede - The NetherlandsPhone: +31 53 489 3827 Fax: +31 53 489 1060a.m.bazen@el.utwente.nlKeywords: Wireless access, image processing, fingerprint recognition, orientation estimation, singular point extraction,registration.AbstractBiometric identification is an emerging subject in appli-cations like high-security wireless access and secure trans-actions across computer networks. Fingerprints are easy touse and provide relatively good performance. Furthermore,fingerprint sensors are cheap and can be integrated easilyin wireless hardware.In this paper, methods are presented for the estimationof a high resolution directional field from fingerprints. Itis shown how, from the directional field, very accurate de-tection of the singular points and the orientations of thosepoints can be obtained. These estimates can for instancebe used for accurate registration (alignment) of two finger-prints in a fingerprint verification system.1. IntroductionBiometric identification is an emerging subject in appli-cations like high-security wireless access and secure trans-actions across computer networks. The use of features di-rectly connected to someone’s body significantly decreasesthe probability of fraud.Among many other biometric features like iris, face,voice, hand geometry, retina, etc., fingerprints are easy touse and provide relatively good performance. Another rea-son for the increasing popularity of the use of fingerprintsfor identification is the relatively low price of fingerprintsensors. Smart cards with built-in fingerprint sensors arealready available on the market, and the sensors can be in-tegrated easily in wireless hardware.120 130 140 150 160 170 180145150155160165170175180185190195200(a) Core130 140 150 160 170 180215220225230235240245250255260265270(b) DeltaFigure 1: Examples of singular points in a fingerprint.As can be seen from Figure 1, a fingerprint is built fromridge-valleystructures. In this figure, the ridges are blackand the valleys are white. When using fingerprints forrecognition systems, the ridge-valley structures are the mainsource for the information to be extracted from the finger-prints.2. Directional field estimationThedirectional field(DF) describes the coarse structure,or basic shape, of a fingerprint. The DF is defined as thelocal orientation of the ridge-valley structures. The DF isfor instance used for classification of fingerprints. In [1], amethod is presented for the estimation of a high-resolutionDF. The main results are repeated here.The method is based on the gradient vector[Gx(x, y) Gy(x, y)]T of the gray-scale imageI (x, y),Mobile Communications in Perspective, Annual CTIT Workshop, Enschede, The Netherlands,University of Twente, Center for Telematics and Information Technology, February 2001.which is defined by:[Gx(x, y)Gy(x, y)]= ∇ I (x, y) =[∂ I (x,y)∂x∂ I (x,y)∂y](1)The DF is, in principle, perpendicular to the gradients.However, the gradients are orientations at pixel scale, whilethe DF describes the orientation of the ridge-valley struc-tures. This requires a much coarser scale in which localfluctuations do not have influence. Therefore, the DF can bederived from the gradients by performing someaveragingoperation on the gradients, involving pixels in some neigh-borhood [2].Gradients cannot simply be averaged in some localneighborhood, since opposite gradient vectors will then can-cel each other, although they indicate the same ridge-valleyorientation. A solution to this problem is to double the an-gles of the gradient vectors before averaging. Then, oppo-site gradient vectors will point in the same direction andtherefore will reinforce each other, while perpendicular gra-dients will cancel. After averaging, the gradient vectorshave to be converted back to their single-angle representa-tion. The main ridge-valley orientation is perpendicular tothe direction of the average gradient vector. This methodwas proposed by [3] and was adopted in some way for theestimation of the DF of fingerprints by various researchers.In the version of algorithm used in this paper, not onlythe angle of the gradients is doubled, but also the lengthof the gradient vectors is squared, as if the gradient vectorsare considered as complex numbers that are squared. Thishas the effect that strong orientations have a higher vote inthe average orientation than weaker orientations and this ap-proach results in the cleanest expressions.Another difference with the methods of other researchersis that we do not estimate the average DF for a numberof blocks in the image. Instead, the DF is estimated foreach pixel in the image using a Gaussian windowW foraveraging. UsingGxx =∑W G2x , Gyy =∑W G2y andGxy =∑W Gx Gy, the average gradient directionθ , with−12π < θ ≤ 12π , is given by:θ = 126 (Gxx − Gyy,2Gxy) (2)3. Singular point extractionSingular points(SPs) are the discontinuities in the DF.They are clearly visible in a fingerprint image, as can beseen from Figure 1, which shows examples of the two dif-ferent types of SPs that are calledcoreanddelta. SPs canfor instance be used for the registration (alignment) of twofingerprints of the same finger.Many different algorithms for SP extraction are knownfrom literature. Examples of these algorithms are based on140 145 150 155 160162164166168170172174176178180(a) DF140 145 150 155 160162164166168170172174176178180(b) Squared DF140 145 150 155 160162164166168170172174176178180(c) Gradient140 145 150 155 160162164166168170172174176178180(d) RotationFigure 2: Processing steps in the extraction of a core.sliding neural networks [4], local energy of the DF [5], ra-tio of the sine of the DF in two adjacent regions [6], andthe Poincar´e index [7]. However, these algorithms providesomewhat unsatisfactory results, since they provide contin-uous measures that indicate how much the local DF resem-bles a SP. Postprocessing steps are necessary to interpret theoutputs of the algorithms and to make the final decisions,resulting in missed and false SPs.The method that is presented here, is based on thePoincaré index [7]. It can be explained using Figure 2(a).Following a counter-clockwise closed contour in the DFaround a core results in a cumulative change ofπ in the ori-entation, while carrying out this procedure around a deltaresults in−π . On the other hand, when applied to a loca-tion that does not contain a SP, the cumulative orientationchange will be zero.Although the Poincar´e index provides means for consis-tent detection of SPs, the question arises how to calculatethis measure. Apart from the problem of how to calculatecumulative orientation changes over contours efficiently, achoice has to be made on the optimal size and shape ofthe contour. A possible implementation is described in [8],which claims that a square curve with a length of 25 pixelsis optimal. A smaller curve results in spurious detections,while a larger curve may ignore core-delta pairs which areclose to each other. Postprocessing steps interpret the re-sults.In the implementation that is proposed in this paper, suchchoices don’t have to be made. The method generates anMobile Communications in Perspective, Annual CTIT Workshop, Enschede, The Netherlands,University of Twente, Center for Telematics and Information Technology, February 2001.exact binary output that indicates whether a SP is present ornot. It doesn’t need postprocessing steps and the cumulativeorientation changes over contours are implemented very ef-ficiently in standard 2-dimensional filters. Furthermore, themethod is capable of detecting SPs that are located only afew pixels apart.In the rest of the text, all calculations are made for thecase of a core. It is left to the reader to adapt them to the caseof a delta. First, the squared DF is taken. This eliminatesthe transition ofπ which is encountered in the DF betweenthe orientationsθ = 12π andθ = −12π . As a result, thePoincaré index is doubled. The orientation of the squaredDF is depicted in Figure 2(b) for the area around the coreexample.Instead of summing the changes in orientation, it is pos-sible to sum the gradients of the squared orientation as well.The gradient vectorJ can be efficiently precalculated for theentire image by:[Jx(x, y)Jy(x, y)]= ∇2θ(x, y) =[∂2θ(x,y)∂x∂2θ(x,y)∂y](3)In the calculation of the discrete version of this gradient,both components ofJ should be calculated ‘modulo 2π ’,such that they are always between−π andπ . This makesthe transition from 2θ = −π to 2θ = π continuous or, inother words, the orientation is considered to be cyclic. Thegradient vectors of the squared orientation around the coreis shown in Figure 2(c).The next step is the application of Green’s Theorem,which states that instead of calculating a closed line-integralover a vector field, the surface integral over the rotation ofthis vector field can be calculated. This theorem is appliedto the summation of the gradients of the squared orientationover the contour:∑∂AJx + Jy =∑Arot[Jx Jy]T =∑A(∂ Jy∂x− ∂ Jx∂y)(4)whereA is the area and∂A is the contour.Since the DF is assumed to be smooth,A can be takenas small as a square of 1× 1 pixel. This results in a veryefficient method for computation of the Poincar´e index. Ap-plication of the proposed method will indeed lead to the de-sired SP locations. Unlike all other SP extraction methods,a core results in a Poincar´e index of 2π , a delta in−2πwhile the index for the rest of the image is exactly equal to0. This is illustrated in Figure 2(d) for the core example andthe area around it.4. Orientation of singular pointsThe last subject of this paper is the estimation of theori-entationsϕ of the extracted SPs. The method that is de-140 145 150 155 160162164166168170172174176178180(a) Squared DF140 145 150 155 160162164166168170172174176178180(b) Reference Core140 145 150 155 160162164166168170172174176178180(c) Conjugated140 145 150 155 160162164166168170172174176178180(d) OrientationFigure 3: Processing steps in the calculation of the ori-entation of a core.scribed here, makes use of the squared gradient vectors inthe neighborhood of an SP, both for the image to be ana-lyzed and for the reference SP. The averaged squared gra-dients of the core, repeated in Figure 3(a), ideally looklike the reference model in Figure 3(b). For a core at(x, y) = (0,0), this reference model is given by:CoreRef = (y,−x)√x2+ y2(5)The usefulness of the squared gradients is caused by thefact that, when the gray-scale image rotates around the core,in effect all components of the averaged squared gradientmatrix rotate over the same angle. Therefore, the model ofa core that has rotated over an angleϕ is given by a referencemodel with all its components multiplied bye jϕ.Coreϕ = CoreRef · e jϕ (6)This property is used for the estimation of the orientationof the core. The orientation of the core, with respect to thereference model, is found by taking the inner product of theestimated squared gradient data and the complex conjugatedof the reference model, depicted in Figure 3(c). Then, it isdivided by the number matrix elementsN , and the angle istaken.ϕ̂ = 6 1N∑x,yCore∗Ref(x, y) · CoreObs(x, y) (7)Mobile Communications in Perspective, Annual CTIT Workshop, Enschede, The Netherlands,University of Twente, Center for Telematics and Information Technology, February 2001.The averaging operator provides an accurate estimate forthe orientationϕ, while, if the observed core is exactly arotated version of the reference core, this estimate gives:ϕ̂ = 6 1N∑x,yCore∗Ref(x, y) ·CoreRef(x, y) · e jϕ= 6 1N∑x,y|CoreRef(x, y)|2 · e jϕ (8)= 6 e jϕ = ϕFor a delta, a related reference model can be made. Be-cause of the symmetries in a delta, its relative orientationwith respect to the reference model is given by one third ofthe angle resulting from Equation 7, which was used for acore.5. ConclusionsIn this paper, methods have been presented for the es-timation of a high resolution directional field from finger-prints. It is shown how, from the directional field, very ac-curate detection of the singular points and the orientationsof those points can be obtained. These estimates can for in-stance be used for accurate registration (alignment) of twofingerprints in a fingerprint verification system.References[1] A.M. Bazen and S.H. Gerez, “Directional field compu-tation for fingerprints based on the principal componentanalysis of local gradients,” inProceedings of ProR-ISC2000, 11th Annual Workshop on Circuits, Systems andSignal Processing, Veldhoven, The Netherlands, Nov. 2000,Available from http://www.sens.el.utwente.nl/research/imageproc/fingiden.shtml .[2] T. Lindeberg, Scale-Space Theory in Computer Vision,Kluwer Academic Publishers, Boston, 1994.[3] M. Kass and A. Witkin, “Analyzing oriented patterns,”Com-puter Vision, Graphics, and Image Processing, vol. 37, no. 3,pp. 362–385, Mar. 1987.[4] G.A. Drets and H.G. Liljenstr¨om, “Fingerprint subclassifica-tion: A neural network approach,” inIntelligent BiometricTechniques in Fingerprint and Face Recognition, L.C. Jain,U. Halici, I. Hayashi, S.B. Lee, and S. Tsutsui, Eds., pp. 109–134. CRC Press, Boca Raton, 1999.[5] P. Perona, “Orientation diffusions,”IEEE Transactions OnImage Processing, vol. 7, no. 3, pp. 457–467, Mar. 1998.[6] A.K. Jain, S. Prabhakar, L. Hong, and S. Pankanti,“Filterbank-based fingerprint matching,”IEEE Transactionson Image Processing, vol. 9, no. 5, pp. 846–859, May 2000.[7] M. Kawagoe and A. Tojo, “Fingerprint pattern classification,”Pattern Recognition, vol. 17, no. 3, pp. 295–303, 1984.[8] L. Hong and A.K. Jain, “Classification of fingerprint images,”in Proceedings of 11th Scandinavian Conference on ImageAnalysis, Kangerlussuaq, Greenland, June 1999.

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Extraction of Singular Points from Directional Fields of Fingerprints

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