A review on fingerprint orientation estimation

Transcription

1 SECURITY AND COMMUNICATION NETWORKS Security Comm. Networks 2011; 4: Published online 9 June 2010 in Wiley Online Library (wileyonlinelibrary.com)..209 SPECIAL ISSUE PAPER A review on fingerprint orientation estimation Zujun Hou *, Wei-Yun Yau and Yue Wang Institute for Infocomm Research, A-Star, 1 Fusionopolis Way #21-01 Connexis, Singapore , Singapore ABSTRACT Fingerprint orientation plays important roles in fingerprint enhancement, fingerprint classification, and fingerprint recognition. This paper critically reviews the primary advances on fingerprint orientation estimation. Advantages and limitations of existing methods have been addressed. Issues on future development have been discussed. Copyright 2010 John Wiley & Sons, Ltd. KEYWORDS fingerprint; orientation; local estimation; structure tensor; global modeling * Correspondence Zujun Hou, Institute for Infocomm Research, A-Star, 1 Fusionopolis Way #21-01 Connexis, Singapore , Singapore. zhou@i2r.a-star.edu.sg 1. INTRODUCTION With the continuous growing on security requirement, fingerprint recognition technology has largely been deployed in a wide range of applications, from civil to forensic, from door access control to custom immigration clearance. The number of users can vary from a few to millions, or even more. Despite of such numerous successes in deployment, the performance of fingerprint recognition system is yet to be further improved, in particular when the acquired fingerprint image is of low quality and the size of fingerprint database is huge, where the number of absolute error cases will be remarkably amplified even the system s relative error rate is low. Fingerprint quality can be degraded for the presence of scars, wounds, etc. Some have dry finger and some have sweat one. For some people like certain manual workers, their fingers can easily get dirty. On top of that, the fingerprint sensor can also lead to low-quality images. Figure 1 illustrates some poor quality fingerprints. A number of efforts have been taken toward the enhancement of the fingerprint recognition system s performance. Critical to boost the system performance is to reliably estimate the orientation field of the fingerprint structure. The orientation field represents a very essential characteristic of a fingerprint. It can be very useful to restore the structure for poor quality fingerprint images [1 4], and is also an important feature for fingerprint classification and matching [5 9]. Figure 2 illustrates the importance of orientation field on fingerprint enhancement, where the original fingerprint image suffers from the problem of creases and latent prints, which is perfectly solved through fingerprint enhancement base on a correct estimation of the fingerprint orientation field. Nevertheless, it is a nontrivial issue to reliably estimate the orientation field for given fingerprint images. A lot of techniques have been proposed to deal with the problem. This paper attempts to review the progress in the field, nevertheless it is by no means an exhaustive summary. For convenience, they are broadly classified into two categories: local estimation and global modeling. Basically the former method estimates the orientation at a pixel using the information in the neighborhood of that pixel only, whereas the latter constructs a model for the whole orientation field as estimated by the former method and reconstructs the orientation field based on the global model. They are further detailed in the following sections. 2. LOCAL ESTIMATION Many methods have been proposed for orientation estimation, which can be carried out in frequency space [10,11] or in spatial domain [12,13]. The most popular one for local direction estimation is the gradient-based method. Let I denote the image and I = (I x,i y ) the gradient of the image, where I x and I y are the partial derivatives of I. Then the orientation is the direction perpendicular to the gradient. Alternatively, the filter-bank method has been utilized to estimate the local orientation [5]. Essentially the filter-bank method is based on the same assumption as the gradient method in the process of orientation estimation, that is to say, the orientation at a position will be the direction for which the signal changes the least. The advantage of the filter-bank method lies in the resistance with respect to the Copyright 2010 John Wiley & Sons, Ltd. 591

2 Fingerprint orientation estimation Z. Hou et al. Figure 1. A sample of fingerprint images with low quality. noise as is well known that the gradient operation is noise sensitive. However, the gradient method is much more computationally efficient. Besides that, efforts have been tried to estimate the direction through the ridge projection [14]. The method needs to firstly separate the primary ridge, and calculate the projection of the primary ridge onto a set of oriented lines. The direction is estimated as the line where the projections attain minimum variance. In general, the idea is similar to the filter-bank method. The problem lies in the identification of the primary ridge, which is not a trivial issue for poor quality images. Recently, Jiang [13] proposed a band-pass filter derived from an integration operator for orientation estimation. The integration operator is defined as a weighted sum of y- and Figure 2. An illustration of the impact of orientation on fingerprint image restoration, where on the left is a fingerprint image with creases and accidental impression of another person s fingerprint. Based on the estimated orientation field as shown in the middle, the reconstructed image is displayed on the right, which perfectly reduces the problem of crease and latent print. 592 Security Comm. Networks 2011; 4: John Wiley & Sons, Ltd.

3 Z. Hou et al. Fingerprint orientation estimation x-integration in interval 2d with shift d as l = R d= R y+d ω d y d f (x + d, z)dz+j x+d x d (z, y + d)dz, (1) where the integration is taken over a support of size 2R 2R. Essentially, the filter is similar to the widely used gradient operators such as the Sobel operator, the Prewitt operator, in the sense that all of them couple a low-pass filter in the orthogonal direction of a high-pass filter. The method has been demonstrated to be advantageous over most gradient operators in accuracy or robustness against noise. To address the noise sensitivity, one may consider to smooth the image before applying the gradient operation, as commonly used in edge detection, or to filter the estimated orientation field with a low-pass filter. However, care should be taken to directly smooth the gradient vectors, as opposite gradients characterizing the same orientation shall cancel out by direct summation. To circumvent this difficulty, Kass and Witkin [12] pioneered the idea of filter-bank approach for orientation estimation although in implementation their method is quite different from the filter-bank one. In this method, the directional derivative is regarded as a random variable and the most reliable gradient is estimated as the greatest variance of the directional derivative with solution as follows: ( ) φ KW = 1 W 2I x I y 2 tan 1 W ( Ix 2 ), (2) I2 y where W represents a low-pass filter, and stands for convolution. Rao and Schunck [15] adapted techniques in the statistics of directional data to the problem of orientation estimation, and formulated the estimation as to find the direction that maximize the sum of the square of the projections. Let φ be the direction of the gradient vector (I x, I y ), then the dominant orientation in a neighborhood is φ RS = 1 ( ) sin 2φ 2 tan 1, (3) cos 2φ where the summation is taken over the local neighborhood. This solution can also be derived from the structure tensor (ST) method. The ST (or second-moment matrix, scatter matrix, Forstner interest operator) is defined as the tensor product of the gradient: M 0 = I I T. (4) The resulting matrix is symmetric and positive semidefinite. Note that the ST is invariant under sign changes ( I and I give rise to the same ST), thus the low-pass filtering upon the ST will not yield the direction cancellation [16]. For convenience, let denote the smoothed ST as M σ = W I I T, (5) where W represents a low-pass filter. It can be shown that φ RS corresponds to the principal axis of M σ, since summation over a neighborhood by itself is low-pass filter. Interestingly, φ KW can also be derived from the ST and equal to φ RS when the same low-pass filtering is applied to both estimations. Interested readers on ST and its application to fingerprint orientation estimation can refer to Refs. [17,18]. 3. GLOBAL MODELING Realizing that the orientation field resulted from local estimation methods is still unsatisfactory for poor quality images, researchers have attempted to refine the estimation through a mathematical model as fitted to the estimated data. The idea behind the efforts lies in two observations. Firstly, at some regions the fingerprint quality is degraded and local information is insufficient to yield a reliable estimation. For most local estimation methods, the basic assumption on the perturbation is the random noise as typically adopted in image processing. However, in fingerprints, as shown before, the more severe challenge encountered is such artifacts as scar to cause ridge discontinuity, or sweat on fingers to smudge marks, or dry finger to result in fragmented ridge structure. These perturbations are typically nonrandom noise. Thus the random-assumption-based estimate of the local orientation will definitely be biased and sometimes even incorrect. Secondly, overall fingerprint orientation field is usually pretty smooth except for some regions near singular points, which enables the possibility to build a more global model and apply in turn to local predictions. A pioneered work in this direction was presented by Sherlock and Monro [19] in 1993, where the orientation field is described by a zero-pole model. The model is formulated in the complex plane with the core point as zero and the delta point as pole. Taking the image plane as complex plane, and denoting a point in the image plane by z, the zero-pole model then is defined as follows: p(z) = e (z z c1) (z z cm ) 2jφ (z z d1 ) (z z dn ), (6) φ(z) = (arg(p(z)))mod π, (7) where φ is a constant correction term, z cr and z ds are the rth core point and the sth delta point, respectively. The orientation at a point is determined by the number of singular points as well as the distance with respect to these singular points. In general, the zero-pole model is almost perfect in regions near singular points, but seems too simple for orientation modeling in other regions. If two fingerprints from different subjects have similar topology in singular points, then the zero-pole model yields little differentiability between these Security Comm. Networks 2011; 4: John Wiley & Sons, Ltd. 593

4 Fingerprint orientation estimation Z. Hou et al. two orientation fields. Nevertheless, this pioneering work has inspired great interests in the mathematical modeling of fingerprint orientation field. The suitability of the model for describing singular points has been employed in other applications such as to detect singular points [20] and to synthesize fingerprint images [21]. An improvement of the zero-pole model was made by Vizcaya and Gerhardt [22] using a piecewise linear approximation model around singular points to adjust the zero and pole s influence: φ VG (z) = φ + 1 [ g dk (arg(z z dk )) 2 ] g ck (arg(z z ck )), (8) where g dk and g ck are the correction term around delta and core points and are modeled as a set of piecewise linear functional. A similar work was proposed by Zhou and Gu [23]: φ ZG (z) = φ + 1 [ f 1 (z) (arg(z z dk )) 2 ] f 2 (z) (arg(z z ck )), (9) where f 1 and f 2 are some complex polynomials (up to order 6). An advantage of this model is its suitability to model fingerprints without singular points such as arch type fingerprints. Although the generalized zero-pole models yield better performance in the description of global orientation pattern, their ability to characterize regions near singular points is attenuated. To address this problem, Zhou and Gu [24,25] proposed a combination model to represent the fingerprint orientation field, where a polynomial model is utilized to describe the global orientation pattern and a point-charge model is designed to characterize the orientation pattern in regions near singular points. The entire orientation field is described through a combination of these two models using an ad hoc weighted function. A similar work was presented by Li et al. [26], which combined the piecewise linear model (suitable for local description in regions near singular points) with the high order phase portrait model (suitable for global description). Very recently, Huckemann et al. [27] presents a unified model based on the framework of quadratic differentials, where the zero-pole model and its various generalizations can be regarded as special cases. For the global modeling methods as aforementioned, they have one common feature; that is the dependency on the knowledge of singular points. Nevertheless, the detection of singular points is never a nontrivial issue and the success of the detection strongly relies on the quality of the derived fingerprint orientation field. Thus, the problem will be as complicated as the chicken-egg paradox. Since the orientation field is generally slowly varying except for singular points, some researchers have tried to describe the entire orientation pattern through functional approximation. Wang et al. [28] presented an orientation estimation method using trigonometric polynomials. A notable feature of this model is that it does not require any prior knowledge of singular points. The method has been demonstrated to outperform the singular point dependent method like the combination model [24] in fingerprint image enhancement. This method has very recently been extended in Ref. [29] where the Legendre polynomials are utilized and the issue of curvature preservation is taken into consideration in the course of orientation estimation. 4. A COMPARATIVE STUDY BETWEEN LOCAL ESTIMATION AND GLOBAL MODELING This section provides a comparative study between the above two types of methods. The structure tensor method (ST) [15] is selected as the local estimation type and the Fourier series model (FS) [28] to represent the global modeling type. The FS method is selected for the following reasons. First, it is fully automatic and does not require any prior knowledge such as the location of singular points. Most other global modeling methods require the information on singular points [19 27]. As aforementioned, the detection of singular points usually relies on the result of orientation estimation. If simple detection method like the Poincare is used for singular points detection, the result will be very noise sensitive, thus the subsequent orientation modeling will be error-prone. On the other hand, if the singular points are detected manually, the whole process will not be automatic and greatly limit the application to practice. Alternatively, the FS method has been demonstrated to be superior to the combination model if singular points are detected automatically. The estimated orientation field is applied to enhance the fingerprint image and the enhancement method employs the short time Fourier transform method (STFT) [30]. The performance is validated using the NIST fingerprint image software (NFIS) [31]. To guarantee a fair comparison, throughout all the processes, the only difference between two experiments is the orientation field estimated by two methods. Figure 3 shows the corresponding receiver operator characteristics curves, where the solid line is the orientation estimated by ST and the dotted line by FS. Overall these two methods deliver very similar performance. The equal error rate (EER) is 5.69 per cent for FS, which is slightly better than that for ST (6.05 per cent). Considering that the EER is 8.24 per cent before enhancement, both methods significantly improve the system performance. Compared with the results in FVC2000 [32], the performance of either ST or FS is only behind the Sagem s solution. Note that NFIS only uses the standard minutia information (coordinates and angle), thus the orientation field estimated by both ST and FS is pretty reasonable. To reveal the difference between these two methods, a further investigation has been carried out. Figure 4 shows an example, where the original image is of low quality. 594 Security Comm. Networks 2011; 4: John Wiley & Sons, Ltd.

5 Z. Hou et al. Fingerprint orientation estimation Figure 3. A comparison on the effect of fingerprint enhancement through orientation estimation using the ST method and the FS model, where the EER is validated on FVC2000 Db1a, using STFT for fingerprint enhancement and NFIS for matching. The EER is 6.05 per cent for ST and 5.69 per cent for FS, respectively. The estimated orientation field is shown in the second row; ST on the left and FS on the right. For this fingerprint, the image contrast is low and the ridge is fragmented. The effect of illumination inhomogeneity is also clearly visible. As a result, the local estimation method, ST, yields quite a lot of errors throughout the image domain. By contrast, the global estimation method, FS, successfully corrects most of such errors, which indicates that global information does help to resolve the ambiguity as confronted by the local method. Another example is depicted in Figure 5, where the image quality is quite good. The estimated orientation is displayed in Row 2, ST on the left, and FS on the right. It is no surprising that the ST method leads to satisfactory result for this case. What is of interest here is the region near the core point as highlighted in the circle. Notable difference between the ST and the FS results can be observed within the highlighted region. Evidently the core point in the orientation field by the FS result has been shifted upward, compared with the original image. Row 3 presents the enhanced results based on the estimated orientation field. The impact of the orientation bias within the highlighted region is clearly visible; the structure of the two innermost ridges is changed falsely and the core point (the topmost pixel of the innermost ridge) shifts almost from the center of the highlighted circle to the boundary of the circle, which is about two ridges in distance. This example exemplifies the limitation of global modeling in terms of singularity preservation, as pointed out by other researchers [29,33]. 5. DISCUSSION As an important topological feature of the fingerprint, singular points play a key role in fingerprint orientation modeling. It is required that an ideal method for orientation estimation should preserve the true singularity due to the presence of singular point. Then the problem arises on how to smooth the orientation artifact without destroying the true singularity. For people working on image restoration, they will immediately find the similarity between these two problems. In image restoration, one need to remove perturbations from noise or partial volume effect, which often turns out to be a low-pass filtering process but results in edge blurring along with the course of noise removal. To overcome this problem, a number of techniques have been designed where prior knowledge on the edge structure is modeled and incorporated into the restoration process. For the problem of fingerprint orientation estimation, although there have been quite a lot of efforts on the global modeling, very few works have been reported on including the prior model of singularity into the orientation modeling process. On the other hand, the zero-pole model as well as its various generalizations exemplify that it would be simple to construct an accurate mathematical model for orientation estimation if the knowledge of singular points is available. In these models, the knowledge of singular points is provided through manual labeling or some typical methods for singular point detection, which is in general an independent process even though the process of orienta- Security Comm. Networks 2011; 4: John Wiley & Sons, Ltd. 595

6 Fingerprint orientation estimation Z. Hou et al. Figure 4. A low-quality fingerprint and the corresponding orientation field as estimated by ST (Row 2 left) and FS (Row 2 right). tion estimation and that of singular point detection are inherently related. As aforementioned, the detection of singular points depends on the quality of orientation field, and a number of errors could arise for poor quality fingerprints. If the resulted error is absorbed into the orientation modeling like the zero-pole model, the model constructed subsequently will definitely be unreliable. This explains why the combination model is inferior to the FS model, which does not take into consideration the information of singular point in the modeling process. Nevertheless, it does not mean that the incorporation of singularity into orientation modeling is less significant. Instead, what it reveals is the lack of suitable model to characterize the fingerprint singularity. Although the zero-pole model can be used to inference the position of fingerprint core or delta point, the process is implicit and involves complicated calculation. For general 2D images, there are usually two types of singularity: curve and point. Compared with other images, singularity in fingerprints has a few specific features. Firstly, fingerprint singularity represents the discontinuity of the fingerprint orientation field, a special vector field, which is different from the singularity in normal images that characterizes the discontinuity of scalar field. Thus, usual techniques for singularity detection are not immediately applicable to handle the fingerprint singularity. Another notable feature for fingerprint singularity is that it is typically of the point type. The point singularity in general images is often represented as junction points, which are connected with the curve singularity, and the latter can be 596 Security Comm. Networks 2011; 4: John Wiley & Sons, Ltd.

7 Z. Hou et al. Fingerprint orientation estimation Figure 5. On the left is the orientation as estimated by the ST method and on the right by the FS modeling. It is visible the distortion in regions near singular points due to the FS modeling. detected explicitly. However, in fingerprints, the discontinuity of the orientation pattern does not explicitly relate to curve singularities, even though there are efforts to segment the orientation pattern and define the orientation singularity as the junction point in the segmentation map [34]. Comparatively, curvature may be a more suitable candidate. It cannot only describe the singularity due to core/delta points, but also be suitable for characterizing the topology of arch type fingerprints where core/delta points are not well defined. But considering the specialty of the perturbation in fingerprints, curvature alone shall not be sufficient to reliably represent the fingerprint topology. Security Comm. Networks 2011; 4: John Wiley & Sons, Ltd. 597

8 Fingerprint orientation estimation Z. Hou et al. As aforementioned, besides the random noise as faced by general images, fingerprint images are subjected to quite a lot nonrandom perturbations, such as creases, ink, sweat, wound, or latent fingerprint, which often exhibit in a regular fashion, at least in a local region. The presence of these secondary structures will compete against the primary fingerprint structure, sometimes even totally changes the local structure. Local estimation methods would generally have difficulty to judge which is the right direction, since in the local neighborhood the strength of the primary structure is too weak or it is almost impossible to differentiate the primary structure from the secondary one, either in image domain or in frequency space. Comparatively, global modeling will have advantages in utilizing more global information for local inference. Nevertheless, most existing methods are based on the assumption of random additive noise in the modeling process, and have not taken into consideration the nonrandom nature of the secondary structure [1 29,35]. As a result, when the region with secondary structure is localized to certain degree, the correction could be successful; otherwise the estimation will be failed. For example, in Figure 1, either local estimation or global modeling methods fail to correct the fingerprint structure where latent fingerprint is present. To address the singularity in the presence of secondary structure, estimation methods based on the law of large numbers or the central limit theorem, as implicitly adopted by most existing techniques, will certainly be insufficient. Other methods such as robust statistics, or global inference methods like topological modeling [36], tensor voting [37 39], which explicitly employs global information for local inference, could be explored and this may be the trend for future investigation. 6. CONCLUSION This paper summarized the progress on fingerprint orientation estimation, which can be categorized into local estimation and global modeling. The former is easy to code and advantageous in preserving true singularities. By contrast, the latter is able to yield more reliable solution in the presence of perturbations. Despite the numerous efforts in this field, the issue of fingerprint orientation estimation is far from being adequately addressed and further exploration is still necessary, in particular, to investigate orientation modeling with ability to preserve singularity and to develop advanced methods for local structure inference using global information. REFERENCES 1. Jain AK, Hong L, Pankanti S, Bolle R. 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