A Matching Method for Fingerprint Images Using Sub-bands of DWT Coefficients

S. Tachaphetpiboon1 and T. Amornraksa2

1Department of Computer Science, Phetchaburi Rajabhat University, 38 Hadchaosumran Rd., Muang, Phetchaburi 76000, Thailand, E-mail: watcom2003@yahoo.com

2Computer Engineering Department, King Mongkut’s University of Technology Thonburi, 91 Pracha-Utid, Toongkru ,Bangkok 10140, Thailand, E-mail: t_amornraksa@cpe.kmutt.ac.th

ABSTRACT

This paper proposes a ridge feature based matching method that uses sub-bands of DWT coefficients to generate fingerprint features. By properly selecting some sub-bands after a fingerprint image is segmented and transformed by the DWT, informative features can be extracted and used for fingerprint matching purpose. In the paper, we examine two possible approaches used in determining the proper sub-bands, obtained from several types of DWT e.g. Daubechies and Symmlet, and evaluate the performance of our approaches by a KNN classifier. The experimental results show that a better improvement in term of recognition rate is accomplished, compared to the DWT based matching methods previously introduced in [6] and [7]. With the proposed method, more accuracy in fingerprint recognition process can be achieved.

Keywords: fingerprint, matching, image processing.

1. INTRODUCTION The matching method is an important process in fingerprint classification which is used in identifying an unknown fingerprint. The methods of fingerprint matching can be categorized into three classes [9]: correlation-based, minutiae-based and ridge feature-based. The first one is achieved by simply laying over two fingerprint images and determining the correlation, a causal relationship at the intensity level, between corresponding pixels. To obtain a higher efficiency, calculations are performed for different alignments, aligned in various displacements and rotations. The second one in contrary is achieved by comparing some features called minutiae, which are extracted from the fingerprints and usually stored as sets of points in the two-dimensional plane. Two most significant features, known as ridge characters, that are widely used nowadays are ridge termination and ridge bifurcation. Basically, the Minutiae-based method finds the alignment between template and testing minutiae sets that have the maximum matched pairs of two of them. Finally, the ridge feature-based method is achieved by extracting some fingerprint features directly from the gray-scale images, for instance, local orientation and frequency, ridge shape and texture information.

Undoubtedly, the correlation-based methods requires huge amount of computation time in searching the fingerprints stored in the database that perfectly matches the unknown entry. This is not practical when implemented in a fingerprint identification system, especially with a large size database. For the minutiae based methods such as those proposed in [1] and [2], where the minutiae were extracted from a fingerprint image, two pre-processing processes called binarization and thinning are normally required to normalize the fingerprint image and to eliminate some background noises. Binarization was used to convert a gray-scale image to a binary image, while thinning was used to convert a thick ridge line to a thin one with merely one pixel width. The designated minutiae extraction process is then applied to extract the minutiae pattern from the fingerprint image [2, 3]. Accordingly, complex algorithm and time consumption required in the pre-processing processes must be considered and included when implementing the minutiae based methods. Differently, the ridge feature-based methods directly extract the ridge features from the gray-scale image, and use them for the fingerprint matching. A GABOR filter-based method [4, 5] was one of them. It extracted the ridge features directly from the fingerprint image in 4 orientations (0° , 45° , 90° and 145°), and used such features to match an unknown fingerprint image to the one kept in the fingerprint database. However, it was shown in [6] that the recognition rate could be increased by using wavelet features. The improved performance was obtained based on the concept that the oscillate pattern within each fingerprint image, which resided in the mid frequency band, consisted of informative features, and its characteristic i.e. standard deviation could be used for the fingerprint matching purpose. The authors also showed that the DWT was more suited for extracting those features than that obtained from the GABOR filter. In their scheme, the fingerprint image was first segmented and decomposed by the Discrete Wavelet Transform (DWT) four times and then the DWT coefficients from three detail sub-bands at each transform level were used to generate the ridge features. Recently, a similar DWT based method was introduced in [7], where the ridge features used in the matching process were the mean and standard deviation values obtained from every

sub-band of DWT coefficients, after three time transforms. In this paper, we show that by properly selecting some sub-bands of DWT coefficients, some significant informative features can be extracted and used to achieve a higher recognition rate, compared to the DWT based methods in [6] and [7]. We propose two possible techniques to select the proper sub-bands which still maintain the complexity level in the matching process. Our approaches are evaluated by the K-NN classifier, and the results were compared with the ones obtained from the previous methods at their optimum performance.

2. FUNDAMENTAL CONCEPTS Conceptually, to extract informative features from a fingerprint image, the local properties of that fingerprint must be identified. This is simply done by first equally segmenting the image into 4 sub-sections. Fig 1 shows the fingerprint image quartered at its center. By considering the sub-sections, the fingerprint image is merely a redundancy of white and black line. This type of pattern normally causes the signal magnitude oscillated in frequency domain i.e. in the middle scale of DWT coefficients, as illustrated in Fig.2. From the figure, most oscillated patterns occur in the top-right and bottom-left sub-bands and some occur in the bottom-right (the highest frequency) sub-band.

Fig.1: Sub-sections of a fingerprint image

Fig.2: Oscillated pattern in each sub-band after the first top-left sub-section was transformed by one time DWT

Thus, identical features from an individual fingerprint can be extracted from above three sub-bands. That is, the standard deviations of the DWT coefficients in each sub-band are determined to obtain the ridge features of fingerprint patterns in three orientations; vertical, horizontal and diagonal. This process is repeated after the

top-left sub-band is transformed again by the same DWT. According to [6], four times of DWT was performed and, twelve standard deviations are calculated and stored in the database. Fingerprint matching process uses these features to classify the fingerprint images. Mathematically, the discrete wavelet transform is defined by

dtb

attfbbafbaWf )(*)(21

,,),( −Ψ∫

∞+

∞−

−>=Ψ=< (1)

where a is translation (wavelet window), b is scale. Two dimensions (2D) wavelet decomposition on L levels of a discrete image represents the image in term of 3×4L-1+1 sub-images.

(2) ⎥⎦⎤

⎢⎣⎡

= Ljjdjdjdja ..1}3,2,1{,

where aj is a low resolution approximation of the original image, and dj

k are the wavelet sub-images containing the image details at different scales and oriented (k)—vertical high frequency, horizontal high frequency, and high frequency of both directions. To produce the wavelet domain features, the standard deviation of the wavelet coefficients was generated. The standard deviations of detail sub-bands are calculated and used to create the features

⎥⎦⎤

⎢⎣⎡

= Ljjjj ..1,}3,2,1{ σσσ (3)

and the standard deviation is defined as follows

N

N

ixix∑

=−

= 12)'(

σ (4)

where is the DWT coefficient in each detail sub-band, x’ is mean of DWT coefficients and N is number of DWT coefficient in each detail sub-band.

ix

3. PROPOSED METHOD The proposed method is matching using sub-bands of DWT coefficients. The sub-bands of DWT coefficients method used the informative data that still in others sub-bands. (High frequency sub-bands) We used sub-bands of DWT method to enhance the features. In this method, we cut the fingerprint image in 4 sub regions to save the local information such as the ridge line characteristic. The features are calculated from the standard deviation of detail coefficients in each sub-band of DWT. In the figure, we saw that the oscillated patterns are in the middle of DWT coefficients and disappear from the high frequency sub-bands. The sub-bands of DWT coefficients features are generated from cropped image.

The cropped image size is 64×64 pixels and it centers at referent point. We quarter it to 4 sub-sections and make 32×32 pixels of image size. The features of sub-bands of DWT coefficients are calculated from the standard deviation of each section called fingerprint features. The features are extracted from DWT area which is defined in figure 1(b) and 1(c) because it still has informative data. In figure 1(d) generated more features which it has not feasible and time consumption in matching process. The minimum distance between two features is classified as the same fingerprint. In the proposed method, the order of our feature extraction method is applied as follows:

1. Find the core point of the fingerprint image and mark it as reference point.

2. Crop the fingerprint image to 64×64 pixels region centered at the reference point.

3. Quarter the cropped region into 4 sub-sections. 4. Calculate DWT coefficient on each sub-section. 5. Calculate the features of each section. We use the

formula that is defined in (3). A number of features are defined as follows.

(a) (b)

(c) (d)

Fig.2: Fingerprint features of DWT transform areas We called figure 2(a) as DWT based method in [6], 2(b) as AL method, 2(c) as AH method and 2(d) as AHL method. All of methods generate 12 features for matching process. The method in [7] generates the features from 4 sub-bands at each levels, and scale in 3 levels. It generates features from standard deviation and mean of the DWT coefficients. So the features of this method are 24 features. The proposed method has more accurate features than the method in [6] and [7]. The proposed method collects all informative data in the middle scale of DWT coefficients without redundancy data to generate the features. The expanded sub-bands made the precise features for the matching process.

4. EXPERIMENTAL RESULTS The experimental results were based on the fingerprint database in [8]. There were 13 people and 8 scans of each person. The fingerprint image resolution was 512×512. We used 64×64 window size of fingerprint image central of the core point of the fingerprint image to extract the feature vectors. K Nearest neighbor (KNN) is classification method that classifies testing set to training set. The testing set is a set of testing fingerprint images. The training set is a set of fingerprint database. The testing set is classified to the minimum distance metric. The distance metric determines the meaning of “nearest neighbor.” The most widely used distance metric is the Euclidean measure which defined as follows.

2)( ba ffD −= (5) where D was the matching score that used in the classification process; fa was the fingerprint feature in training set and fb was the fingerprint feature in the testing set. Papers in [7, 10] were the sample of applied Euclidean measurement. KNN classifier took K fingerprint per person to set up the training set and took the 8-K fingerprint per person to set up the testing set. In the classification process, we used the minimum value of D to classify two fingerprint images were as the same finger. As the DWT transform area in figure 2, recognition rate shows that two areas of DWT coefficients are sufficient features for classification process.

Table 1: Recognition rate using Daubechies8

Method 1-NN 2-NN 3-NN 4-NN

DWT based in [6] 95.60% 97.44% 98.46% 100.00% DWT based in [7] 73.63% 82.05% 87.69% 76.92%

AL 98.90% 100.00% 100.00% 100.00% AH 98.90% 100.00% 100.00% 100.00%

AHL 98.90% 100.00% 100.00% 100.00%

Table 2: Recognition rate using Daubechies9

Method 1-NN 2-NN 3-NN 4-NN

DWT based in [6] 97.80% 100.00% 100.00% 100.00% DWT based in [7] 73.63% 82.05% 87.69% 78.85%

AL 100.00% 100.00% 100.00% 100.00% AH 100.00% 100.00% 100.00% 100.00%

AHL 98.90% 100.00% 100.00% 100.00%

Table 3: Recognition rate using Symmlet5

Method 1-NN 2-NN 3-NN 4-NN

DWT based in [6] 86.81% 98.72% 100.00% 100.00% DWT based in [7] 62.64% 64.10% 72.31% 65.39% Proposed(AL) 96.70% 100.00% 100.00% 100.00% Proposed (AH) 94.51% 100.00% 100.00% 100.00%

AHL 94.51% 100.00% 100.00% 100.00%

Table 4: Recognition rate using Sym9

Method 1-NN 2-NN 3-NN 4-NN

DWT based in [6] 85.71% 98.72% 98.46% 98.08% DWT based in [7] 70.33% 80.77% 83.08% 76.92%

AL 87.91% 97.44% 98.46% 98.08% AH 87.91% 98.72% 98.46% 98.08%

AHL 87.91% 98.72% 98.46% 98.08% As the result, the sub-bands of DWT coefficients recognition rate was 100% (db9) when we transformed at 2 sub-bands. Matching results of feature proposed in Figure 2(b), 2(c) and 2(d) have nearly recognition rate. So we proposed the sub-band of DWT feature extraction at 2 sub-bands. The recognition rate of proposed method is higher than methods in [6-7].

4.1. Complexity The matching method based on sub-bands of DWT coefficients was more the computation time cause of the step of decomposition to produce the feature vectors from the sub-images in the image sections. We compared the computation time between proposed method and method in [6, 7] as follows.

Computation time

0

100

200

300

400

500

db8 db9 sym5 sym9Wavelet

Tim

e (m

s.)

DWT based method in [6] DWT based method in [7] Proposed method Fig.3: Computation time in millisecond.

Computation time of the proposed method has more a few milliseconds than the method in [6, 7]. A number of features are 12 features that it has the same as the method in [6, 7]. Therefore, the computation time in the matching process is the same as method in [6, 7] but it has higher the recognition rate than the others. In the feature extraction process, it just use one time for a classification process. So the feature extraction processing time is not a major concern to the complexity of the algorithm. From the experimental results, it showed the proposed algorithms have more the recognition rate. The features are extracted from the selected sub-bands that still have the significant data. The significant data are extracted from some sub-bands of the DWT coefficients. The results showed that 2 sub-bands of DWT are sufficient to match the fingerprint images. if we use more than 2 sub-bands of DWT, it increase a few of the recognition rate but the features are increased largely that it takes more computation time.

5. CONCLUSIONS The matching method using sub-bands of wavelet feature extraction has more recognition rate than the wavelet feature extraction method. We improve this method to extract more DWT detail coefficients to generate the fingerprint features. It shows the better result than the method proposed in [6]. The proposed method has high recognition rate because it has more detail coefficients to generate the features. By the means of sub-bands of DWT coefficients, the recognition rate is gradually increased when we compare sub-bands of DWT coefficients method with the DWT method. The DWT just only transform in low frequency area at each level of DWT. The recognition rate of sub-bands of DWT coefficients is more accurate than DWT method. It has high recognition rate than the DWT method that proposed in [6]. The sub-bands of DWT coefficients transform in horizontal high frequency, vertical high frequency and both; we call area of sub-bands. The sub-bands of DWT coefficients method transforms in two, three and four areas. The four areas is the wavelet packet transform (WPT) method. The feature of sub-bands of DWT coefficients generates from the standard deviation of DWT coefficients at each sub-band. The feature is used in the classification process to evaluate recognition rate. We use KNN classifier in the classification process. KNN is widely used in fingerprint matching process. It matches the fingerprint features by the Euclidean minimum distance. [6-7], [10] REFERENCES [1] Simon-Zorita D., Ortega-Garcia J., Cruz-Llanas S., Gonzalez-

Rodriguez J., “Minutiae Extraction Scheme for Fingerprint Recognition Systems”, Proceedings of International Conference on Image Processing, Volume: 3, pp. 254–257, 7-11 October 2001.

[2] Arantes M., Ide A.N., Saito J.H., “A System for Fingerprint Minutiae Classification and Recognition”, Proceedings of ICONIP’02, Vol. 5, pp.2474–2478, 18-22 November 2002.

[3] Espinosa-Duro V., “Minutiae Detection Algorithm for Fingerprint Recognition”, IEEE Aerospace and Electronics Systems Magazine, Vol. 17 Issue: 3, pp.7–10, March 2002.

[4] Lee C.J., Wang S.D., “A GABOR Filter-Based Approach to Fingerprint Recognition”, Proceedings of SIPS 99, pp.371–378, 20-22 October 1999.

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[6] Tico M., Immonen E., Ramo P., Kuosmanen P., Saarinen J, “Fingerprint Recognition Using Wavelet Features”, Proceedings of ISCAS 2001, Vol. 2, pp.21–24, 6-9 May 2001.

[7] Selvaraj H., Arivazhagan S., Ganesan L., “Fingerprint Verification Using Wavelet Transform”, Proceedings of ICCIMA 2003, pp.430–435, 27-30 September 2003.

[8] Biometric System Lab., University of Bologna, Cesena-Italy. (www.csr.unibo.it/research/biolab/).

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