Final Project Report Fingerprint Enhancement and Identification by Adaptive Directional Filtering. EE5359- Multimedia Processing Spring 2015

Transcription

1 Final Project Report Fingerprint Enhancement and Identification by Adaptive Directional Filtering EE5359- Multimedia Processing Spring 2015 Under the guidance of Dr. K. R. Rao Submitted by Vishwak R Tadisina Vishwak.tadisina@mavs.uta.edu ID:

2 List of Acronyms: 1D- One Dimension 2D- Two Dimension AFIS Automatic Fingerprint Identification System DC- Direct Current ECTI-CON - Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology Conference FBI Federal Bureau of Investigation FFT- Fast Fourier Transform ICBA- International Conference on Bioinformatics and its Applications ICPR International Conference on Pattern Recognition IEE Institution of Electrical Engineers IEEE- Institute of Electrical and Electronics Engineers ISCV International symposium on Computer Vision LCNS- Lecture Notes in Computer Science LPF- Low Pass Filter MATLAB Matrix Laboratory MTF Modulation Transfer Function WACV- Winter Conference on Applications of Computer Vision 2

3 Index S. No. Chapter Name Pg. No 1 Introduction 4 2 Structure of a fingerprint 5 3 Algorithm for Fingerprint Enhancement Normalization Ridge orientation and Frequency Directional Filtering (a) Butterworth Filter (b) Gabor Filter 15 4 Fingerprint Identification Reference Point Location Feature vector Fingerprint Matching 20 5 Implementation 22 6 Scope of the Project 27 7 References 27 3

4 1. Introduction A person can be recognized using different means of identification, but identifying a person based on the biometrics has become important in current diverse businesses like law enforcement, information system security, finance physical access control etc. [4]. Fingerprint based identification is one of the most important biometric technologies which has drawn a substantial amount of attention recently [4]. It is one of the most reliable mode of authentication. It has been extensively used by forensic experts in criminal investigations for decades [2]. The best aspect of fingerprintbased identification is that the fingerprints of a person are unique and does not alter with aging of an individual [1]. Law enforcement agencies developed a method to manually match fingerprint. But this method is tedious and time taking. So in early 1960s automatic fingerprint identification system (AFIS) [2] was started. There are different ways for obtaining a fingerprint. It can be done either by digitalizing the image taken by ink or by using inkless scanners. So from this it can be observed that the reliability of a fingerprint identification method depends mainly on the quality of the extracted features (minutiae) [1]. Various processing stages are included in an AFIS as shown in Fig. 1 [11]. Representation of fingerprints plays a vital role for automation in AFIS. This representation should have the following properties. 1. Keep back the uniqueness of each fingerprint in various levels of resolution. 2. Distinct characteristics of a fingerprint can be estimated easily. 3. Easy to apply automatic matching algorithms. 4. Immune to noise distortions. 5. Effective and simple representation [11]. 4

5 Fig. 1 Stages in an AFIS [11]. 2. Structure of a fingerprint: An image of the surface of the skin of the fingertip is called a fingerprint. It consists of ridges (black lines) separated by valleys as shown in Fig. 2 [2]. The design of the ridge in a fingerprint can be depicted as an oriented texture pattern with constant prevalent spatial frequency and orientation in a local neighbourhood. Orientation depends on flow pattern of the ridges, and frequency on inter-ridge spacing [2]. Fig. 2 Ridges and valleys in a fingerprint image [2] 5

6 The places which are visually striking on the ridge pattern of a fingerprint are called singularities. There are two types of fingerprint singularities: core and delta. The ridges of a fingerprint have irregularities, such as ridge endings, bifurcations, crossovers, short ridges, etc. shown in Fig. 3 [11]. These anomalies can be used for manual or automatic fingerprint identification and they are called minutiae. In a good quality fingerprint, 60 to 140 minutiae can be found, but number of minutiae varies from fingerprint to fingerprint [2]. The characteristics of fingerprint images are shown in Fig. 4 [2]. Fig. 3 Bifurcations and short ridges [11] Fig. 4 A fingerprint image with marked singularities, minutiae and the frequency spectra corresponding to the local regions [2]. 6

7 3. Algorithm for Fingerprint Enhancement: There are numerous algorithms for fingerprint enhancement [4]. An ideal algorithm must increase the contrast between the ridges and valleys of a fingerprint for visual examination or automatic feature extraction. In this algorithm during the processing of each pixel, a local neighbourhood of that pixel is considered. Directional filters are used as the ridges and valleys have well-defined frequency and orientation in the local area. Here the filtering process is adaptive as the parameters of these directional filters depend on the local ridge frequency and orientation. So in frequency domain, directional filters are used for fingerprint enhancement [2]. The flowchart of the fingerprint enhancement algorithm is shown in Fig. 5 [4]. The main steps of the algorithm include: 1. Normalization: To obtain a pre-specified mean and variance, an input fingerprint image is normalized [2]. 2. Local orientation and Frequency estimation: The normalized input fingerprint image is used for computing orientation and frequency images [2]. 3. Region mask estimation: Each block in the normalized input fingerprint image are sorted out into a recoverable or an unrecoverable block to find a region mask estimate [2]. 4. Filtering: An enhanced image is obtained from the ridge-and-valley pixels in the normalized input fingerprint image by using a bank of Gabor filters or Butterworth filters that are tuned to local ridge orientation and ridge frequency [2]. Fig. 5 A flowchart of fingerprint enhancement algorithm [4] 7

8 Fig. 6 Various stages in a fingerprint enhancement and identification algorithm [15] Fig. 7 In (a) the pixel with three neighbours is a ridge bifurcation and in (b), pixel with only one neighbour is a ridge ending [15]. 8

9 3.1 Normalization: Normalization is a process that is pixel wise. The clarity of the ridge and valley structures are not affected by normalization. It inhibits the variations in grey-level values along ridges and valleys [2]. Let, I(x, y) denote the grey-level value at pixel (x, y), M i and V i denote the estimated mean and variance of I, respectively, and N i (x, y) denote the normalized grey-level value at pixel (x, y). The normalized image is defined as follows [2]: N i (x, y) = { M 0 + V 0(I(x, y) M i ) 2 V i, if I(x, y) > M i M 0 V 0(I(x, y) M i ) 2 V i, Otherwise (1) M 0 and V 0 are the desired mean and variance values, respectively [2]. 3.2 Ridge orientation and Frequency: The orientation field O is defined as a P Q image (called orientation or directional image), where O (i, j) represents the local ridge orientation at pixel (i, j). It is used for fingerprint enhancement, classification and ridge detection [4]. Block wise representation is used for local ridge orientation. There are a number of techniques that can be used to calculate orientation fields [4]. Least mean square orientation estimation based on gradient is used [12] At first, the input fingerprint image is arranged into non-overlapping blocks of size W W. The gradients g x (i, j) and g y (i, j) for each pixel (i, j) of the block, are calculated. Simple Sobel operator [4] is used for calculating the gradient. The average squared gradient [g sx, g sy ] [12] in a block specified by window size W is given by: 9

10 [ g sx g sy ] = [ i+ W 2 j+ W 2 [g x 2 (u, v) gy 2 (u, v)] u=i W 2 v=j W 2 i+ W 2 j+ W 2 u=i W 2 v=j W 2 ] 2 g x (u, v)g y (u, v) (2) The average gradient ϕ direction and dominant local orientation for the block are given by: Φ(i, j) = 1 2 tan 1 i+ W 2 j+ W 2 2 g x (u, v) g y (u, v) u=i W 2 i+ W 2 v=j W 2 j+ W 2 [g x2 (u, v) g y2 (u, v)] ( u=i W v=j W 2 2 ) O(i, j) = Φ(i, j) + π 2 (3) (4) as the angle of gradient is perpendicular to the ridge orientation a correction of 90 degrees is essential. Here blocks of size W W for orientation estimation and gradients g x and g y are used and calculated using Sobel operator [2]. To remove faulty ridge orientation values at the distorted and noisy regions further smoothing is required on orientation values. It is done by converting orientation image into a continuous vector field as shown in the Fig. 8, defined as follows: Ψ x (i, j) = cos[2 O(i, j)] (5) Ψ y (i, j) = sin[2 O(i, j)] (6) where Ψ x (i, j) and Ψ y (i, j) are the x and y components of the continuous vector field respectively. 10

11 Fig.8 A continuous vector field formed by a local orientation image with a block of size W x W and center O (i, j). Then the filter implementation [1] is given by, W Ψ /2 W Ψ /2 Ψ x (i, j) = L(u, v) Ψ x (i uw, j vw) u= W Ψ /2 v= W Ψ /2 (7) W Ψ /2 W Ψ /2 Ψ y (i, j) = L(u, v) Ψ y (i uw, j vw) u= W Ψ /2 v= W Ψ /2 (8) O (i, j) = 1 2 tan 1 ( Ψ y (i, j) Ψ x (i, j) ) (9) where L is a 2D LPF, W is the block size and W Ψ W Ψ specifies the size of the filter, Ψ x (i, j) and Ψ y (i, j) are the x and y components of the continuous vector field respectively after smoothing. Local ridge frequency can be estimated by: The grey values of all the pixels situated in each block are projected along a direction perpendicular to the local orientation and computed. This projection forms a 1D wave with the local extrema relevant to the ridges and valleys of the fingerprint [2]; 11

12 The average number of pixels between two consecutive peaks in the 1D wave generated above is denoted by K (i, j). The frequency ω(i, j) is computed as, ω(i, j) = 1 K (i, j) (10) in order to explain the above estimation a modeled fingerprint image instead of the original raw fingerprint images can be used. A one dimensional (1D) modeled fingerprint image is used. A finite rectangular wave (as seen in Fig. 9) which is regarded as the simplification of the projection of all grey values of the pixels in a direction, normal to the local orientation of the block with local extrema corresponding to the ridges and valleys of the fingerprint. Fig. 9 Finite rectangular wave as a modeled fingerprint [15]. 3.3 Directional filtering: In frequency domain local ridge spacing (ρ) gives radial component and local ridge orientation (ϕ) gives angular component of a filter. An ideal model of band pass directional filter in Fourier domain [1] can be expressed using polar coordinates (ρ, ϕ) as 12

13 H(ρ, ϕ) = H r (ρ)h a (ϕ) (11) H r (ρ) and H a (ϕ) depend on local ridge spacing and local ridge orientation respectively [12]. Fig. 10 Filter in Fourier domain (a) band pass (radial) component, (b) directional (angular) component, (c) combination of previous two [1]. Instead of applying appropriate filter for each pixel, a finite number of predefined filters (regarding to finite number of discrete orientations, and fixed frequency) are applied. The degradation of the filter image and number of filters must be small and it can be obtained in following way: 1. Either an average ridge frequency or a constant is set empirically for entire database set to eliminate filter dependence on local ridge frequency. So that the context of the filter is determined only by the orientation 2. A fixed number (8 or 16) of orientation values by discretization is formed from which a small number of directional filter components can be obtained. The Fourier transform P i, i = 1, 2,..., n of the filters is pre-computed and stored. Filtering an input fingerprint image q(x, y) with dimensions C D is performed as follows [3]: The 2D-FFT F(u, v) of input fingerprint q(x, y) image is computed, F(u, v) = 1 C. D C 1 D 1 q(x, y) exp [ j2π (ux C + vy D )] x=0 y=0 (12) here u= 0, 1, 2,, 31 and v = 0, 1, 2,, 31. Each directional filter P i is point-by-point multiplied by F(u, v), obtaining n filtered image transforms PF i (u, v), i = 1, 2,..., n. Inverse 2D-FFT is computed for each PF i (u, v) resulting in n filtered images pf i (x, y), i = 1, 2,..., n (spatial domain) [3]. For x = 0, 1, 2 31 and y = 0, 1,

14 C 1 D 1 pf i (x, y) = PF i (u, v) exp [j2π ( ux C + vy D )] u=0 v=0 (13) All the value of pixels in one block of enhanced image take on the same position from the filtered image which emphasizes determined orientation for corresponding block. So enhanced image can be obtained from the filtered image [3] as seen in Fig. 11. Fig. 11 Block diagram of a fingerprint enhancement algorithm [3] 3.3(a) Butterworth filter: The band pass Butterworth filter [14] for radial component H r (ρ) of order k, having center frequency ρ0 and bandwidth ρbw [14] is given as: (ρρ BW ) 2k H r (ρ) = (ρρ BW ) 2k + (ρ 2 ρ 2 0 ) 2k (14) Then (15) gives the directional component 14

15 H a (ϕ) = { cos2 π(ϕ ϕ c) 2ϕ Bw if ϕ < ϕ Bw 0 Otherwise (15) where ϕbw is the angular bandwidth, and ϕ c is the orientation of the filter [14]. Fig. 12 Butterworth bandpass frequency response 3.3(b) Gabor Filter: Frequency-selective and orientation-selective properties of Gabor filters [6] make them significant both in frequency and spatial domain. By simple adjustment of mutually independent parameters, configuration of Gabor filters can be varied based on different shapes, orientations, width of band pass and central frequencies. The significant characteristic of a Gabor filter is, if properly tuned it can perform frequency selective filtering on an image maintaining only regions of a given frequency and orientation. This fundamental implications are used for research in fingerprint image analysis and enhancement using this filter [4, 6]. An even symmetric Gabor filter general form [4] in the spatial domain is given by 15

16 h(x, y, ϕ, Ω) = exp [ 0.5 {( x σ x 16

17 Fig. 13 An even-symmetric Gabor filter. (a) The Gabor filter with f = 10 and ϕ = 0. (b) The corresponding MTF [4]. 4. Fingerprint Identification For fingerprint identification it is ideal to get representations of fingerprints which are invariant with reference to scale, translation and rotation [22]. The scale variance difficulty can be eliminated easily since most fingerprint images could be scaled as per the dpi specification of the sensors. To remove the other two variance problems a reference frame can be formed which is rotation and translation invariant [22]. The translation invariance is handled by establishing a single reference point (core point). This reference point is obtained based on the assumption that all the fingerprints are vertically oriented. But practically the fingerprint images may be oriented up to ± 45º away from actual assumed vertical orientation. Cyclic rotation of the feature values in the Fingercode in the matching stage handles this image rotation partially [22]. 4.1 Reference Point Location Fingerprints have many perceptible landmark structures which can be used collectively for finding a reference point [22]. The reference point or core point of a 17

18 fingerprint is the point at which the curvature of the concave ridges is maximum as shown in Fig.14. Fig. 14 Concave and convex ridges in a fingerprint image when the finger is positioned upright [22]. After finding the smoothened orientation image in section 3.2. From equation (9) compute E, an image containing only the sine component of O [22] E p (i, j) = sin(o (i, j)). (24) A label image A(i, j) which indicates the reference point is initialized. Integrate pixel intensities R 1 and R 2 for each pixel (i, j) in E p (i, j) as shown in Fig. 15. Assign the value of their difference in corresponding pixels to A(i, j) [22] R 1 R 2 A(i, j) = E p (i, j) E p (i, j). p=0 p=0 (25) On a large database a reference point algorithm is used to empirically determine the regions R 1 and R 2 [22]. The maximum curvature in concave ridges can be captured making use of the geometry of regions R 1 and R 2. Find the maximum value in A(i, j) [22] and assign its coordinate to the core, i.e., the reference point. 18

19 Fig. 15 Regions for integrating E pixel intensities for A (i, j) [22]. After finding the core point the fingerprint image undergoes directional filtering in eight different directions. 4.2 Feature vector From [22] it is clear that a fingerprint image can be sectored into a total of 16 5 = 80 sectors (S 0 through S 79 ) whose core point [22] is the center of these sectors as shown in Fig. 16. Fig. 16 Reference point (x), the region of interest, and 80 sectors [22]. Let F iϕ (x, y) be the ϕ - direction filtered image for sector S i. Now i ϵ {1, 2, 3, 79} and ϕ ϵ {0º, 22.5º, 45º, 67.5º, 90º, 112.5º, 135º, 157.5º}. The feature value V iϕ [22] is the average absolute deviation from mean defined as n i V iφ = 1 n i ( F liφ (x, y) P liφ l=0 ) (26) 19

20 where n i is the number of pixels in Si and P i ϕ is the mean of pixel values in a sector. The average absolute deviation of each sector in each of the eight filtered images defines the components of the feature vector. 4.3 Fingerprint matching Based on the Euclidean distance between the corresponding Fingercode, fingerprint matching is done. A Fingercode is a compact length code obtained by the filter-based bank algorithm in [22] which uses a bank of Gabor filters to capture both local and global details in a fingerprint. Reference point removes the translation variance problem. To eliminate rotational variance the Fingercode is rotated cyclically [22]. The steps corresponding to single step cyclic rotation [22] of the features of the Fingercode are described by (27)-(29). This corresponds to a feature vector which would be obtained if the image were rotated by 22.5º. A rotation by R steps corresponds to a rotation R 22.5º of the image. A positive and negative rotation implies clockwise and counterclockwise rotation respectively. The Fingercode [22] obtained after R steps of rotation is given by V iφ R = V i φ (27) i = (i + m + R) m + ( i m ) m (28) φ = (φ + 180º º R) 180º (29) where m is the number of sectors in a band, i ϵ {0,1, 2, 79} and ϕ ϵ {0º, 22.5º, 45º, 67.5º, 90º, 112.5º, 135º, 157.5º}. Five templates are stored corresponding to the following five rotations of the Fingercode: V iφ 2, V iφ 1, V iφ 0, V iφ 1 and V iφ 2. To obtain five different matching scores, input Fingercode is matched with these five templates. The Fingercode corresponds to a rotation of 22.5º. But the fingerprints are rotation invariant to small rotation within ± 11.25º. So another feature vector for each fingerprint is generated which corresponds to a rotation of 11.25º. To generate this, the original fingerprint is rotated by 11.25º. From the above rotated fingerprint image five more templates are formed. So a total of ten templates for each fingerprint [22] are formed as shown in Fig. 17. Fingercodes are generated for every 11.25º of rotation of the fingerprint image this takes care of rotation invariance [21]. The matching is done by taking into account the minimum matching distance score of the ten stored templates [22]. Matching can be done with this minimum score which 20

21 gives the best alignment of the two fingerprints. So the fingerprints are matched using this minimum score. Fig. 17 Examples of 640-dimensional feature vectors: (a) First impression of finger 1, (b) second impression of finger 1, (c) Fingercode of (a), (d) Fingercode of (b), (e) first impression of finger 2, (f) second impression of finger 2, and (g) Fingercode of (e), and (h) Fingercode of (f) [22]. 21

22 5. Implementation The performance of the proposed algorithm is tested using the fingerprint database in [24]. The fingerprint images in this database are greyscale images. They have a spatial resolution of 96 dpi and an amplitude resolution of 8 bits per pixel. Dimension of each image is 640 x 480 pixels. Normalization Parameters for normalization are set to 100 for both M 0 and V 0. The ridge orientations were discretized to 8 values (step 22.5 ). The original fingerprint images and their normalized images are shown in the Fig. 18. Fig. 18 a, b, c and d: Original fingerprint images; i, ii, iii and iv: Corresponding normalized images. Ridge orientation and frequency To determine ridge orientation, the input fingerprint images are divided into nonoverlapping blocks of size 8 8. Then the gradients g x (i, j) and g y (i, j) for each pixel (i, j) of the block, are calculated by Sobel edge-emphasizing filter. The gradient and edge detected images are shown in Fig. 19. Then all these gradient values are used to compute average squared gradient and the average gradient ϕ direction. This image is smoothened further using a 2D LPF to remove noise. Original fingerprint 22

23 images and their orientation images are shown as quiver plots in the Fig. 20. A quiver plot is vector plot which displays the direction of the ridges in the fingerprint as arrows with components (u, v) at the points (x, y). Fig. 19 (a), (b), (c) and (d) are original fingerprint images; (i), (ii), (iii) and (iv) are their respective Edge detected images; (1), (2), (3) and (4) are their respective Gradient images. 23

24 Fig. 20 (a), (b) and (c) are original fingerprint images; (1), (2) and (3) are their respective orientation image quiver plots. 24

25 Directional filtering Bank of Gabor filters: The inter-ridge distance in the fingerprint image is the main factor in determining the parameters Ω, σ x and σ y, for optimal Gabor filter operation. The filter frequency is the average ridge frequency Ω = 1/B where B is the average inter-ridge distance. If Ω is too large spurious ridges are created in the filtered image, whereas if Ω is too small nearby ridges are merged into one. The parameters are set to be Ω = 1/5, and σ x = σ y = 4.0 [21]. Trade-off in selection of σ x and σ y is done based on empirical data [5], so that the filter is robust to noise, but still can capture ridge information at fine level. Eight different values for ϕ = iπ/8, i= 1, 2,, 7 (0º, 22.5º, 45º, 67.5º, 90º, 112.5º, 135º, 157.5º) with respect to the x-axis are used. A 0º oriented filter accentuates those ridges which are parallel to the x-axis and smoothens the ridges in the other directions [21]. Filters tuned to other directions work in a similar way. These eight directional-sensitive filters capture most of the global ridge directionality information as well as the local ridge characteristics present in a fingerprint [22]. Original fingerprint images and enhanced images obtained by filtering with eight Gabor filter are shown in Fig. 21. To seize the whole global ridge information in a fingerprint at least four directional filters are necessary [22], but in order to capture local characteristics eight directional filters are required. So, four directions are required for classification and eight directions for matching. Although there is some redundancy among the eight filtered images, the verification accuracy is improved by capturing both the global and local information [22]. 25

26 Fig. 21 (a), (b) and (c) are original fingerprint images; (1), (2) and (3) are the enhanced images obtained by directional filtering using a series of Gabor filters. 26

27 6. Scope of the Project: The objective of this project is to apply the algorithm proposed in section 3 to smudged and corrupted fingerprints to obtain enhanced images. This is done by adaptive directional filtering in the frequency domain by using Butterworth [2] and Gabor filters [1] for fingerprint image enhancement and also for removing noise. MATLAB is used to normalize the corrupted fingerprints. Then the frequency and ridge orientation are computed for each fingerprint image. After that the image is filtered using directional filters. Here Butterworth and Gabor filters are used to obtain an enhanced image. The quality of the images obtained from both filters is compared visually. Fingerprint identification is done using MATLAB coding on the filtered enhanced image by detecting reference point and storing a feature vector in the form of a Fingercode in a data file. This data file is used as a database for fingerprint matching [21]. 7. References: [1] A. M. Raiˇcevi c and B. M. Popovi c, An Effective and Robust Fingerprint Enhancement by Adaptive Filtering in Frequency Domain, Facta Universitatis (NIS) Ser.: Elec. Energ., vol. 22, no. 1, pp , April [2] J. E. Hoover, The Science of Fingerprints: Classification and Uses, Federal Bureau of Investigation, Washington, D.C., Aug [3] B. G. Sherlock, D. M. Monro and K. Millard, Fingerprint enhancement by directional Fourier filtering, IEE Proc. Vision Image Signal Process., vol. 141, no. 2, pp.87 94, April [4] L. Hong, Y. Wan and A. K. Jain, Fingerprint image enhancement: Algorithm and performance evaluation, IEEE Trans. Pattern Anal. Machine Intell. vol. 20, no. 8, pp , Aug [5] A. Willis and L. Myers, A cost-effective fingerprint recognition system for use with lowquality prints and damaged fingertips, Pattern Recognition, vol. 34, pp , Jan [6] J. Yang, L. Lin, T. Jiang and Y. Fan, A modified Gabor filter design method for fingerprint image enhancement, Pattern Recognition Letters, vol. 24, pp , Jan [7] L. Hong, A.K. Jain, S. Pankanti and R. Bolle, Fingerprint Enhancement, Proc. First IEEE- WACV, pp , Sarasota, Fla., Dec [8] T. Kamei and M. Mizoguchi, Image Filter Design for Fingerprint Enhancement, Proc. ISCV 95, pp , Coral Gables, Fla., Nov

28 [9] K. Karu and A.K. Jain, Fingerprint Classification, Pattern Recognition, vol. 29, no. 3, pp , July [10] L. O Gorman and J.V. Nickerson, An Approach to Fingerprint Filter Design, Pattern Recognition, vol. 22, no. 1, pp , Jan [11] N. Ratha, S. Chen and A.K. Jain, Adaptive Flow Orientation Based Feature Extraction in Fingerprint Images, Pattern Recognition, vol. 28, no. 11, pp , March [12] Y. Wang, J. Hu and F. Han, Enhanced gradient-based algorithm for the estimation of fingerprint orientation fields, Applied Mathematics and Computation, vol. 185, no. 2, pp , Feb [13] D. L. Hartmann, Filtering of Time Series, [Online]. Available: [14] S. Chikkerur, A. N. Cartwright and V. Govindaraju, Fingerprint enhancement using STFT analysis, Pattern Recognition, vol. 40, pp , Jan [15] R. Iwai and H. Yoshimura, "A New Method for Improving Robustness of Registered Fingerprint Data Using the Fractional Fourier Transform", International Journal of Communications, Network and System Sciences, vol. 3, no. 9, pp , Sept [16] A. Sherstinsky and R.W. Picard, Restoration and Enhancement of Fingerprint Images Using M-Lattice: A Novel Non-Linear Dynamical System, Proc. 12th ICPR-B, pp , Oct [17] E. Bezhani, D. Sun, J. Nagel and S. Carrato, Optimized filterbank fingerprint recognition, Proc. SPIE 5014, Image Processing: Algorithms and Systems, vol. 2, pp , May [18] Project Idea, EE5359-Multimedia Processing Course Website. [Online]. Available: [19] P. Salil, J. Anil and P. Sharath, Learning fingerprint minutiae location and type, Pattern Recognition, vol. 36, pp , Oct [20] MATLAB version , Release R2013a, The MathWorks, Inc., Natick, Massachusetts, United States, Feb [21] E. Zhu, J. Yin, G. Zhang and C. Hu, A Gabor Filter Based Fingerprint Enhancement Scheme Using average Frequency, International Journal of Pattern Recognition and Artificial Intelligence, vol. 20, no. 3, pp , May [22] A. K. Jain, S. Prabhakar, L. Hong and S. Pankanti, Filterbank-Based Fingerprint Matching, IEEE Transactions on Image Processing, vol. 9, no. 5, pp , May [23] A. K. Jain, S. Prabhakar and L. Hong, A multichannel approach to fingerprint classification, IEEE Trans. Pattern Anal. Machine Intell. vol. 21, no. 4, pp , Apr [24] Fingerprint Verification Competition, The Biometric system lab, University of Bologna, Cesena-Italy, [Online]. Available: [25] FBI Fingerprint Database, Washington, D. C., United States. [Online]. Available: [26] K. R. Rao and S. Chakraborthy, Fingerprint Enhancement by Directional Filtering, ECTI-CON, Hua Hin, Thailand, May [27] K. R. Rao, D. N. Kim and J. J. Hwang, Fast Fourier Transform - Algorithms and Applications, Springer Science & Business Media, New York,

29 [28] S. Chikkerur, C. Wu and V. Govindaraju, "A systematic approach for feature extraction in fingerprint images", ICBA, LCNS, vol. 3072, pp , July [29] K. Nilsson and J. Bigun, Localization of corresponding points in fingerprints by complex filtering, Pattern Recognition Letters, vol. 24, no. 13, pp , Sept [30] A. R. Rao, A Taxonomy for Texture Description and Identification, Springer Series in Perception Engineering, New York, [31] M. Kass and A. Witkin. "Analyzing oriented patterns", Computer vision, graphics and image processing, vol. 37, no. 3, pp , March [32] Image Processing Toolbox User s guide, The MathWorks, Inc., Natick, Massachusetts, United States, March [Online]. Available: [33] L. Rosa, MATLAB Fingerprint Recognition Functions Code, L'Aquila, Italy. [Online]. Available: 29