An Approach for Enhancing Fingerprint Images using

APPLICATION PROBLEM

An Approach for Enhancing Fingerprint Images using Adaptive Gabor Filter Parameters1 S. L. Gonzaga de O., F. Viola, and A. Conci Universidade Federal Fluminense, Passo da P@atria St.,156, Bl. E, 24.210–240, Niteroi, RJ, Brazil e-mail: {[email protected]; fviola,[email protected] Abstract—This work proposes a technique to enhance fingerprint images through the Gabor filter with adaptive parameters. Firstly, average ridge and valley regions are evaluated as is their direction by a specific directional field algorithm. Secondly, the fingerprint topological structure is enhanced by the Gabor filter with adaptive parameters according to specific regions of the image, since filter orientation and frequency parameters vary according to the fingerprint area. Experimental tests show accurate final results for the recognition processes. Since the algorithm presents low computational cost, this scheme can be applied to an on-line recognition process. Keywords: biometrics, fingerprints, Gabor filter, directional field, image processing. DOI: 10.1134/S105466180803019X

1. INTRODUCTION The increasing demand for reliable human identification on a large scale in governmental and civil applications has boosted interest in scientific testing of biometric systems. Biometrics is an emerging technology that is used to identify people by their physical and/or behavioral characteristics. In addition, it inherently requires that the one to be identified be physically present at the identification point. Fingerprint identification is one of the most used and important biometrics. In fact, fingerprints offer advantages when compared with other biometrics: there are no difficult to capture a fingerprint image; there are not real problems with reader position and it is considered safe since it is not an intrusive system; every individual has these patterns; fingerprint recognition technology is a mature technology; fingerprint recognition and capture have gained acceptance by users; fingerprints are difficult to imitate; and fingerprints can be acquired on a large scale. Fingerprints are a pattern of ridges and valleys on the finger surface. Also, fingerprints are known for the uniqueness of the topological structure and immutability. Furthermore, they are currently the most used biometric technology, mainly as one of the most reliable identification methods. Generally, cases of individuals who have alterations on the topological structure of their fingerprints are rare. Although fingerprint images have between sixty and eighty minutia, two fingerprint images are considered identical when at least twelve singular points with the same configuration that have exactly the same location are present. Usually, an auto-

Received January 15, 2007

matic fingerprint identification system is done through minutiae matching, i.e., the fingerprint pattern points are matched, instead of matching pixels of a certain pattern ridge. Moreover, minutia are ridge bifurcations, terminations, deltas, cores, and other fingerprint singular points. Furthermore, fingerprint patterns are completely characterized by ridges and valleys. Ideally, two narrow parallel valleys separate each ridge, and two narrow parallel ridges separate each valley. As established, minutia are defined in the ridges. Following this brief introduction, Section 2 introduces the fingerprint quality issue. Section 3 describes the theory of directional fields and smoothing. Section 4 introduces Gabor filtering. Results are presented in Section 5. Finally, some conclusion remarks are shown in Section 6. 2. MOTIVATION AND REVIEW Although the problem of minutia automatic extraction has been studied quite well; it is not completely solved when the fingerprint image has low quality. In addition, low contrast and noise can produce false minutia and hide real minutia. The topographic relief of a fingerprint ridge structure and the presence of ridge anomalies, named minutiae points, dictate the uniqueness of a fingerprint. Afterwards, the problem of automatic fingerprint matching involves determining the degree of similarity between two fingerprint impressions by comparing their ridge structure and the spatial distribution of the minutiae points. Due those features, the main disadvantage of fingerprint recognition is the bad quality of its images in the matching step. Thus, fingerprint image enhancement has a great deal of importance and it is the focus of this work. To be precise, the main objective of

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this work is the application of adaptative parameters of Gabor filter to enhance fingerprint images. There are recent approaches that use other techniques, for instance, [1] described an approach to enhance the fingerprint image based on integrating an anisotropic filter and a directional median filter. In [2], a two-level convolution template is designed according to ridge direction and ridge circle. Afterwards, a simplified convolution is used to enhance fingerprints. In [3], the authors proposed a fingerprint enhancement algorithm based on contextual filtering in the DCT domain. All intrinsic fingerprint features, including ridge orientation and frequency, are estimated simultaneously from DCT analysis. On the other hand, one of the most well-known and used techniques of fingerprint image enhancement is the Gabor filter application. In the last decades, the Gabor filter has been used in automatic fingerprint identification research. For instance, [4] proposed a unified viewpoint for fingerprint representation and recognition and [5] presented a hybrid-matching algo2 rithm that uses both minuatiae (point) information and texture (region) information for matching fingerprints. Another example is [6], which presented a system for fingerprint verification that approaches the matter as a two-class pattern recognition problem. Additionally, [7] proposed a technique for extracting minutiae based on representing the ridge structure of a fingerprint image as a run length code, among many other works. In [8], the authors proposed a method that applies a 1-D Gabor filter for ridge orientation estimation and image enhancement as well. The bandpass Gabor filter is used for estimation of a fingerprint ridge orientation map. Relying on the information of the orientation map, the fingerprint image is reinforced in the ridge and valley contrast and ridge smoothness. The Gabor filter is a very useful tool for texture analysis in both domains, and it combines the advantages of them. Hence, several works on enhancing and minutia detection in fingerprint images use the Gabor filter. In many of them, the parameters of frequency f, the standard deviation σ of the two-dimensional Gaussian that modulates the filter, the spatial domain window, and also the orientation angles θk were empirically found or computed by a neural network. Thus, even using many samples, empirical values may lead to inconsistencies in some fingerprint image types. Along the same lines, neural networks do not permit simple and complete control over what occurs when determining some parameters. The Gabor filter is better applied to a specific image region when the used orientation angle and frequency are extracted from the proper image region, i.e., the directional angle and frequency of ridges and valleys of that region. There were works that used the Gabor filter to adaptively compute the orientation angle and frequency to improve the enhancement process. For instance, [9] proposed a decomposition method to esti1

mate the orientation field from a set of filtered images obtained by applying a bank of Gabor filters on the input fingerprint images. It takes significant effort to estimate local orientation from the filtered images. Similarly, considering frequency and orientation-selective properties and optimal joint resolution in both domains, [10] used Gabor filter banks to enhance fingerprint images. Moreover, [10] assumed that the parallel ridges and valleys exhibit plane waves with an ideal sinusoidal-shaped which were associated with some noises. In other words, the ID orthogonal signal to the local orientation is approximately a digital sinusoidal wave. Later, the method proposed by [10] was tuned to the corresponding local orientation and ridge frequency (reciprocal of ridge distance) in order to remove noises and preserve the genuine ridge and valley structures. The prior sinusoidal plane wave assumption of [10] should be studied more because the orthogonal signal to the local orientation in practice does not consist of plane waves with an ideal digital sinusoidalshape in some fingerprint images or some regions. In the same vein, [11] implemented an algorithm to enhance fingerprints, which modified the method proposed by [10]. Thus, [11] improved the algorithm performance by selecting optimal filters. It was further customized using an object-oriented approach to improve run processing. Citing another example, parameters in [12] are deliberately specified through some principles instead of experience and an imageindependent parameter selection scheme is applied. Thus, modulating the periodic function by a 2D anisotropic Gaussian function can specify that method. Hence, the frequency representation is a band-pass filter associated with a bank of low pass filters. As a result, it can more straightforwardly express the texture characteristics of fingerprint images than the method proposed by [10]. Continuing this brief review, [13] introduced a fingerprint image enhancement based on the Gabor filter in wavelets domains. Namely, frequency is not adaptively performed and the authors used Rao’s algorithm in order to perform the local orientation. Likewise, [14] described a Fourier transform approach to enhance fingerprints. It uses simple gradient operators for the image orientation. In the following, the frequency image is estimated based on the sum of the projections taken along an oriented orthogonal line to the ridges or based on the gray level variation in an oriented orthogonal window to the ridge flow. Next, [15] used directional fields for enhancing fingerprint images. Furthermore, this work uses directional fields to stipulate the Gabor filter orientation angles. On the whole, those works evaluate the directional field through using gradient operators for the orientation image. Thus, a simpler algorithm can be applied to adaptively evaluate the directional field and frequency. In fact, frequency and orientation angle evaluation algorithms are well known, but here they are newly used as Gabor filter parameters. Therefore, this work proposes

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an alternative algorithm to fingerprint enhancement using adaptive Gabor filter parameters. Namely, the frequency and orientation angle are adaptively evaluated from the input image. Furthermore, a specific direction field algorithm obtains the orientation angle. 3. DIRECTIONAL FIELD AND SMOOTHING As described earlier, a digital fingerprint is formed by ridge and valley structures. Moreover, ridges are the black lines and valleys are the white ones. Thus, Grasseli proposed directional fields in a digital fingerprint image in 1969 [16]. Briefly, a directional field (or directional image) describes either the course of those structures or the basic form of a digital fingerprint. In other words, a directional field is defined by the local orientation of ridge and valley structure. Moreover, a directional field of a fingerprint image represents the ridge direction in the image; i.e., it is a matrix that represents ridge and valley orientation for each block in the fingerprint image. Such a matrix is defined by a generic pixel [n, m] of the fingerprint image, where n refers to the columns and m, the lines. The local orientation ridge of the [n, m] pixel is the angle θ formed in relation to the horizontal axis. This angle is computed according to nearby pixels with the center at [n, m]. Furthermore, the directional field gives information about the fingerprint pattern. It can be computed even in images with noise by calculating the average direction to reduce noise influence. The directional field is used in most methods that extract minutia and classify fingerprints. Figure 1 shows an example of a fingerprint image and its directional field extracted from this approach. This work calculates the directional field through a 9 × 9 mask with the reference pixel in the center, as Fig. 2 shows. Many methods have been proposed to estimate directional fields [16, 17]. The main approaches are techniques based on the local gradient to compute the main direction of the local block [16, 18], the use of an algorithm to estimate the orientation by least squares [7, 16], the use of predefined local windows in order to calculate the magnitude of certain directions [19], algoPATTERN RECOGNITION AND IMAGE ANALYSIS

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rithms that consider estimates with arithmetical average about large regions [16], and the use of the Gabor filter to obtain ridge directions [18]. Although there are still other techniques [13], they are not often employed. The approach used in this work estimates the direction of each pixel from the results of eight orientated filters. Those filters add the difference of the pixel [i, j ] and eight or sixteen neighboring pixels using a mask comprised of 9 × 9 pixels as proposed by Stock and Swonger [19, 20] or a mask made up of 17 × 17 pixels [21]. Such directions are shown in Fig. 2. Thus, this method was adopted because it is one of the most reliable. Average estimates are arithmetically calculated over a large region of the image, and the results obtained have more accurate measures as well. Furthermore, its implementation is simple; namely, it is computationally performed with low cost and also it captures the main directions of local ridges. In addition, sixteen angles are possible, which are enough for the approach described here. The pixel values of Fig. 2 have directions identified by numbers 0 to 7. They are added to obtain the values S0 to S7, and I(n, m) presents the gray level value of that position in the image. Let [i, j ] be a generic pixel in a fingerprint image. Thus, the local ridge orientation at [i, j ] is the angle θij between the fingerprint ridges and the horizontal axis. This work estimates the direction at each pixel from the output of eight oriented filters. These filters calculate the addition of the differences between pixel [i, j] and eight or sixteen neighbors along eight directions using an appropriate mask. A 9 × 9 or a 17 × 17 pixel mask is centered at pixel [i, j] to compute the direction in a block. As a result, the gray values of neighboring pixels in eight directions, which are the positions marked by numbers 0 to 7 in Fig. 2, are added to obtain additions S0 to S7. Overall, both 9 × 9 and 17 × 17 pixel masks adaptively compute the additions as Eq. (1),

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Fig. 3. Directional field scanning the first block with a 3 × 3 filter, a 4 × 4 filter, and the central angle set. n

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where m = |min(l, 2, 8 – l )|, m' = 0 if l = 4, m' = –2 if l = 7, otherwise m' = |min(4 – l, 2)|(4 – l )/|4 – l |. The difference between pixel masks 9 × 9 and 17 × 17 in Eq. (1) is the use of n as 2 or 4 and the use of a unitary or double increment in K, respectively, in the additions. Thus, if pixel [i, j ] has a value C, its angle is given by Eq. (2), 3 d = p whether ( 2nC + Sp + Sq ) < --8

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otherwise d = q. Let p and q be integers in [0, 7] such that Sp = minimum Sl (l = 0…7), Sq = maximum Sl (l = 0…1), and Sl is each one of S0 to S7 on Eq. (1). In other words, p is the index of the minimum Sl and q is the index of maximum Sl. Therefore, Eq. (2) gives an average direction of each block of 9 × 9 or 17 × 17 pixels, quantified to eight possible angles, namely, l = lπ/8 radians. Regarding direction d, it is p if the center pixel C is located in a ridge and q if it is in a valley. Each block represents a directional matrix cell, which is a directional field representation of the considered neighborhood. In addition, the directional field, if directly computed by the directional matrix, may contain several unreliable elements due to the local process characteristics. In this situation, regularization or a smoothing step is very useful for enhancing directional fields. After computing the directional matrix, this work 3 smoothes it in order to reduce noise and increase the accuracy of the correct angle localization. Generally, several methods for smoothing the directional field are described in the literature, such as Gaussian filters [22, 23], sine–cosine, and statistic calculus of component with more frequency, among others. This work uses the more frequent angle in a 3 × 3 block. Such a block, which is comprised of 3 × 3 pixels, is an angle filter, which scans the image setting its central angle with the more frequent angle. In the end, the reference pixel receives such an angle. When two or more angles have the same number of elements in the 3 × 3 angle block, the number of angles in the block fil-

ter is increased and the process is repeated. The next time, a block of 4 × 4 angles is used. Afterwards, a block with 5 × 5 angles is used, and so on. Thus, it is performed until the most frequent direction is found. Figure 3 depicts a 3 × 3 filter scanning the first block, which occurs three times the angle 3π/4 radians, three times the angle 0 radian, once π/2, and twice the angle π/4 radian. Incrementing the block to 4 × 4 pixels, the direction of angle 3π/4 radians appears six times, 0 radian makes up four components, angle π/2 radians comprises two components, and angle π/4 radians occurs four times. Finally, the central angle of such block is set with the more frequent angle, namely, π/4 radians. In conclusion, after the directional field is smoothed, Gabor filtering can be performed. Moreover, this work uses the bandpass filter by convolution in the frequency domain with specific parameters by each region. 4. GABOR FILTER Dennis Gabor developed the 1-D filter in 1946 [24]. Gabor filter-based features have been successfully and widely applied into several biometric systems, such as texture segmentation, face and handwriting recognition, and fingerprint enhancement [25]. This is due to the Gabor filter characteristics, especially the frequency and orientation representation that are similar to those of the human visual system [26, 27]. Along the same lines, the Gabor function has been recognized as a very useful tool in computer vision and image processing, especially for texture analysis, due to its optimal localization properties in both the spatial and the frequency domain. The family of 2D Gabor filters was originally presented by Daugman in 1980 as a framework for understanding the orientation-selective and spatial-frequency–selective receptive field properties of neurons in the visual cortex of the brain, and then was further elaborated mathematically by Daugman in 1985. Briefly, the 2D Gabor function is a harmonic oscillator, composed of a sinusoidal plane wave of a particular frequency and orientation, within a Gaussian envelope [12]. Gabor filters have the properties of spatial localization, orientation, and spatial-frequency selectivity. The literature broadly explains and uses this space domain filter, for instance, in [23]. Depending on the parameters used, this filter makes it possible to characterize information about the structure of directional angles and width of ridges and valleys in fingerprint images. The Gabor filter is projected in the spatial domain, modulated by a two-dimensional Gaussian. The Gaussian function envelope is proportional to the standard deviation σ, which determines the channel bandwidth [28]. The Gabor filter is both frequency- and orientation-selective. In addition to that, it has optimal joint resolution in both spatial and spatial-frequency


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Fig. 5. Partial fingerprint image (128 × 128) and filtered image with element xθ in the first term of the Gabor filter expression with 0 degree orientation angle, respectively.

Fig. 4. Example of fingerprint image (275 × 270 pixels).

domains [29]. Since fingerprints possess locally parallel ridges and valleys with well-defined local spatialfrequency and orientation, this filter reduces noise in fingerprint images [25]. Thus, filtering the fingerprint by using Gabor filters can enhance the ridge and valley structures. The planar sinusoidal effectively removes undesired noise, preserves true ridge and valley structures, and isolates feature information contained in a particular image orientation [25]. Thus, the Gabor filter general form is presented in Eq. (3) [30], 2

in [28, 31, 32, 33] and f = 1/2 2 in [30]. Moreover, by using a too big f, noise can be created in the filtered image. On the other hand, if f is too small, ridges can be interlaced. In fact, if parameter K is variable in the automatic process, it permits identification of fingerprint images from a unique finger with better accuracy in the matching step and a better image distinction from different fingers as well. Next, the filter orientation is θk = π(k – 1)/m, k = 1, …, m, where m is the number of Gabor filter directions. Similarly to [25], this work uses m = 3. Finally, the standard deviation of a 2D normal (or Gaussian) distribution (or envelope) is represented by σ, which is related to the Gaussian width which modulates the Gabor filter. Consequently, if σ is too big, the filter is more robust to noise; however, it does not capture the ridge details. On the other hand, if σ is too small, the filter does not remove noise; however, it captures the ridge details. In this work, it is empirically used as σ = σx = σy = 0.5 [25]. The use of the rectangular coordinate origin in the spatial window of the filter in the spatial domain permits the filtering process independent from the domain used. Because of that, the domains used in the experimental tests are [–15, 15] or [–7, 7] in coordinates [x, y] due to symmetry in the convolution process.

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 xθ yθ  -2 + --------2 , (3) G ( x, y, f , θ, σ ) = exp  2πjf ( x θ ) – -------2σ x 2σ y   where xθ = xcosθk + ysenθk, yθ = –xsinθk + ycosθk, x, y are the integer spatial coordinates of the image and j = – 1 . Alternatively, yθ can be used in the first right term of Eq. 3, instead of xθ. Furthermore, parameter f denotes the frequency of the wave in the sinusoidal plan. The frequency parameter f set in the spatial domain is the 2D Gaussian top in the frequency domain. This feature attenuates or rejects frequencies with longer distances than the standard deviation, where frequency f is the center. Therefore, finding precise values for such parameters in each image is very important. Since most local ridge structures of fingerprints have well-defined local frequency and orienta5 tion, f can be set by the reciprocal average of the interridge distance K. Therefore, frequency is set as f = 1/K 4


5. EXPERIMENTAL INVESTIGATION A high-quality fingerprint image presents a unique standard for the gray level ridge, and this standard is different from the unique standard of the gray level valley. Thus, Fig. 4 presents an example of a fingerprint image. In some regions, ridges do not have an appropriate standard of gray levels; i.e., ridges are not sufficiently dark compared to valleys. In addition to that, valleys do not present appropriate gray levels. Finally, some image regions were lost. In such images, ridges and valleys should have more contrast. In the following, although several experiments were performed, just a few images are shown as examples in order to show how fingerprint images are enhanced through this approach. Figure 5 shows a selected region of Fig. 4 for filtering and its filtered image. The parameter values used

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Fig. 6. Original partial fingerprint image (128 × 128) and filtered image with element yθ in the first term of the Gabor filter expression with 0 degree orientation angle, respectively.

Fig. 7. Original partial fingerprint image (128 × 128) and filtered image with element xθ in the first term of the Gabor filter expression with π/2 radians orientation angle, respectively.

Fig. 8. Original partial fingerprint image (128 × 128) and filtered image with element yθ in the first term of Gabor filter expression with π/2 radians orientation angle, respectively.

Fig. 9. Original partial fingerprint image (128 × 128) and filtered image with element xθ in the first term of the Gabor filter expression with π/4 radians orientation angle, respectively.

for such filtering are a frequency of 0.33, 2D Gaussian width of 0.7, directional angle of 0 degree, and a spatial window domain of the filter between –15 and 15. Those values were empirically employed. Figure 5 presents a marked region with noise, for instance, in the second ridge from the bottom up. Figure 5 shows filtering with an usual element xθ in the first term of the Gabor filter expression. The partial image on the right of Fig. 5 has valleys that are lighter and marked ridges that present less noise compared with the left side. On the other hand, inclined and vertical ridges still present noise. Such filtering should be applied in smaller regions of the image, determining the orientation angle of the Gabor filter by directional fields. The same values of the Gabor filter parameters earlier presented are applied for filtering the partial image shown in Fig. 6, except filtering with the element yθ in the first term of the Gabor filter expression. After filtering, valleys also become lighter and better defined, for instance, in the marked zone of the image. Inclined and mainly vertical ridges presented better definition for the indirect π/2 radians usage, although horizontal ridges are damaged in such a test. Figure 7 presents the same region of the image filtered with element xθ in the first term of the Gabor filter expression. The same parameters mentioned earlier are used, except the orientation angle of π/2 radians. This filtering results in a well-defined image with darker ridges and lighter valleys in relation to the original partial image. Although vertical ridges present better defi-

nition, horizontal and inclined ridges present lower quality. Figure 8 presents the same partial fingerprint image filtered with element yθ in the first term of the Gabor filter expression and the same parameter values described earlier, with the exception of the orientation angle of π/2 radians. In the same way, the filtered image also results in a better definition among ridges and valleys as well as horizontal ridges. Figure 9 presents the same filtered partial fingerprint image with element xθ in the first term of the Gabor filter expression and the same values of the parameters described earlier. However, a directional angle of π/4 radians is used. The filtering image results show inclined ridges with better definition. It also presents better definition between ridge and valleys. Figure 10 presents the same filtered partial fingerprint image with element yθ in the first term of the Gabor filter expression and same parameter values described earlier. However, a directional angle of π/4 radians is used. The filter answer does not present any better result, either in the different gray levels between ridges and valleys or for reduction of noise in ridges. Figure 11 presents the same filtered partial fingerprint image with element xθ in the first term of the Gabor filter expression and the same parameter values described earlier. However, a directional angle of 3π/4 radians is used. Filtering results present a larger difference among gray levels of ridges and valleys, and inclined ridges presented better definition.


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Fig. 10. Original partial fingerprint image (128 × 128) and filtered image with element yθ in the first term of the Gabor filter expression with π/4 radians orientation angle, respectively.

Fig. 11. Original partial fingerprint image (128 × 128) and filtered image with element xθ in the first term of the Gabor filter expression with 3π/4 radians orientation angle, respectively.

Fig. 12. Original partial fingerprint image (128 × 128) and filtered image with element yθ in the first term of the Gabor filter expression with 3π/4 radians orientation angle, respectively.

Fig. 13. Original partial fingerprint image (128 × 128) and filtered image with adaptive orientation angle of the Gabor filter, respectively.

Figure 12 presents the same filtered partial fingerprint image with element yθ in the first term of the Gabor filter expression and the same parameter values described earlier. However, a directional angle of 3π/4 radians is used. The filter answer does not present any better result, either in the different gray levels between ridges and valleys or reduction of noise in ridges. Figure 13 shows a filtered partial fingerprint image by an adaptive orientation angle of the Gabor filter. Such filtering results in better ridge definition and different gray levels between ridges and valleys. Figure 14 shows a partial fingerprint image on the left, its directional field in the center, and a convoluted image with the Gabor filter on the right. The parameter values are a frequency of 0.33, Gaussian width of 0.8, and a 3π/4 radians orientation angle, according to the computed directional field. Filtering results present better definition in the bottom-up right region.

Figure 15 shows a 256 × 256 low quality image. It demonstrates another example of tests performed through evaluating the frequency parameter of the Gabor filter in order to adaptively enhance fingerprint images. The original fourth quadrant of Fig. 15 and its filtered result are represented in Fig. 16 with a 128 × 128 partial image. The Gabor filter parameters used in such a test are the 2D Gaussian width of 0.7, and the spatial window filter domain is between –15 and 15, both empirically employed. A directional angle of 3π/4 degree is employed. The filter frequency used is 0.18 because the calculated average ridge and valley of the region is K = 5.44. In the filtered and inverted image of Fig. 16, noise is reduced, except in ridges that do not present directional angle of 3π/4 degrees, for which the adaptive filter must be applied, according to the orientations extracted from the directional field.

Fig. 14. Original partial image (128 × 128), directional field overlapped, and partial image inverted after filtering, respectively. PATTERN RECOGNITION AND IMAGE ANALYSIS

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Fig. 15. An example of a low quality fingerprint image (256 × 256).

Figure 17 presents details of the previous test with a 64 × 64 partial image. This test uses a 2D Gaussian width of 0.7 and a spatial window domain of the filter between –15 and 15, where the Gabor filter parameters are empirically employed in both. The directional angle used is 3π/4 degrees. The filter frequency used is 0.333. This value was employed because the calculated ridge width average near regions that present noise is K = 3. The image taken from the filtered region presents better definition, and noise is reduced in ridges which present a directional angle of 3π/4 degrees and a frequency of 1/K. The upper right region of the filtered image in Fig. 17 presents low definition. An adaptive filter should be employed with a directional angle near π/2 radians. Along the same lines, Fig. 18 shows the same partial image of Fig. 17 with the same Gabor filter parameters, except for the directional angle with π/2 radians degrees. The upper right filtered image of Fig. 18 presents better definition, and the upper left region of the filtered image presents low definition because it has a directional angle of 3π/4 radians degrees. Tests show that evaluating the Gabor filter parameters on each image

region can present adequate results. Thus, directional field images are used for defining the orientation angle parameter. In order to demonstrate the effectiveness of the proposed approach, a set of low-quality fingerprint images as experimental samples was adopted. The images were extracted from FVC2000 database [34], which contains four types of fingerprint dataset: db1 (low-cost optical sensor), db2 (low-cost capacitive sensor), db3 (optical sensor), and db4 (synthetic fingerprint generation). Several low-quality images from each dataset were chosen, and the enhancement process was executed. For a small number of fingerprints, the most used method to test image quality measures is based on visual (and thus subjective) assessments of images [35]. Thus, relying on subjective judgment, minutia from more than 15 enhanced images of the four datasets were manually extract. Thus, the number of correct minutiae obtained through this approach is on average 10–15% superior to the conventional 2-D Gabor filtering. 6. CONCLUSIONS This work studies the enhancement of fingerprint images using Gabor filter parameters depending on each image region. One of the Gabor filter parameters is the standard deviation. Calculating the standard deviation of the input image and using this value as a parameter of the two-dimensional Gaussian width did not present accurate results. According to the tests performed, this parameter as well as the frequency f must be between 0 and 1. Generally, frequency f is defined as the inverse of the interridge pixel number of fingerprint 5 images, which here is adaptively implemented using the average ridge and valley of each region. Tests show the relation of the directional angle used as the Gabor filter parameter with the directional angle of image ridges. Using the Gabor filter with the usual element xθ in the first term of the equation reduces noise in horizontal directional ridges when an appropriate directional angle is employed, and it corrects black points in valleys and white points in ridges. Additionally, it corrects bonding ridges that have inconsistencies. Similarly, the use of the Gabor filter with element yθ in the first term of the equation and the use of the cor-

Fig. 16. Partial fingerprint image (128 × 128), its directional field overlapped, and filtered and inverted image, respectively. PATTERN RECOGNITION AND IMAGE ANALYSIS

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6. 7. Fig. 17. Directional field overlapped a partial fingerprint (64 × 64), its filtered and inverted image with 3π/4 radians degrees in the directional angle of the Gabor filter, respectively.

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10. Fig. 18. Partial image (64 × 64), its directional field overlapped, and filtered and inverted image with π/2 radians degrees in directional angle of Gabor filter, respectively.

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rect directional angle reduce noise of vertical directional ridges, also including bonding ridges that have inconsistencies. Although the average of both approaches in the frequency domain has been tested out, better results were not achieved. The use of the directional angles π/4 and 3π/4 is related to inclined ridges of the fingerprint image, and horizontal and vertical ridges are related to the 0 and π/2 directional angles. Thus, computing the directional field is important for an automatic process, which follows this scheme. Tests demonstrate that the Gabor filter using the orientation angle and frequency evaluated through the proposed technique can be used efficiently for enhancing fingerprint images. Intensive tests in large-scale and standard fingerprint databases in order to verify the accuracy and efficiency, comparisons to other approaches, and the study of the correct usage of the standard deviation parameter of the Gabor filter should be developed in future work. REFERENCES 1. C. Wu, Z. Shi, and V. Govindaraju, “Fingerprint Image Enhancement Method Using Directional Median Filter,” in Proceedings of the SPIE, 2004, vol. 5404, pp. 66–75. 2. X. F. Tong, S. B. Liu, J. H. Huang, and X. L. Tang, “A Fast Image Enhancement Algorithm for Fingerprint,” in Proceedings of the Sixth International Conference on Machine Learning and Cybernetics, Hong Kong, 2007, pp. 76–180. 3. S. Jirachaweng and V. Areekul, “Fingerprint Enhancement Based on Discrete Cosine Transform,” Lecture Notes in Computer Science 4642, 96–105 (2007). 4. C. J. Lee, S. D. Wang, and K. P. Wu, “Fingerprint Recognition Using Principal Gabor Basis Function,” in International Symposium on Intelligent Multimedia, Video and Speech Processing, 2001, pp. 393–396. 5. A. K. Jain, A. Ross, and S. Prabhakar, “Fingerprint Matching Using Minutiae and Texture Features,” in PATTERN RECOGNITION AND IMAGE ANALYSIS

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34. D. Maio, D. Maltoni, R. Cappelli, J. L. Wayman, and A. K. Jain, “FVC2000: Fingerprint Verification Competition,” IEEE Transactions on Pattern Analysis and Machine Intelligence Archive 24 (3), 402–412 (2002). 35. E. Tabassi, C. L. Wilson, and C. I. Watson, “Fingerprint Image Quality,” Technical Report: NIST, 2004. Sanderson L. Gonzaga de Oliveira received his B.Sc. in Computer Science at Pontificia Universidade Catolica do Parana in 1996 and his M.Sc. at Universidade do Estado do Rio de Janeiro in 2004. Currently, he is a PhD candidate in the Universidade Federal Fluminense. His research interests include Image Processing and Computer Modeling (www.ic.uff.br/~sgonzaga).

F. M. Viola received his B.Sc. in Computer Science in 1999 and his M.Sc. at Universidade Federal Fluminense in 2006. His research interests include Biometrics and Image Processing (www.ic.uff.br/~fviola).

A. Conci is a Dr.Sc. professor in the Department of Computer Science in Universidade Federal Fluminense. Her research interests include Biomechanics, Applications of Computer Vision, and Image Processing (www.ic.uff.br/~aconci).

SPELL: 1. adaptative, 2. minuatiae, 3. smoothes, 4. sen, 5. interridge


Vol. 18

No. 3

2008