Elsevier

Pattern Recognition

Volume 39, Issue 1, January 2006, Pages 102-114
Pattern Recognition

Constrained nonlinear models of fingerprint orientations with prediction

https://doi.org/10.1016/j.patcog.2005.08.010Get rights and content

Abstract

In this paper, we developed an algorithm to model the fingerprint orientation field. The algorithm comprises two steps, orientation prediction and model computation. Orientation prediction is based on piece-wise first-order phase portrait model. It is used to estimate the orientation in areas where there is no ridge information in the input image or the coherence of the orientation field is low. In the model computation, a constrained nonlinear phase portrait algorithm is proposed, which aims to get an accurate mathematical model of the fingerprint orientation field. Compared to the prior works, this algorithm is able to predict orientation even in noisy regions and it integrates the global and local orientation description into a unified mathematical form. Experiments conducted on the first 500 images of the NIST-4 database showed that the proposed algorithm is able to model all the fingerprint orientation patterns except those with very poor quality images where the orientation information cannot be clearly extracted.

Introduction

At present the most widely used biometrics is fingerprint because it is accurate and affordable. With the increasing emphasis on identity management, automatic fingerprint recognition has received wide attention commercially. Nevertheless there still exist critical research issues such as the long processing time in large databases and dealing with poor quality images. Solving these two problems will require improvement to fingerprint classification and identification. In both topics, orientation pattern, which can be defined by a local direction of ridge-valley structure, plays an important role [1], [2], [3], [4].

However there are many poor quality fingerprint images caused by dust, oil, moisture, scars, poor impression or excessively wet or dry fingers. As such, we cannot always obtain clear orientation patterns. Several methods have been proposed to improve the estimation of the orientation field, which can broadly be categorized as filtering-based [1], [2] and model-based [5], [6], [7], [8]. Filtering-based methods improve the orientations at a local region and are not able to solve large noisy or missing patches in the image. Such methods can also be viewed as the local constraint methods. On the other hand, model-based methods consider the global constraint and regularity of orientation field except for the area near the singular point. These methods are able to overcome the limitation of filtering-based methods. This paper will focus on the model-based methods.

Several model-based methods have been proposed in the literature. Sherlock and Monro [5] presented the zero-pole approach to model the fingerprint orientation topology using:Om(z)=O0+12l=1Larg(z-zcl)-k=1Karg(z-zdk),where zdk, zcl are the positions of the deltas and cores. However, it is clear that for any two fingerprints with the same singular points, both will be modeled by the same function even though their local ridge orientation values may differ significantly. Furthermore, it cannot handle the fingerprints where there are no singular points. In other words, the zero-pole model cannot model all possible fingerprint orientation patterns accurately. Vizcaya and Gerhardt [6] revised the zero-pole model to a non-linear orientation model as in (2):Om(z)=O0+12k=1Kgdkarg(z-zdk)-l=1Lgclarg(z-zcl),where g is the correction term, which essentially is any nonlinear function that preserves the singularity at the given point. However, this additional correction is not precise enough to approximate all orientation fields. Gu et al. [7] then proposed a combination model to reconstruct the fingerprint orientation fields. The combination consists of a polynomial model and a point charge model, where the polynomial model is used to approximate the global orientation fields and the point charge model is used to correct the orientation fields formed by the polynomial model near the singular points. This combination model gives better estimation of the orientation compared to the other previous models. Zhou and Gu [8] also presented another complex model, which is based on zero-pole model but with high order rational function used as the non-linear correction instead.

There were other works in orientation modeling not directly related to fingerprint. Jain and Rao [9] used the geometric theory of differential equations to derive a symbol set based on the visual appearance of phase portraits. This approach is able to provide a reconstruction of salient features of the original texture based on the symbolic descriptor. The work is expanded in Ref. [10] with the use of a weighted estimation algorithm for single linear oriented pattern, which is robust to noise in the orientation pattern. Ford and Strickland [11] used the phase portraits to model the flow-like orientation patterns. They suggested that flows are modeled as a superposition of primitives, where their associated strengths were determined from the orientation patterns. Compared to [9], such an approach provides a framework to describe and reconstruct global complex orientation patterns. In addition, they also showed that even when the data is occluded by up to 40%, the proposed phase portrait approach is still able to approximate the orientation quite accurately. Ford et al. expanded their works in Refs. [12] and [13] by proposing the non-linear phase portrait models. In these papers, they decomposed the flow field into simple component flows based on the singular point pattern. Then a Taylor's model was used for the velocity components, and the model coefficients were computed by considering both local singular points and global flow field pattern. This model's advantage is that it can provide a better approximation in the singular point regions compared to the linear phase portrait approach. However, their method is aimed at orientation field with symmetric orientation structure. In addition, only two and three order phase portraits have been reported with good performance. At such low orders, the proposed approach is not able to cater to complex patterns present in fingerprints.

In our opinion, a good orientation model should not only be accurate, but also should have prediction capability. When the ridge information is not available in the images (due to noise or when the acquired images are relatively small), the algorithm should still be able to predict the orientation information from known data. This is possible and reasonable, as the fingerprint orientation field will not change abruptly except for the orientation fields at the singular points. This is the basic idea of our proposed prediction algorithm. To the best of our knowledge there is no prior work related to prediction of fingerprint orientation

The main contributions of this paper are:

1. A prediction model based on first-order phase portrait is proposed to estimate the orientation fields where no reliable information is available in the input image.

2. We propose the descriptors for the local orientation behaviors near the singular points using phase portrait. Compared with the descriptors used in Ref. [14], these descriptors are able to describe the different local orientation patterns near the singular points of the same class. Furthermore, we introduced two practical approaches to reconstruct the local orientation near the singular points.

3. A constrained nonlinear phase portrait model is introduced. This model integrates the local descriptor at the singular points into the overall descriptor. Thus a unified approach is formulated to describe the entire fingerprint orientation field.

This paper will be organized as follows. Section 2 gives a brief overview of phase portrait, followed by prediction algorithm in Section 3. Here three models based on phase portrait are presented to analyze the orientation behaviors at the singular point, followed by a prediction model based on piece wise first-order phase portrait. In Section 4, a constrained nonlinear phase portrait model is used to model the fingerprint orientation fields. In Section 5, detailed implementation of complete model is described followed by experiments in Section 6. The last section will conclude this paper.

Section snippets

First-order phase portrait overview

First-order phase portrait has been proposed to describe the local orientation fields [9], [10], [11], [12], [13]. A brief description of first-order phase portrait will be given here. The first-order phase portrait can be expressed by (3) in the Cartesian coordinate system:dxdy=cdabxy+fe=AX+B.Therefore the orientation is given byθ(x,y)=tan-1dydx=tan-1ax+by+ecx+dy+f,where dx and dy are the x,y components of the orientation, (x,y) is the coordinate and (a,b,c,d,e, and f) are the coefficients

Behaviors analysis near the singular points

By observing the original fingerprint orientation fields as shown in Fig. 3a and b, there is no simple canonical form suitable to model the orientation field near the singular points. However, the square of the orientation field (Fig. 3(c, d)) shows the pattern of spiral at the core and saddle at the delta [14]. The orientation of the squared orientation field is denoted by 2θ. It expands the original orientation range from [-π/2,π/2] to [-π,π], as its x,y components will be continuous when

Constrained nonlinear phase portrait model

Gu et al. used two polynomial functions to model the fingerprint orientation fields [7]. This method can be viewed as the unconstrained phase portrait model, and it performs well for the global description. However at the region near the singular points this unconstrained phase portrait model is not able to model the local orientation fields as well as the global orientation fields at the same time. From the analysis in Section 3.1, for a given region at the singular point a first-order phase

Implementation of the proposed model

In this section, we will describe in detail the proposed algorithm.

Step 1: Compute the original orientation field Oorig and its coherence Worig [14] respectively using the Eqs. (21) and (22);Oorig(xi,yj)=12tan-1r2GxGyGx2-Gy2+π2andWorig(xi,yj)=rGx2-Gy22+4rGxGy2rGx2+Gy22,where r is a small window region of (xi,yj), (Gx,Gy) is the gradient vector along the x and y direction respectively computed in the window region centered at (x,y). The singular points can be determined using the

Experiments

Three experiments are conducted. Experiment I aims to test the performance of the prediction model quantitatively. Experiment II is used to evaluate the constrained nonlinear phase portrait model quantitatively, while Experiment III is designed to show the effectiveness of the algorithm qualitatively in the region that does not contain full ridge information.

Conclusion and future works

In this paper, an orientation prediction algorithm is proposed, which uses the phase portrait approach to compute the predicted orientation. This allows us to reconstruct the orientation using only the data around the singular points. In order to increase the accuracy of the prediction, we refine the orientation fields by replacing the unreliable orientation in the original orientation fields with the predicted orientation according to its coherence value. This refined orientation is then used

About the Author—JUN LI received his B.S. in mechanical and electrical engineering and M. Eng. in the biometrics processing from the University of Science and Technology of China, Hefei, China, in 1997 and 2002, respectively. He is currently working towards the Ph.D. degree in the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore. His research interests include biometrics (fingerprints and iris), image processing, and pattern recognition.

References (14)

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About the Author—JUN LI received his B.S. in mechanical and electrical engineering and M. Eng. in the biometrics processing from the University of Science and Technology of China, Hefei, China, in 1997 and 2002, respectively. He is currently working towards the Ph.D. degree in the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore. His research interests include biometrics (fingerprints and iris), image processing, and pattern recognition.

About the Author—WEI-YUN YAU received his B.Eng. (electrical) from the National University of Singapore (1992), M.Eng. in biomedical image processing (1995) and Ph.D. in computer vision (1999) from the Nanyang Technological University. From 1997 to 2002, he was a Research Engineer and then Program Manager at the Centre for Signal Processing, Singapore, leading the research and development effort in biometrics. His team won the top three positions in both speed and accuracy in the International Fingerprint Verification Competition 2000 (FVC2000). He also participates in both national and international biometric standard activities. Currently he is the Chair of the Biometrics Technical Committee, Singapore. Wei-Yun was also the recipient of the TEC Innovator Award in 2002 and the Tan Kah Kee Young Inventors Award 2003 (Merit). Currently, he is with the Institute for Infocomm Research as a Department Manager. His research interest includes biomedical engineering, biometrics, computer vision and intelligent systems.

About the Author—HAN WANG graduated from Northeastern Heavy Machinery Institute with B.Eng. in Computers and Applications, Ph.D. from Leeds University in Parallel Image Processing. He spent three years in Oxford University, working on real time obstacle detection as research officer, half year in CMU on parallel processing as research scientist, and one year sabbatical in Monash University. He is currently associate professor in the Nanyang Technological University. His research interests include computer vision, evolutionary computing, and robotics.

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