Fingerprint Image Segmentation Based on Quadric Surface Model *

Transcription

1 Fingerprint Image Segmentation Based on Quadric Surface Model * Yilong Yin, Yanrong ang, and Xiukun Yang Computer Department, Shandong Universit, Jinan, 5, China lin@sdu.edu.cn Identi Incorporated, One Echange Place, Jerse Cit, NJ 73, USA susan.ang@identi.com Abstract. It is essential to segment fingerprint image from background effectivel, which could improve image processing speed and fingerprint recognition accurac. his paper proposes a novel fingerprint segmentation method at piel level based on quadric surface model. hree parameters, Coherence, Mean and Variance of each piel are etracted and spatial distribution model of fingerprint piels is acquired and analzed. Our stud indicates that the performance of fingerprint image segmentation with a linear classifier is ver limited. o deal with this problem, we develop a quadric surface formula for fingerprint image segmentation and acquire coefficients of the quadric surface formula using BP neural network trained on sample images. In order to evaluate the performance of our proposed method in comparison to linear classifiers, eperiments are performed on public database FVC DB. Eperimental result indicates that the proposed model can reduce piel misclassification rate to.53%, which is significantl better than the linear classifier s misclassification rate of 6.8%. Introduction In recent ears, automatic fingerprint identification has alwas been a research focus in academic research and industr field of the world. ith the efforts of man researchers, the main technical sstem of automatic fingerprint identification has been built alread, and it has been applied in man fields. However, to meet the needs of applications, it s necessar to improve the performance of ke algorithms, such as fingerprint image preprocessing, feature etraction and fingerprint matching algorithms, etc. e can sa that the researches on fingerprint identification algorithms have developed into a procedure full of competitive. Qualit of fingerprint itself and image capture conditions directl influence the performance of the sstem, which makes fingerprint preprocessing be a necessar step. In addition, the separation of fingerprint image from background is the first step in preprocessing. A valid and effective segmentation could not onl reduce time consumed on image preprocessing and minutiae etraction time but also improve the reliabilit of identification. So research on fingerprint segmentation has important meaning to the whole fingerprint identification sstem. * Supported b the National Natural Science Foundation of China under Grant No. 643 and Shandong Province Science Foundation of China under Grant No. Z4G5. Kanade, A. Jain, and N.K. Ratha (Eds.): AVBPA 5, LNCS 3546, pp , 5. Springer-Verlag Berlin Heidelberg 5

2 648 Yilong Yin, Yanrong ang, and Xiukun Yang here are man literatures about fingerprint image segmentation. Overall, the current approaches for fingerprint image segmentation can be classified into the following two categories. One method is based on the block level. B.M.Methre classifies each block into foreground or background according to the distribution of the gradients and gra-scale variance in that block [,]. X.Chen et al use linear classifier to classif the block [3]. L.R.ang et al propose a fingerprint segmentation method based on D-S evidence theor [4]. It is carried out b the direction and contrast of block. S.ang et al make use of contrast and main energ ratio to complete the separation of valid fingerprint part from background [5]. Q.Ren et al give the method based on feature statistics [6]. Obviousl, the resolution of this method onl reaches the block level, and the border of foreground and background obtained b this method is rather serrate, which makes it difficult to judge the reliabilit of features etracted from the border. he other method is based on piel level. A.M.Bazen [7,8] et al use three features of piel and establish a linear classifier to implement a piel-based segmentation. Up to the present, prevailing method of fingerprint segmentation is still based on block. he number of method based on piel is ver little. In this paper, a method based on quadric surface model for fingerprint image segmentation is presented. According to the spatial distributions of the piel features in the foreground and background areas of database, it implements the segmentation of fingerprints using quadric surface model. In algorithm, we transfer the quadric discriminant to broad sense discriminant for reducing the computation compleit. Eperiments have shown that the performance is ecellent. his paper is organized as follows. Section studies the spatial distribution of piels based on CMV. Section 3 presents development of the quadric surface model. Section 4 is the eperimental results on fingerprint database and section 5 gives conclusions and some discussions about this presented method. Spatial Distribution of Piels Based on CMV his section consists of two parts: one is description of piel features and the other is spatial distribution of piels based on above features.. Description of the Piel Features In brief, segmentation is the classification of piels, so the first important problem of the fingerprint segmentation is to define proper parameters to describe the piel features. he valid and distinguishable features of the piel should pla vital roles in the segmentation. For the piels in the valid fingerprint foreground and background, the parameters should sufficientl represent their differences on these features. In this paper, Coherence, Mean and Variance are selected as the piel features [8]. he definition of each feature is as following... Coherence(C). he Coherence of the piel measures how well the gradients are pointing in the same direction around a piel, which is abbreviated ascoh [7,8,]. Since a fingerprint mainl consists of parallel line structures, the coherence will be considerabl higher in the foreground than in the background. In a window around a piel, it is defined as follows:

3 Coh Fingerprint Image Segmentation Based on Quadric Surface Model 64 = here ( G ) G s s, ( Gs, Gs, ) ( G, G ) ( G G ), + 4 s, s, = G + G,, is the squared gradient, G = G G. (), G = G = GG G, G is the local gradient. is the two-dimensional lowpass template sized of 7 7 used for noise reduction. From the formula, we can see that the coherence is among [,]. he coherence of piel in foreground is near, while in background it is close to, because the directions of noise areas are in chaos. G and ( ).. Mean (M). he second piel feature is the average gra value. It measures how gra the piel is. For most fingerprint sensors, the ridge-valle structures can be approimated as black and white lines. So the foreground is composed of black and white lines, while the background, where the finger doesn t touch the sensor, is rather white. his means that the mean gra value in the foreground is lower than it is in the background. he local mean of the piel is defined as follows: Mean = I. () here I is the local intensit of the image. he definition of is the same as above...3 Variance (V). he Variance is the third piel features used in the algorithm, which measures the gra variance around the local area. In general, the variance of the ridge-valle structures in the foreground is higher than the variance of the noise in the background. It is defined as follows: ( I Mean) Var =. (3) here the definitions of I, are the same as above too...4 CMV Normalization. Since the value ranges of the three features are different, after etracting the three features of a piel, we need to normalize them to the range of [,].,. Spatial Distribution of Piels Based on CMV It is important to make deep insight into the spatial distribution based on the CMV of the piel. According to this distribution, we ma get the appropriate segmentation model b certain technique and achieve the satisfactor segmentation results. herefore, 6 representative fingerprint images from FVC Database have been selected as samples. Each piel s CMV values of all the images are etracted and the spatial distributions of these piels are shown in Fig. (a)(where the ellow section is composed of the piels in the background, while the blue sections is composed of the piels in the foreground. hich parts the piels belongs to is decided

4 65 Yilong Yin, Yanrong ang, and Xiukun Yang manuall and the three coordinates of a point in the figure represented the CMV values of a piel in the fingerprint image). Fig. (b) is obtained b etending the foreground and background piels in Fig. (a) in order to see the overlapping section clearl. (a) (b) Fig.. Spatial distributions of piels based on CMV (a)(the ellow section is composed of the piels in the background, while the blue section is composed of the piels in the foreground), (b)(obtained b etending (a)) From the distributions of piels, we can see that the piels of different parts (background and foreground) have different clusters, which indicates that the piels of the same class have similar features, and that two clusters are not apart completel. Obviousl, based on this spatial distribution, it is difficult to get satisfactor results onl using the plane. In addition, linear classifier has its limitations and can t solve such nonlinear problems. All these factors make us select the quadric surface model. 3 Development of Quadric Surface Model 3. Selection of Segmentation Model As we can see from the spatial distribution based on CMV of piels, piels from foreground and background are hard to separate with plane. if we select the quadric surface model, we ma get better results. In general, suppose the quadric surface model is as follows: d d d = wkk k + k = j= k = j+ g( ) = + w + w w jk j k + w j k + w is a real smmetric matri and w is a d -dimension vector. From (4), L = d( d + 3) + coefficients are needed and the calculation cost is large. So in order to simplif the algorithm, we define as a matri that onl elements on main d j= (4)

5 Fingerprint Image Segmentation Based on Quadric Surface Model 65. hen for- diagonal is non-zero, others are all zero. ] mula (4) can be rewritten as following, g = [ C, M, V, and d = ( ) = + w + w = wkk k + w j k + w k = j=. (5) Apparentl, this quadric discriminant is nonlinear, which is difficult to handle with. So b increasing the dimension, the above can be translated into a broad sense linear discriminant. Under this theor, formula (5) can be translated to following, here, = [ g( ) = = 6 i= + w a i i = a + w =,,, 3, 4, 5, 6 ] = a = a, a, a, a, a, a, a ] [ k = [ C w kk k, M +, V 3 j= w j k + w, C, M, V,] hen the rest problem is how to get the coefficients ( i 6) samples.. (6) a i from a lot of 3. Acquisition of Relative Coefficients BP network algorithm is a relativel good feed-forward neural network algorithm in theor, and it is also widel used in practice. It is a supervised leaning algorithm used in man fields to simulate some ver complicated nonlinear relationships when the conventional methods do not work. In this paper, we use the perception of BP learning algorithm to obtain the relative coefficients a i ( i 6). Different fingerprint database need to establish different model coefficients [8], in this paper, 3 representative fingerprint images respectivel from FVC DB, FVC DB and FVC DB3 are selected to get according model coefficients. his neural network has 7 inputs and output. Inputs of the network: = [,,, 3, 4, 5, 6 ], eight vector: a = [ a, a, a, a3, a4, a5, a6 ]. ransfer function: f ( g) =. (7) g + e he structure of the network is shown in Fig., where the real directional arrow denotes the direction of working signals, while the dashed directional arrow denotes the back error signals.

6 65 Yilong Yin, Yanrong ang, and Xiukun Yang Fig.. he structure of network he segmentation method presented in this paper uses supervised training. he classifications of the piels (background or foreground) that are involved in the network training are selected manuall. he fingerprint image samples are the same as described above, which are representative enough. 3.3 Implementation of Segmentation Since we have got the coefficients of the models, segmentation can be implemented using quadric surface model. Suppose ω denotes the piel that belongs to foreground, ω denotes the piel that belongs to background and ω denotes the piel s classification. he decision function used in the segmentation is: ω ω = ω here the definition of g is in formula (6). if if g > g <=. (8) 3.4 Visualization of Quadric Surface Model Using the above neural network model to train three different sample databases, we obtain three different sets of coefficients, indicating that the optimal quadric surface models for fingerprint images acquired b different sensors are different. It also proves the theor proposed b A. M. Bazen regarding the necessit of training different fingerprint databases independentl. he quadric surface models obtained from fingerprint training samples in database FVC DB, DB and DB3 are illustrated in Fig.3 (a), (b) and (c), respectivel. Blue dots stand for foreground piels, ellow dots represent background, and red surfaces denote segmentation surfaces.

7 Fingerprint Image Segmentation Based on Quadric Surface Model 653 (a) (b) (c) Fig. 3. he quadric surface models (a)(obtained from FVC DB), (b)(obtained from FVC DB), (c)(obtained from FVC DB3) 4 Eperimental Results Eperiment : Evaluating the validit of the model for each fingerprint database. From each database (FVC DB, DB, DB3), select 3 images respectivel and form testing sets (estdb, estdb, estdb3) different from training sets. Now we are intended to evaluate if the model is validate for the training databases. For each piel, calculate CMV values and put them to formula (6), then calculate (7) to get f (g), and make it among [,]. he probabilit densit of Piels from foreground and background of each database is given in Fig. 4. Make (,) to (,), and disperse it to equal parts. Define Fingerf ( ) {,,,3,4,5,6,7,8, } as the probabilit of foreground piels in (, + ) and Fingerb ( ) {,,,3,4,5,6,7,8, } as the probabilit of background piels in (, + ). Obviousl, Fingerf ( ) = and Fingerb ( ) =. he point = 5 is the threshold of differentiating piels from foreground and background. = = Eperiment : Doing comparison eperiments with A.M.Bazen s method on the second database of FVC. he parameters that measure the performance of the segmentation are defined as follows: p ω ω ) : he probabilit that a foreground piel is classified as background. ( p ω ω ) : he probabilit that a background piel is classified as foreground. ( p : he average of error p ( ω ω ) and p ( ω ω ). he eperimental results for the Database of FVC, using our method and the method presented in [8], are shown in able. able. he segmentation results of our method and the method in[8] on FVC DB Method p ω ω ) p ω ω ) ( ( Our method.%.85%.53% Method in [6] 6.% 7.4% 6.8% p error

8 654 Yilong Yin, Yanrong ang, and Xiukun Yang probabilit of piel probabilit of piel 6.66 Fingerf Fingerb Fingerf Fingerb probabilit of piel Fingerf Fingerb quadric surface value of piel quadric surface value of piel quadric surface value of piel (a) Fig. 4. he probabilit of piels from foreground and background in (a)(estdb), (b)(estdb) and (c)(estdb3) (c) (b)

9 Fingerprint Image Segmentation Based on Quadric Surface Model Conclusion and Discussions In this paper, a fingerprint segmentation algorithm using quadric surface model is proposed, which is based on the spatial distribution of the piels derived from coherence, local mean and local variance. he spatial distribution of the piels has special meaning for the segmentation. Eperimental results on fingerprint images of FCV database have demonstrated that the proposed segmentation method has ecellent performance and the segmentation result is significantl better than that of the linear classifier. he selection of curve surface model, and finding the optimal model to achieve more satisfactor segmentation result would be the net important step in fingerprint image segmentation stud. Moreover, how to prove that the distribution of piels based on CMV from foreground and background is a non-linear problem in theor and the reasonable feature selection of piel are another worthwhile research. References. B.M. Mehtre, N.N. Murth, S.Kapoor, and B.Chatterjee. Segmentation of fingerprint images using the directional images, Pattern Recognition, (4): 4-435, 87. B.M. Mehtre and B.Chatterjee. Segmentation of fingerprint images-a composite method, Pattern Recognition, (4): , 8 3. Xinjian Chen, Jie ian, Jiangang Cheng, Xin Yang. Segmentation of fingerprint images using linear classifier, EURASIP Journal on Applied Signal Processing,.4(4): 48-44, 4 4. L.R.ang, X.H.Xie, A.N.Cai and J.A.Sun. Fingerprint Image Segmentation Based on D-S Evidence heor, Chinese Journal of Computers, 6(7): 887-8, 3(in Chinese) 5. S.ang,..Zhang and Y.S.ang. New Features Etraction and Application in Fingerprint Segmentation. ACA AUOMAICA SINICA, (4): 6-66, 3 6. Qun Ren, Jie ian, Xiaopeng Zhang. Automatic segmentation of fingerprint images, the hird orkshop on Automatic Identification Advanced echnologies (AutoID ), Oral Report, arrtown, New York, USA, 37-4, 7. A.M.Bazen and S.H.Gerez. Directional field computation for fingerprints based on the principal component analsis of local gradients, Proc. ProRISC, 5-, th Annual orkshop on Circuits, Sstems and Signal Processing, Veldhoven, he Netherlands, Nov. 3-Dec., 8. A.M.Bazen and S.H.Gerez. Segmentation of Fingerprint Images, Proc. ProRISC, 76-8, th Annual orkshop on Circuits, Sstems and Signal Processing, Veldhoven, he Netherlands, Nov. -3,. A.M.Bazen and S.H.Gerez. Sstematic methods for the computation of the directional field and singular points of fingerprints, IEEE ransactions on Pattern Analsis and Machine Intelligence, vol. 4, no.7, 5-,