DSpace at VNU: An efficient method for fingerprint matching based on local point model

An Efficient Method for Fingerprint Matching Based on Local Point Model Nguyen Thi Huong Thuy1, Hoang Xuan Huan2, and Nguyen Ngoc Ky1 Information Technology Faculty, Vietnam National University - Hanoi College of Technology, huanhx@vnu.edu.vn General Department of Technique - Logistic, Vietnam Ministry of Public Security huongthuykta@yahoo.com, kynguyen22@gmail.com Abstract - This paper proposes a fingerprint matching method based on local Thin-Plate-Spline (TPS) deformation model, a warping technique, to deal with non-linear distorted fingerprints After determining the set of corresponding minutiae pairs between two fingerprints by using an affine transformation, a set of corresponding pseudo-minutiae pairs are created based on their local ridge-valley structure comparison These points are associated with the known corresponding point pairs to select a suitable landmark point set for using Local Thin Plate Spline deformation model over partial areas of fingerprint images in order to find new corresponding minutiae pairs This procedure is repeated until no more new corresponding minutiae pairs are distinguished or the number of corresponding point pairs is large enough The experimental results on the database FVC2004 show that the proposed method significantly improves matching performance compared to the global TPS warping method Keywords: Fingerprint verification; Minutiae matching; Elastic deformations; Thin-Plate-Spline models; Local deformation models I INTRODUCTION Automatic Fingerprint Identification and Authentication (AFIA) is a biometric technology which had been considered for a long time [13] but it is still an active research area [4, 7, 8, 13, 15] In the fingerprint identification system, the matching algorithm is the most important stage Many fingerprint matching algorithms have been published [4, 7, 8, 13, 14, 15], and can be classified into three main categories [12] based on: minutiae sets, texture and greyscale correlation The minutiae based [5, 7-11, 15, 19], the most widely used algorithm, is of concern in this paper In a fingerprint image, minutiae such as end points or bifurcation points are called the minutiae In order to match the query fingerprint image Iq with the template fingerprint image It in a database, a general approach of the fingerprint matching algorithm based on minutiae attempts to estimate the affine transformation to align two minutiae sets of two fingerprint images originated from the same finger so that the respective minutiae pairs “match fit” together in pairs The most popular but simple deformation is affine deformation (combining translation, rotation and scale) However, in general, distorted fingerprint is non-linear therefore the mathematical efficiency using affine transformation is limited Nowadays, it usually used for simple matching as an initial stage and then warping methods are applied [10, 12] to determine the similarity scores of two fingerprints Amanssa et al [1] and other authors [2, 5, 11, 12, 17] used additional sheets tuning adapter model (thin-plate spline: TPS) in this procedure Particularly, after using affine transformation to calculate the number of corresponding minutiae pairs, Li et al [12] used these corresponding minutiae pairs for landmark points which help warping TPS and combined with greyscale 978-1-4673-2088-7/13/$31.00 ©2013 IEEE correlation to decide the similarity This method is called global TPS In global TPS, we have to calculate local correlation and solve simultaneous linear equations The size of these linear equations directly proportionates to the number of landmark points It normally takes a considerable amount of calculation time when landmark points are large Moreover, this method cannot process distorted fingerprints in image’s area which is far from landmark point pairs In facts, the efficiency of warping TPS depends on the distribution of landmark points on fingerprint images Points, which are far from landmark points, will be variously affected by non-linear distortion and give different matching results Furthermore, by using affine transformations, the originally detected landmark points are normally focused on the little nonlinear deformed area It makes a paradox: the no need warping and less distorted areas contain too much landmark points whereas the far and more deformed areas have no landmark point for warping In order to improve this approach, we propose a warping method P-TPS with two steps The first step is to determine the set of initial corresponding minutiae pairs by applying an affine transformation then using the sequence of quantized points of their ridge-valley pair associated to choose the set of landmark points with higher reliability The second step is based on convex hull of all known corresponding pairs, fingerprint images are divided into areas New created corresponding points are combined with available corresponding minutiae pairs to choose suitable landmark points on each area for warping in order to calculate new set of corresponding minutiae pairs The new set of corresponding minutiae pairs is able to reuse iteratively until there are no more corresponding point pairs or the number of corresponding pairs is large enough to distinguish Our new method is suitable for both roll/full and plain/flat fingerprint images Experimental results on the database of the fingerprint FVC2004 (DB1 and DB3) [20] show that our proposed method provides better results than global TPS method Calculation time and memory usage also has been significantly reduced The rest of the paper is presented as following: Section introduces the method of fingerprint matching based on minutiae and some methodologies which will be used New proposed algorithm is described in Section Section presents experimental results and the final section is reserved for evaluation and conclusion II MINUTIAE BASED FINGERPRINT MATCHING AND RELATED WORKS This section briefly introduces minutiae based matching method, distorted TPS model and global TPS method 334 A Fingerprint matching problem and matching scheme based on minutiae Fingerprint matching problems can be described as following: Give a query fingerprint Iq and a template fingerprint It, it is to determine whether the two images are originated from the same finger or not The answer is firstly determined by calculating the similarity scores and then by decision yes or no base on the similarity threshold Fingerprint matching algorithms can be classified into three main categories [12] based on: minutiae, texture and greyscale correlation Within these categories, the method based on minutiae is simple but yet efficient therefore it is the most widely used in [5, 8-10, 15, 19] A short scheme of this method is outlined below and the detail is in [10, 14] (combined with linear transformations: translation, rotation and scale) However, due to the nonlinear distorted fingerprints when capturing fingerprint images, the efficiency of this method is not enough and is usually employed to determine initial corresponding minutiae pairs for advanced warping methods One of widely used warping transformations is TPS deformation model in [1, 2, -10, 15, 19] The thresholds Stmax and Stmin together with the false rejected rate FRR(St) and the false accepted rate FAR(St) as function of St are commonly determined by learning on the two sets of genuine and impostor fingerprint images In this case, Stmax is the largest value for FAR = and Stmin is the smallest value for FRR=0 1) Minutiae based method In a fingerprint image, points, which represent discontinuities of fingerprint local structure such as end points, bifurcation points, are called minutiae From two fingerprint images Iq, It, we define two sets of minutiae Mq and Mt as follows: Mq = {m1, m2, …, mM}; with mi= (xi,yi,θi), i = 1, ,M (1) where (xi, yi) are coordinates of mi on the image plane R2 of Iq, and θi is the fingerprint direction at mi Mt = {m1’, m2’, …, mN'}; with mi'= (xi’,yi’,θi’), i = 1, ,N (2) where (xi’,yi’) are coordinates of mi' on the image plane R2 of It, and θi’ is the fingerprint direction at mi' B Thin-Plate Spline deformation model and global TPS matching 2) Matching scheme based on minutiae A suitable aligned transformation from image plane of Iq to image plane of It is required to determine corresponding point pairs of Mq and Mt Point pair mi (Mq) and mj'(Mt) are called correspondent if image mi” of mi via this transformation belongs to the neighbourhood (with a small values of r and θ) of mj' In this case, it is said that mi matched with mj' When two images Iq and It are genuine (from the same finger), the number of corresponding minutiae pairs is much more than in the case they are impostor (not from the same finger) In fact, due to non-linear distorted fingerprints and noise, even two images are genuine, it is not simple to find corresponding minutiae pairs Suppose that there are n corresponding minutiae pairs found from two images, M is the number of minutiae on the query fingerprint and N is the number of minutiae on the sample fingerprint, the similarity of two fingerprint images is characterized by the measurement S(It,Iq) given by the following formula: S(It,Iq) = n2/M× N (3) In the general algorithm, one is interested only in the similarity S(It,Iq), which is also the output Based on predefined thresholds of scores Stmax and Stmin, we conclude that two fingerprints are matched if S(It,Iq) > Stmax, otherwise they are mismatched (S(It,Iq) < Stmin) For the pairs of fingerprints having the similarity scores in interval [Stmin, Stmax] the warping stage is needed The simplest and most general transformation used in matching methods to align two images is affine transformation 1) Thin-Plate-Spline deformation model After determining the n pairs of corresponding minutiae by using affine transformations for creating an initial set of landmark points, the image is warped by TPS model [1], [11] This method uses affine transformations and radial interpolation functions of two-dimensional as follows: n f(x,y) = a1 + axx + ayy + ∑ w U ( P − ( x, y ) ) i i (4) i =1 Where, U ( r ) = r log r , (u, v) = u + v and by convention U(0)=0; Pi are landmark points, the first three terms describes full affine transformations with affine parameters a1, ax, ay and the rest term describes the non linear deformation with weight values wi which need to find so that the landmark points matched The coefficients of f(x,y) transformation are determined by solving linear equations (4) Based on this warping method, if two fingerprints are genuine, it is expected to detect more new corresponding point pairs for calculating similarity Actually, while determining corresponding minutiae pairs based on tolerance, there are some ambiguity correspondence cases In order to overcome this issue, the two-way graph and FordFulkerson algorithm are applied to determine this correspondence [16, 19] Occasionally, additional local information of minutiae pairs is used as secondary feature [9], [10] Based on this technique, the similarity between corresponding pairs could be calculated by using local greyscale correlation [12] 2) Global TPS matching Li et al [12] proposed fingerprint matching method known as global TPS In this method, after determining TPS transformation, they calculate local greyscale correlation in corresponding pairs Based on the similarity of corresponding pairs via this greyscale correlation, the decision for identification is then determined The detail of this method is given in [12] 335 III NEW METHOD: PARTIAL TPS FINGERPRINT MATCHING The TPS method is a good solution to overcome non-linear non distorted fingerprints but it still has some following disadvantages: i) By considering all sets of initial corresponding minutiae pairs as landmark points without using local information info for verification, it is easily to introduce some false landmark points However, using local greyscale correlation before warping is not reliable because it is highly sensitive with distortion, noise, and incomplete information ii) Because landmark k points are determined by global affine transformation, therefore they generally focus on areas with only few non-linear linear distortions and not distributed equally over the entire overlapping area of two fingerprints It and Iq Therefore, minutiae which are far away from non non-linear distorted landmark points, are often disregarded iii) Warping global fingerprint one requires solving large linear equations that takes a lot of calculation time but the result normally has high variation In reality, fingerprint distortion is local natured and closer points have fewer distortions In order to overcome the first disadvantage, we propose using local structure known as ridge-valley valley pair associated with each minutia to verifying and select a set of corresponding minutiae iae pairs with higher reliability In order to deal with the second disadvantage, our method proposes an additional technique to strengthen the set of landmark points by utilizing more pseudo-minutiae minutiae belonged to this ridgeridge valley pair associated Based on the distribution of pseudopseudo minutiae on fingerprint image, a subset with more equal distribution on the overlapping area of two fingerprints is chosen as additional landmark points for warping Finally, our method uses partial TPS warping method instead of global TPS method to overcome the third disadvantage A Associated ridge-valley valley structure and pseudo-minutiae pseudo 1) Associated ridge-valley structure As aforementioned, components of the minutiae including only positions and orientations not have enough information rmation to present the local structure, therefore Ross et al [18] proposed to use associated ridge information to match corresponding minutiae pairs In order to get more local information at these points, we also considered the valley which associated with th dual minutiae on the valley image Our consideration is based on the duality that can be formulated as follows: Opposing with a minutiae "bifurcation/end" point on the ridge image, there always exist a dual minutiae "end/bifurcation" point on valley image ge It is also true for valley images (negative image) Thus ridge-valley ridge pair associated with one minutiae composed from associated ridge with this minutiae and associated valley associated with its dual one on the valley image Fig describes some minu minutiae on the ridge image and its dual minutiae on the valley image (a) (b) Fig 1: The minutiae on the ridge (thick line) have it's dual minutiae on the valleys (thin line) Some configurations of figured minutiae with their ridge ridgevalley pair associated are described in Fig (a) (b) (c) (d) Fig (a) A "short ridge or island" and its dual valley form "lake"; (b) A "spur form" ridge and its dual spur form valley reverted; (c) A "Crossover" and its dual "two meeting ridges"; (d) Not exist the dual for line break, the extracted minutiae is rejected 2) Sampling ridge-valley valley pair associated and appending corresponding point pairs Note that l0 is the length (usually chosen as the double distance of ridges space) and lmax =4l0 The set of pseudo minutiae is generated on associated ridge ridge-valley structure of corresponding minutiae pairs as follows: From each minutiae, on ridge image and from dual minutiae on valley image we used the contour tracing algorithm proposed in [10] to following along ridge and valley to sampling quantized points with equidistant step l0 until meeting the border or the length overcome the threshold lmax These quantized po points of two corresponding minutiae are characterized by positions and directions hence called pseudo-minutiae minutiae For each genuine corresponding minutiae pairs, ridge-valley valley pair associated is also corresponding, but it is not true for impostor case Therefore, e, after checking the coordination and the orientation of these pseudo-minutiae, minutiae, we select only corresponding pseudo-minutiae minutiae to append into set of landmark points Fig described pseudo-minutiae minutiae sampled with equidistance of l0 Pseudo point mj Fig The minutiae mj and its sampled points with equidistance l0 B Area Division and choice the landmark points set for local deformation model In order to warp the image using partial TPS, it is required to divide an image into areas and choose landmark points for TPS transformation of each area 1) Area Division for TPS warping 336 For each known corresponding minutiae pairs set, it is possible to estimate the aligned region by determination their convex hull on the image plane based on the proposed technique in [6] The largest diameter of convex hull is chosen as the horizontal axis of corresponding image plane and the center is its midpoint We divided the plane into areas by rays from center with an angles separated regularly of 450 Taking central area with radius R0 (predefined as 4mm), the outside is areas separated by rays So fingerprint image is divided into areas to compare minutiae Procedure P-TPS Fingerprint Matching Input: Two sets of minutiae Mt, Mq with M, N; The initial corresponding minutiae pairs set M1 with n pairs [21], Set M1 * with n* of quantized points (pseudo minutiae) Warping threshold Stmin , Stmax ; ridge step: step; Output: The corresponding minutiae pairs set with n" pairs found after warping and overall similarity of the two fingerprints S Verification the initial set of corresponding minutiae pairs by comparing two pairs vectors of quantized points sampled from its the ridge-valley pairs associated (n – the original minutiae pair), The output result of this step is the number n' (