An Efficient Fingerprint Ridge Distance Estimation Using Typical ...
An Efficient Fingerprint Ridge Distance Estimation Using Typical Image Blocks Xuzhou Li1,2, Dong Yang1, and Yilong Yin1,* 1
School of Computer Science and Technology, Shandong University, Jinan 250101, China 2 Shandong Youth University of Political Science, Jinan 250014, China [email protected], [email protected], [email protected]
Abstract. The average ridge distance of fingerprint images is a very important parameter for fingerprint image enhancement, which will greatly affect the performance of fingerprint recognition. A method of efficient ridge distance estimation based on typical image blocks is proposed. First, we obtain some typical candidate image blocks through the initial selection according to the orientation curvature of each block; Then better quality blocks from these candidate blocks are selected by taking quality strategy into account, while the remaining blocks are used to compute ridge distance using statistical window method; Finally, the average ridge distance is estimated through averaging several ridge distances in the remaining blocks. The experimental results show that our method is fast enough for real applications and is robust and reliable in estimating average fingerprint ridge distance. Keywords: fingerprint, ridge distance, typical image blocks, statistical window.
1
Introduction
Fingerprints have been used for identifications and verifications for many years because of their uniqueness and reliability. Frequency, that is, the reciprocal of ridge distance, is an important parameter used in fingerprint preprocessing. Many ridge distance methods have been put forward, such as methodologies based on spatial domain and methods based on the frequency field. The former is usually performed based on fingerprint blocks or the entire fingerprint images; the latter is often conducted by transforming the fingerprint images from spatial domain to frequency field, and then computing the ridge distance in that domain. Zs.M. Kovács-Vajna et al. [1] computed average ridge distance based on a twostep procedure: first, geometric and spectral approaches are used to compute the distance; second, the computation of harmonic coefficients leads to effective estimation of the average ridge period. Hong et al. [2] divided the input fingerprint images into blocks of same size, and then compute the gray values for central pixel of each block within the oriented window; the ridge distance is obtained by computing *
Corresponding author.
C.-L. Liu, C. Zhang, and L. Wang (Eds.): CCPR 2012, CCIS 321, pp. 308–315, 2012. © Springer-Verlag Berlin Heidelberg 2012
An Efficient Fingerprint Ridge Distance Estimation Using Typical Image Blocks
309
distribution of gray histogram. Yin et al. [4] defined statistical window and baseline for each non-overlapped block, which is binarized to acquire the distribution of ridge distances, and peak positions are detected after computing the distance from ridges to baseline of statistical windows. Maio et al. [5] did mathematical characterization of the local frequency of sinusoidal signals and developed a two-dimensional model in order to approximate the ridge-line patterns for ridgeline density estimation in digital images. Ren et al. [3] proposed a new method to estimate the ridge distance, which employs discrete Fourier transform, discrete information entropy theory, and weighted Euclidean distance to deal with fingerprint image accurately. The above estimation methods are based on the whole image or on each block of the entire image. Therefore, they all share a common approach of trying to utilize as many blocks in the images as possible to estimate the ridge distance. As a matter of fact, it is not always suitable, because it usually does not take the quality of each block into consideration, while the accuracy of ridge distance of each block in fingerprint images is not guaranteed. There is no doubt that these methods can get good performances when the fingerprint image is of good quality. In practice, however, not all the blocks are of good quality, the existence of great noise may have significant impact on the accuracy of average ridge distance. As the traditional methods use as many blocks or regions as possible to estimate the ridge distance, meanwhile, the time consumption of these traditional methods will inevitably increase as the image size increases. In this paper we present a novel method to solve the above problems by selecting so called typical blocks whose average ridge distance can represent the real value of the whole image instead of all available blocks of various quality. First, several low curvature blocks are selected based on the orientation curvature, second, some quality evaluation methods are adopted to perform a secondary selection. Statistical window method is used on the remaining blocks for average ridge distance estimation. Experimental results show that it achieves satisfying estimation accuracy with high computational efficiency. This paper is organized as follows. Section 2 describes the initial and secondary selections of typical blocks. Performance evaluation and experimental results are shown in Section 3. Section 4 states conclusions and discussions.
2
Typical Blocks Selection and Ridge Distance Estimation
In order to overcome the difficulties described above, we estimate average ridge distance by utilizing typical blocks, which are defined as fingerprint blocks that can accurately and reliably estimate ridge distance by using statistical window. Thus, the selection of typical blocks has to meet the following requirements: (1) the quality of blocks should be as good as possible, that is, fingerprint ridge is clear enough, the contrast between pixels is distinct (2) The ridge directions in the blocks should be consistent; we should avoid the presence of high-curvature ridges particularly in pattern area for selection of typical blocks. (3) The selected block should avoid the existence of endings and bifurcations
310
X. Li, D. Yang, and Y. Yin
We first compute block orientation for the sake of getting the degree of curvature. We divide fingerprint image into block of size 8 × 8 and estimate the orientation for each block. For the purpose of getting curvature of ridges in blocks, we used the curvature measure method, which is given by Wang[6]. Here, we give some notations, let SWi , j denote the ith row and the jth column of a statistical window, SWi , j is the total curvature value of a statistical window, C (m, n) is i +3 j +3
the orientation for each the block, we can get SW (i, j ) = C (m, n) . Thus, the set of m =i n = j
all
possible
statistical
windows can be expressed as: , where and are the width and H W P = {SW (i, j ) 0 ≤ i < H / b − 3, 0 ≤ j < W / b − 3}
height of fingerprint image, respectively, also, we use Flag[i][j] to denote whether the ith row and the jth column statistical window is available, Flag[i][j] = 0 and Flag[i][j] = 1 indicate that the statistical window SWi , j is unavailable and available, respectively. The detailed steps of constructing statistical windows by utilizing typical blocks are as follows: (1) For all the possible statistical windows SWi , j , which contains at least one background block of size 8 × 8 , label it as unavailable, namely, Flag[i][j] = 0 . Otherwise, compute SW (i, j ) , and set Flag[i][j] = 1 . (2) For all the statistical windows which satisfy P ' = {SW (i, j ) 0 ≤ i < H / b − 3, 0 ≤ j < W / b − 3 Flag[i ][ j ] == 1} , sort them in ascending order according to SW (i, j ) , thus, we can get the sorted set of statistical window Psorted . (3) For any element SWi , j included in the set Psorted and Flag[i][j] ≠ 0 , sort them in ascending order according to SW (i, j ) and do as follows: for all SWm,n which satisfy SW (m, n) ≤ SW (i, j ) and Flag[m][n] ≠ 0 if SWi , j and SWm,n are overlapped, then set Flag[m][n] = 0 . (4) Let N denote the number of statistical windows which are included in Psorted
，
and satisfy Flag[i][j] ≠ 0 . If N > T1 ( T1 is the threshold of initial selection number of statistical window). Select the first T1 available statistical windows in ascending order according to the value of SW (i, j ) , otherwise, select the N available statistical windows as candidate windows. After the initial selection according to the ridge curvature, the candidate statistical windows are illustrated in Figure 1 (d). Figure 1 (a) is the original image of FVC2004. It is a relatively low quality fingerprint image which varies in quality in different blocks and has some ridge conglutination regions. Figure 1 (b) shows the orientation fields of non-smoothing of different blocks. Different curvature of blocks are demonstrated in Figure 1 (c), the gray level of each blocks of size 8 × 8 reflects the curvature of ridge directions, a lighter block means a higher curvature value, thus, it can be seen from Figure 1 (d) that the candidate statistical windows mostly lie in the areas which have better quality.
An Efficient Fingerprint Ridge Distance Estimation Using Typical Image Blocks
(a)
(b)
(c)
311
(d)
Fig. 1. Statistical window image after the initial selection. (a) an original fingerprint in DB2_A of FVC2004 (b) orientation field (c) direction curvature image of blocks (d) candidate statistical windows in curvature image.
After the above initial selection, ridges with high curvature in the pattern area are filtered. Furthermore, because of non-smoothing orientation field, blocks with image noise generated by smudges, creases, scars and so forth are also nearly eliminated. Nevertheless, for the candidate statistical windows, even if the ridge directions have low curvature, the gray-level varies greatly in different areas under some circumstances. This will result in bad binaried blocks, which are not suitable to estimate the average ridge distance. Figure 2 shows examples of candidate statistical windows which have low curvature but have bad quality.
(a)
(b)
(c)
(d)
Fig. 2. Bad quality candidate statistical windows after the initial selection. (a) an original fingerprint in DB2_A of FVC2004, (b) orientation field, (c) candidate statistical windows in curvature image(d) its binaried statistical windows.
In order to acquire better quality blocks in candidate statistical windows, it is necessary to bring in some quality check strategies to select blocks which have clearer ridges and valleys. The mean and the variance of gray-level pixels in valid area of fingerprint images are two of most useful indicators to measure the quality of fingerprint. For good quality blocks, staggered changes between valleys and ridges usually increase their variances; the situation is contrary when the fingerprint blocks are blurred. The mean of gray-level pixels reflects the intensity of blocks or images, if the value in a block is too large, the ridges are probably blurred. If the adhesion between ridges is severe, the mean value is usually small.
312
X. Li, D. Yang, and Y. Yin
According to the above two quality check indicators, we make secondary selection from the candidate statistical windows, which can be described as follows: (1) For all the candidate statistical windows, compute gray-level mean M sw variance Vswi , j .
i, j
(a)
(d)
(g)
and
(j)
(b)
(e)
(h)
(k)
(c)
(f)
(i)
(l)
Fig. 3. Selected statistical windows after two selections.(a)(b)(c) are three original fingerprint images in DB2_A of FVC2004; (d)(e)(f) show the curvature of each block; (g)(h)(i) shows the statistical windows after the initial selections; (j)(k)(l) show the results after the secondary selections.
(2) Sort all the M sw and Vsw in ascending order. MScorei , j and VScorei , j are i, j i, j defined as the scores of mean and variance of candidate statistical windows, respectively. First, we eliminate the statistical windows which satisfies that M sw > M SMAX or M sw < M SMIN or Vsw < VSMIN ( M SMAX , M SMIN , VSMIN are i, j
i, j
i, j
predefined thresholds). (3) After the last step, we assume that the number of remaining candidate statistical windows is T1 , rank the remaining statistical windows according to
An Efficient Fingerprint Ridge Distance Estimation Using Typical Image Blocks
313
M swi , j and Vswi , j , respectively. If the M swi , j ranks T1 / 2 , MScorei , j is set to T1 .
For the other statistical windows, MScorei , j is calculated by subtracting one from T1 according to the distance between their rankings and T1 / 2 .To compute VScorei , j , the statistical windows with the largest Vsw is set to i, j
decrease progressively according to Vswi , j .
T1 ,other VScorei , j (4) SWScorei , j is defined as the curvature score during the initial selection. SWScorei , j increases progressively from one to T1 according to SW (i, j ) .
(5) The
total
score
is
+ ω3VScorei, j , where ω1
defined
，ω ，ω 2
3
as
Scorei , j = ω1SWScorei , j + ω2 MScorei , j +
are the weights and ω1 + ω2 + ω3 = 1 .
(6) Rank the remaining statistical windows according to Scorei , j . After the above steps, relatively good quality blocks are remained, the secondary selection can effectively remove blocks with poor quality from candidate statistical windows just as shown in Figure 3. Finally, if the number of rest candidate blocks after second selections is T2 , in certain cases, if T2 ≤ 0 , let T2 = T1 / 2 , so we can
compute the average ridge distance by using these candidate statistical windows,
3
Experimental Results
After two selections of blocks, statistical windows which are located in the pattern areas or blurred areas will be eliminated. Those blocks which have high curvature or too small or too large gray mean will also be removed. The existence of minutia in blocks may have impact on the accurate and reliable estimation of ridge distance; we have selected 100 fingerprint images from each database of FVC2004 using random function, a total of 400 fingerprint images. We define PEM as the Probability of Existence of Minutiae. Experimental results show that PEM in our selected blocks has been greatly reduced after the two-pass selections comparing with that in all valid blocks, as shown in Table 1. We count the number of minutiae and then compute the rate of their existence in blocks through random selection of fingerprint images. The PEM among selected statistical windows is only 20.05 %. The explanation to this experiment is relatively simple: The orientation in blocks containing minutiae sometimes has relatively high curvature compared with the blocks with continuous ridges. Thus, the blocks containing minutiae are more likely to be eliminated after the initial selection. Table 1. Minutiae-appeared probability among selected statistical windows
PEM in all valid blocks PEM in our selected blocks
DB1_A 55.65% 19.6%
DB2_A 56.45% 26.0%
DB3_A 58.20% 16.80%
DB4_A 59.09% 17.80%
average 57.35% 20.05%
314
X. Li, D. Yang, and Y. Yin
For the purpose of evaluating the performance of our algorithm in estimating the average ridge distance, we introduce two evaluation indicators: time consumption (TC) and estimation accuracy (EA) proposed by Yin [4]. TC is the average time needed for handling one fingerprint image. EA shows the deviation between the estimation result and the actual value of the ridge distance. Table 2 summarizes the computation times of ridge distance estimation compared with the other two methods. The processing time is measured by using a 2.2 GHz Pentium(R) dual and 2GB memory Windows PC. We can learn from the table that our method runs faster than the other two methods due to the selections of several typical blocks which are used to estimate the ridge distance. Table 2. Time consumption (TC) of three methods in four databases of FVC2004
Methods Hong[2] Yin[4] Our method
TC in DB1_A 6.149140 ms 23.269108 ms 4.295114 ms
TC in DB2_A 4.784723 ms 19.686329 ms 3.412346 ms
TC in DB3_A 4.917718 ms 29.035925 ms 4.155792 ms
TC in DB4_A 4.704217 ms 18.398619 ms 3.204255 ms
To compare our method with Hong [2] and Yin [4]’s methods , we have selected 10 good-quality images, 10 fair-quality images and 10 poor-quality images randomly from FVC2004 to verify the effectiveness and robustness of our algorithm, the experimental results are illustrated in Table 3. Table 3. Estimation accuracy (EA) of three methods
Methods Hong[2] Yin[4] Our method
good-quality 93.56% 96.78% 93.75%
fair-quality 92.5% 93% 93.42%
poor-quality 85.5% 90.75% 90.75%
From Table 3 we can see that for fingerprint images with good-quality, our method is no better than Yin [4]’s statistical method, but is somewhat better than Hong [2]’s orientation window method. The reason is that good quality images often have clear ridge-valley structures and orientation fields can be accurately acquired from these images. Therefore, relatively good results can be achieved from good-quality images in comparison with fair-quality and poor-quality images. On the basis of statistical method, our method does not take sufficient blocks into account, ridge distance in different blocks may vary greatly, and the average ridge distances computed by some of the blocks tend to have a certain deviation from the real average distance value. There is no distinct difference among the three methods for fair-quality images, however, for poor-quality images the estimation accuracy (EA) of Hong [2]’s method decreases drastically from 92.5% to 85.5%, whereas statistical method and our method still have high performance with the same EA (90.75%). Meanwhile, our method only decreases 3 percent as fingerprint images vary in quality. To sum up, our method has a certain advantage when the images are of poor quality. Yin [4]’s method, to some extent, is affected by the existence of great noise. Hong [2]’s method is obviously affected more than Yin [4]’s. Although, fewer blocks are selected, our
An Efficient Fingerprint Ridge Distance Estimation Using Typical Image Blocks
315
method still achieves good result. The accuracy of each of our selected blocks is almost guaranteed. The average value is more robust and reliable than that of the other two methods.
4
Conclusions and Discussion
In this work, we propose using several typical blocks to estimate the ridge distance. The key step is to select satisfying blocks for accurate and reliable ridge distance estimation. We have selected blocks of relatively low-curvature and good-quality blocks according to curvature of orientation and the quality of blocks. Experimental results show that our method is fast enough for online and offline applications. Besides, part of blocks can also be used to estimate the average ridge distance accurately and reliably. Compared with the other methods of ridge distance estimation, our proposed method can to some extent relieve the influence of inaccuracy of orientation fields’ estimation. However, the proposed method has some limitations when the quality of fingerprint images is good enough or the selected blocks are few enough. On one hand, if the fingerprint is of good quality, part of blocks cannot represent all the ridge distributions, thus the estimation conducted on these selected blocks may have some deviations; On the other hand, if the selected blocks are of poor quality, the final estimation result will not be accurate. In future work, we will focus on a better anti-noise method based on spectral analysis. Acknowledgments. This work was supported by the Project of Shandong Province Higher Educational Science and Technology Program under Grant No.J11LG28.
References [1] Kovács-Vajna, Z., Rovatti, R., Frazzoni, M.: Fingerprint ridge distance computation methodologies. Pattern Recognition 33(1), 69–80 (2000) [2] Hong, L., Wan, Y., Jain, A.: Fingerprint image enhancement: algorithm and performance evaluation. IEEE Transactions on Pattern Analysis and Machine Intelligence 20(8), 777– 789 (1998) [3] Ren, C., Yin, Y., Ma, J., Zhan, X.: Estimating Fingerprint Ridge Distance Based on FEE. Journal of Computational Information Systems 5(4), 1713–1721 (2008) [4] Yin, Y., Tian, J., Yang, X.: Ridge Distance Estimation in Fingerprint Images: Algorithm and Performance Evaluation. EURASIP Journal on Applied Signal Processing 2004(4), 495–502 (2004) [5] Maio, D., Maltoni, D.: Ridge-line density estimation in digital images. In: Proc. 14th International Conference on Pattern Recognition, Brisbane, Australia, vol. 1, pp. 534–538 (August 1998) [6] Wang, W., Li, J., Huang, F., Feng, H.: Design and implementation of Log-Gabor filter in fingerprint image enhancement. Pattern Recognition Letters 29, 301–308 (2008)
School of Computer Science and Technology, Shandong University, Jinan 250101, China 2 Shandong Youth University of Political Science, Jinan 250014, China [email protected], [email protected], [email protected]
Abstract. The average ridge distance of fingerprint images is a very important parameter for fingerprint image enhancement, which will greatly affect the performance of fingerprint recognition. A method of efficient ridge distance estimation based on typical image blocks is proposed. First, we obtain some typical candidate image blocks through the initial selection according to the orientation curvature of each block; Then better quality blocks from these candidate blocks are selected by taking quality strategy into account, while the remaining blocks are used to compute ridge distance using statistical window method; Finally, the average ridge distance is estimated through averaging several ridge distances in the remaining blocks. The experimental results show that our method is fast enough for real applications and is robust and reliable in estimating average fingerprint ridge distance. Keywords: fingerprint, ridge distance, typical image blocks, statistical window.
1
Introduction
Fingerprints have been used for identifications and verifications for many years because of their uniqueness and reliability. Frequency, that is, the reciprocal of ridge distance, is an important parameter used in fingerprint preprocessing. Many ridge distance methods have been put forward, such as methodologies based on spatial domain and methods based on the frequency field. The former is usually performed based on fingerprint blocks or the entire fingerprint images; the latter is often conducted by transforming the fingerprint images from spatial domain to frequency field, and then computing the ridge distance in that domain. Zs.M. Kovács-Vajna et al. [1] computed average ridge distance based on a twostep procedure: first, geometric and spectral approaches are used to compute the distance; second, the computation of harmonic coefficients leads to effective estimation of the average ridge period. Hong et al. [2] divided the input fingerprint images into blocks of same size, and then compute the gray values for central pixel of each block within the oriented window; the ridge distance is obtained by computing *
Corresponding author.
C.-L. Liu, C. Zhang, and L. Wang (Eds.): CCPR 2012, CCIS 321, pp. 308–315, 2012. © Springer-Verlag Berlin Heidelberg 2012
An Efficient Fingerprint Ridge Distance Estimation Using Typical Image Blocks
309
distribution of gray histogram. Yin et al. [4] defined statistical window and baseline for each non-overlapped block, which is binarized to acquire the distribution of ridge distances, and peak positions are detected after computing the distance from ridges to baseline of statistical windows. Maio et al. [5] did mathematical characterization of the local frequency of sinusoidal signals and developed a two-dimensional model in order to approximate the ridge-line patterns for ridgeline density estimation in digital images. Ren et al. [3] proposed a new method to estimate the ridge distance, which employs discrete Fourier transform, discrete information entropy theory, and weighted Euclidean distance to deal with fingerprint image accurately. The above estimation methods are based on the whole image or on each block of the entire image. Therefore, they all share a common approach of trying to utilize as many blocks in the images as possible to estimate the ridge distance. As a matter of fact, it is not always suitable, because it usually does not take the quality of each block into consideration, while the accuracy of ridge distance of each block in fingerprint images is not guaranteed. There is no doubt that these methods can get good performances when the fingerprint image is of good quality. In practice, however, not all the blocks are of good quality, the existence of great noise may have significant impact on the accuracy of average ridge distance. As the traditional methods use as many blocks or regions as possible to estimate the ridge distance, meanwhile, the time consumption of these traditional methods will inevitably increase as the image size increases. In this paper we present a novel method to solve the above problems by selecting so called typical blocks whose average ridge distance can represent the real value of the whole image instead of all available blocks of various quality. First, several low curvature blocks are selected based on the orientation curvature, second, some quality evaluation methods are adopted to perform a secondary selection. Statistical window method is used on the remaining blocks for average ridge distance estimation. Experimental results show that it achieves satisfying estimation accuracy with high computational efficiency. This paper is organized as follows. Section 2 describes the initial and secondary selections of typical blocks. Performance evaluation and experimental results are shown in Section 3. Section 4 states conclusions and discussions.
2
Typical Blocks Selection and Ridge Distance Estimation
In order to overcome the difficulties described above, we estimate average ridge distance by utilizing typical blocks, which are defined as fingerprint blocks that can accurately and reliably estimate ridge distance by using statistical window. Thus, the selection of typical blocks has to meet the following requirements: (1) the quality of blocks should be as good as possible, that is, fingerprint ridge is clear enough, the contrast between pixels is distinct (2) The ridge directions in the blocks should be consistent; we should avoid the presence of high-curvature ridges particularly in pattern area for selection of typical blocks. (3) The selected block should avoid the existence of endings and bifurcations
310
X. Li, D. Yang, and Y. Yin
We first compute block orientation for the sake of getting the degree of curvature. We divide fingerprint image into block of size 8 × 8 and estimate the orientation for each block. For the purpose of getting curvature of ridges in blocks, we used the curvature measure method, which is given by Wang[6]. Here, we give some notations, let SWi , j denote the ith row and the jth column of a statistical window, SWi , j is the total curvature value of a statistical window, C (m, n) is i +3 j +3
the orientation for each the block, we can get SW (i, j ) = C (m, n) . Thus, the set of m =i n = j
all
possible
statistical
windows can be expressed as: , where and are the width and H W P = {SW (i, j ) 0 ≤ i < H / b − 3, 0 ≤ j < W / b − 3}
height of fingerprint image, respectively, also, we use Flag[i][j] to denote whether the ith row and the jth column statistical window is available, Flag[i][j] = 0 and Flag[i][j] = 1 indicate that the statistical window SWi , j is unavailable and available, respectively. The detailed steps of constructing statistical windows by utilizing typical blocks are as follows: (1) For all the possible statistical windows SWi , j , which contains at least one background block of size 8 × 8 , label it as unavailable, namely, Flag[i][j] = 0 . Otherwise, compute SW (i, j ) , and set Flag[i][j] = 1 . (2) For all the statistical windows which satisfy P ' = {SW (i, j ) 0 ≤ i < H / b − 3, 0 ≤ j < W / b − 3 Flag[i ][ j ] == 1} , sort them in ascending order according to SW (i, j ) , thus, we can get the sorted set of statistical window Psorted . (3) For any element SWi , j included in the set Psorted and Flag[i][j] ≠ 0 , sort them in ascending order according to SW (i, j ) and do as follows: for all SWm,n which satisfy SW (m, n) ≤ SW (i, j ) and Flag[m][n] ≠ 0 if SWi , j and SWm,n are overlapped, then set Flag[m][n] = 0 . (4) Let N denote the number of statistical windows which are included in Psorted
，
and satisfy Flag[i][j] ≠ 0 . If N > T1 ( T1 is the threshold of initial selection number of statistical window). Select the first T1 available statistical windows in ascending order according to the value of SW (i, j ) , otherwise, select the N available statistical windows as candidate windows. After the initial selection according to the ridge curvature, the candidate statistical windows are illustrated in Figure 1 (d). Figure 1 (a) is the original image of FVC2004. It is a relatively low quality fingerprint image which varies in quality in different blocks and has some ridge conglutination regions. Figure 1 (b) shows the orientation fields of non-smoothing of different blocks. Different curvature of blocks are demonstrated in Figure 1 (c), the gray level of each blocks of size 8 × 8 reflects the curvature of ridge directions, a lighter block means a higher curvature value, thus, it can be seen from Figure 1 (d) that the candidate statistical windows mostly lie in the areas which have better quality.
An Efficient Fingerprint Ridge Distance Estimation Using Typical Image Blocks
(a)
(b)
(c)
311
(d)
Fig. 1. Statistical window image after the initial selection. (a) an original fingerprint in DB2_A of FVC2004 (b) orientation field (c) direction curvature image of blocks (d) candidate statistical windows in curvature image.
After the above initial selection, ridges with high curvature in the pattern area are filtered. Furthermore, because of non-smoothing orientation field, blocks with image noise generated by smudges, creases, scars and so forth are also nearly eliminated. Nevertheless, for the candidate statistical windows, even if the ridge directions have low curvature, the gray-level varies greatly in different areas under some circumstances. This will result in bad binaried blocks, which are not suitable to estimate the average ridge distance. Figure 2 shows examples of candidate statistical windows which have low curvature but have bad quality.
(a)
(b)
(c)
(d)
Fig. 2. Bad quality candidate statistical windows after the initial selection. (a) an original fingerprint in DB2_A of FVC2004, (b) orientation field, (c) candidate statistical windows in curvature image(d) its binaried statistical windows.
In order to acquire better quality blocks in candidate statistical windows, it is necessary to bring in some quality check strategies to select blocks which have clearer ridges and valleys. The mean and the variance of gray-level pixels in valid area of fingerprint images are two of most useful indicators to measure the quality of fingerprint. For good quality blocks, staggered changes between valleys and ridges usually increase their variances; the situation is contrary when the fingerprint blocks are blurred. The mean of gray-level pixels reflects the intensity of blocks or images, if the value in a block is too large, the ridges are probably blurred. If the adhesion between ridges is severe, the mean value is usually small.
312
X. Li, D. Yang, and Y. Yin
According to the above two quality check indicators, we make secondary selection from the candidate statistical windows, which can be described as follows: (1) For all the candidate statistical windows, compute gray-level mean M sw variance Vswi , j .
i, j
(a)
(d)
(g)
and
(j)
(b)
(e)
(h)
(k)
(c)
(f)
(i)
(l)
Fig. 3. Selected statistical windows after two selections.(a)(b)(c) are three original fingerprint images in DB2_A of FVC2004; (d)(e)(f) show the curvature of each block; (g)(h)(i) shows the statistical windows after the initial selections; (j)(k)(l) show the results after the secondary selections.
(2) Sort all the M sw and Vsw in ascending order. MScorei , j and VScorei , j are i, j i, j defined as the scores of mean and variance of candidate statistical windows, respectively. First, we eliminate the statistical windows which satisfies that M sw > M SMAX or M sw < M SMIN or Vsw < VSMIN ( M SMAX , M SMIN , VSMIN are i, j
i, j
i, j
predefined thresholds). (3) After the last step, we assume that the number of remaining candidate statistical windows is T1 , rank the remaining statistical windows according to
An Efficient Fingerprint Ridge Distance Estimation Using Typical Image Blocks
313
M swi , j and Vswi , j , respectively. If the M swi , j ranks T1 / 2 , MScorei , j is set to T1 .
For the other statistical windows, MScorei , j is calculated by subtracting one from T1 according to the distance between their rankings and T1 / 2 .To compute VScorei , j , the statistical windows with the largest Vsw is set to i, j
decrease progressively according to Vswi , j .
T1 ,other VScorei , j (4) SWScorei , j is defined as the curvature score during the initial selection. SWScorei , j increases progressively from one to T1 according to SW (i, j ) .
(5) The
total
score
is
+ ω3VScorei, j , where ω1
defined
，ω ，ω 2
3
as
Scorei , j = ω1SWScorei , j + ω2 MScorei , j +
are the weights and ω1 + ω2 + ω3 = 1 .
(6) Rank the remaining statistical windows according to Scorei , j . After the above steps, relatively good quality blocks are remained, the secondary selection can effectively remove blocks with poor quality from candidate statistical windows just as shown in Figure 3. Finally, if the number of rest candidate blocks after second selections is T2 , in certain cases, if T2 ≤ 0 , let T2 = T1 / 2 , so we can
compute the average ridge distance by using these candidate statistical windows,
3
Experimental Results
After two selections of blocks, statistical windows which are located in the pattern areas or blurred areas will be eliminated. Those blocks which have high curvature or too small or too large gray mean will also be removed. The existence of minutia in blocks may have impact on the accurate and reliable estimation of ridge distance; we have selected 100 fingerprint images from each database of FVC2004 using random function, a total of 400 fingerprint images. We define PEM as the Probability of Existence of Minutiae. Experimental results show that PEM in our selected blocks has been greatly reduced after the two-pass selections comparing with that in all valid blocks, as shown in Table 1. We count the number of minutiae and then compute the rate of their existence in blocks through random selection of fingerprint images. The PEM among selected statistical windows is only 20.05 %. The explanation to this experiment is relatively simple: The orientation in blocks containing minutiae sometimes has relatively high curvature compared with the blocks with continuous ridges. Thus, the blocks containing minutiae are more likely to be eliminated after the initial selection. Table 1. Minutiae-appeared probability among selected statistical windows
PEM in all valid blocks PEM in our selected blocks
DB1_A 55.65% 19.6%
DB2_A 56.45% 26.0%
DB3_A 58.20% 16.80%
DB4_A 59.09% 17.80%
average 57.35% 20.05%
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X. Li, D. Yang, and Y. Yin
For the purpose of evaluating the performance of our algorithm in estimating the average ridge distance, we introduce two evaluation indicators: time consumption (TC) and estimation accuracy (EA) proposed by Yin [4]. TC is the average time needed for handling one fingerprint image. EA shows the deviation between the estimation result and the actual value of the ridge distance. Table 2 summarizes the computation times of ridge distance estimation compared with the other two methods. The processing time is measured by using a 2.2 GHz Pentium(R) dual and 2GB memory Windows PC. We can learn from the table that our method runs faster than the other two methods due to the selections of several typical blocks which are used to estimate the ridge distance. Table 2. Time consumption (TC) of three methods in four databases of FVC2004
Methods Hong[2] Yin[4] Our method
TC in DB1_A 6.149140 ms 23.269108 ms 4.295114 ms
TC in DB2_A 4.784723 ms 19.686329 ms 3.412346 ms
TC in DB3_A 4.917718 ms 29.035925 ms 4.155792 ms
TC in DB4_A 4.704217 ms 18.398619 ms 3.204255 ms
To compare our method with Hong [2] and Yin [4]’s methods , we have selected 10 good-quality images, 10 fair-quality images and 10 poor-quality images randomly from FVC2004 to verify the effectiveness and robustness of our algorithm, the experimental results are illustrated in Table 3. Table 3. Estimation accuracy (EA) of three methods
Methods Hong[2] Yin[4] Our method
good-quality 93.56% 96.78% 93.75%
fair-quality 92.5% 93% 93.42%
poor-quality 85.5% 90.75% 90.75%
From Table 3 we can see that for fingerprint images with good-quality, our method is no better than Yin [4]’s statistical method, but is somewhat better than Hong [2]’s orientation window method. The reason is that good quality images often have clear ridge-valley structures and orientation fields can be accurately acquired from these images. Therefore, relatively good results can be achieved from good-quality images in comparison with fair-quality and poor-quality images. On the basis of statistical method, our method does not take sufficient blocks into account, ridge distance in different blocks may vary greatly, and the average ridge distances computed by some of the blocks tend to have a certain deviation from the real average distance value. There is no distinct difference among the three methods for fair-quality images, however, for poor-quality images the estimation accuracy (EA) of Hong [2]’s method decreases drastically from 92.5% to 85.5%, whereas statistical method and our method still have high performance with the same EA (90.75%). Meanwhile, our method only decreases 3 percent as fingerprint images vary in quality. To sum up, our method has a certain advantage when the images are of poor quality. Yin [4]’s method, to some extent, is affected by the existence of great noise. Hong [2]’s method is obviously affected more than Yin [4]’s. Although, fewer blocks are selected, our
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method still achieves good result. The accuracy of each of our selected blocks is almost guaranteed. The average value is more robust and reliable than that of the other two methods.
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Conclusions and Discussion
In this work, we propose using several typical blocks to estimate the ridge distance. The key step is to select satisfying blocks for accurate and reliable ridge distance estimation. We have selected blocks of relatively low-curvature and good-quality blocks according to curvature of orientation and the quality of blocks. Experimental results show that our method is fast enough for online and offline applications. Besides, part of blocks can also be used to estimate the average ridge distance accurately and reliably. Compared with the other methods of ridge distance estimation, our proposed method can to some extent relieve the influence of inaccuracy of orientation fields’ estimation. However, the proposed method has some limitations when the quality of fingerprint images is good enough or the selected blocks are few enough. On one hand, if the fingerprint is of good quality, part of blocks cannot represent all the ridge distributions, thus the estimation conducted on these selected blocks may have some deviations; On the other hand, if the selected blocks are of poor quality, the final estimation result will not be accurate. In future work, we will focus on a better anti-noise method based on spectral analysis. Acknowledgments. This work was supported by the Project of Shandong Province Higher Educational Science and Technology Program under Grant No.J11LG28.
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