Rolled Fingerprint Construction Using MRF-Based Nonrigid Image ...

IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 19, NO. 12, DECEMBER 2010

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Rolled Fingerprint Construction Using MRF-Based Nonrigid Image Registration Dongjin Kwon, Student Member, IEEE, Il Dong Yun, Member, IEEE, and Sang Uk Lee, Fellow, IEEE

Abstract—This paper proposes a new rolled fingerprint construction approach incorporating a state-of-the-art nonrigid image registration method based upon a Markov random field (MRF) energy model. The proposed method finds dense correspondences between images from a rolled fingerprint sequence and warps the entire fingerprint area to synthesize a rolled fingerprint. This method can generate conceptually more accurate rolled fingerprints by preserving the geometric properties of the finger surface as opposed to ink-based rolled impressions and other existing rolled fingerprint construction methods. To verify the accuracy of the proposed method, various comparative experiments were designed to reveal differences among the rolled construction methods. The results show that the proposed method is significantly superior in various aspects compared to previous approaches. Index Terms—Fingerprint recognition, nonrigid image registration, rolled fingerprint construction.

I. INTRODUCTION OWADAYS, law enforcement agencies typically utilize an automated fingerprint identification system (AFIS) as a primary investigation tool for identifying a person suspected of committing a crime or linking a suspect to other unsolved crimes. Compared to conventional civil fingerprint applications such as time attendance or access control systems, AFIS systems specialize in high-performance identification and are known for their ability to manage a very large fingerprint database. To accomplish high-performance identification from such a large database, AFIS systems use a rolled fingerprint during enrollment while a flat fingerprint is commonly used in civil fingerprint systems. A rolled fingerprint is preferred, as it contains almost all the surface information of the finger. Therefore it provides a higher degree of certainty for identification purposes compared to a flat fingerprint [1].

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Manuscript received August 23, 2009; revised January 07, 2010, May 12, 2010; accepted May 16, 2010. Date of publication June 07, 2010; date of current version November 17, 2010. This work was supported in part by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) under Grant KRF-2006-311-D00168 and in part by the National Research Foundation of Korea (NRF) Grant funded by the Korean Government (MEST) (20090083815). The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Ferran Marques. D. Kwon and S. U. Lee are with the Department of Electrical Engineering and Computer Science, ASRI, Seoul National University, Seoul, 151-742, Korea (e-mail: [email protected]; [email protected]). I. D. Yun is with the Department of Digital Information Engineering, Hankuk University of Foreign Studies, Yongin, 449-791, Korea (e-mail: [email protected]. kr). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIP.2010.2052272

Until recently, a rolled fingerprint was acquired by rolling a finger from nail to nail on a paper form (e.g., the tenprint card) after applying ink onto the finger [2]. In this procedure, a human expert supervises the entire process and checks the quality of the final fingerprint. Several years ago, live fingerprint scanners equipped with a large sensor and an automatic roll synthesis function were introduced and quickly supplanted ink-based fingerprint acquisition methods [3]. Rolled fingerprint acquisition using a live scanner is preferred to ink-based methods, as the former does not require an application of ink onto the fingers of the subject or digitization of the paper form with the ink fingerprints, which is a costly and time-consuming process; moreover, problems due to the poor quality of the fingerprints caused by the ink and paper method are yet another issue. Although rolled fingerprint acquisition processes using live scanners have many benefits compared to ink-based methods, supervision of the entire process by human experts continues to be necessary to ensure that a high-quality rolled fingerprint is obtained. To mitigate the need for human supervision, accuracy is an important issue for the rolled fingerprint construction method. Many existing rolled fingerprint construction methods suffer from various nonlinear distortions due to factors such as the different 3-D shapes of the finger tip, nonuniform finger pressures, and the elastic characteristics of the skin. The development of an accurate rolled fingerprint construction method which addresses these issues will allow rolled fingerprints to be used in a wider range of fingerprint applications and will increase fingerprint recognition performance. This paper proposes a new rolled fingerprint construction method incorporating the state-of-the-art nonrigid image registration method. As the proposed method precisely estimates nonrigid transformations among a rolled image sequence, it typically performs well in difficult situations involving nonlinear distortions. In addition, the proposed method generates conceptually more accurate rolled fingerprints by preserving the geometric properties of the finger surface more accurately compared to ink-based rolled impressions and other previous rolled fingerprint construction methods [4], [5]. A detailed explanation of the conceptual differences is given in Section III-A after the preliminary information is introduced. This paper is organized as follows: Section II describes the various works to date that are related to the proposed method. The overall procedure of the proposed method is explained in Section III. Section IV describes the nonrigid image registration of two images from a rolled fingerprint sequence, which is the main part of this paper. In Section V, various comparative experiments are introduced to reveal the differences among the rolled

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Fig. 1. Example of a rolled fingerprint sequence. We mark a reference frame with a box.

construction methods. Finally, the conclusion is presented in Section VI. II. RELATED WORKS In the literature, most of the papers related to rolled fingerprint construction focus on fingerprint mosaicking for smallarea sensors. As different impressions of the same finger on small-area sensors usually share a small overlapping area, this is an important area of study for achieving better fingerprint recognition performance. Fingerprint mosaicking is broadly categorized into feature-level mosaicking and image-level mosaicking. Feature-level mosaicking [6]–[12] involves building a single template by rearranging the minutiae from several fingerprint impressions. Feature-level mosaicking is especially useful for minutiae-based fingerprint matching algorithms. However, it is not completely suitable for rolled fingerprint construction when nonrigid transformations among rolled image sequences need to be estimated. Estimating nonrigid transformations using a limited number of features typically results in poorer quality in terms of registration accuracy compared to an image-based method. Image-level mosaicking [4], [5], [11]–[14] involves building a synthesized image by combining aligned images from several fingerprint impressions. For small-area sensors, many imagelevel mosaicking approaches [11], [12], [14] use minutiae information to estimate transformations among fingerprint impressions. With these methods, the use of minutiae information represents an alternative to using the image information directly in an effort to avoid photometric inconsistencies caused by several independent fingerprint impressions. In this approach, densely and evenly distributed features are needed to estimate nonrigid transformations accurately. However, this requirement is not always satisfied by fingerprints; therefore, additional information of the fingerprint in addition to the minutiae must be incorporated. For example, Choi et al. [14] incorporated the ridge information into their recursive ridge mapping structure to estimate transformations. However, even if additional information is used, extracting reliable extra features from a low-quality area of the fingerprint is still challenging. In rolled fingerprint construction, several problems associated with image-level mosaicking are avoided. As rolled fingerprint sequences are initially aligned and the photometric consistencies between neighboring images on rolling sequences are preserved, we focus on problems due to nonlinear distortions among image sequences. In addition, finding a better image synthesis order is another important problem, as the number of image sequences is generally large. In the literature, there are few papers dedicated to rolled fingerprint construction methods. Ratha et al. [4] introduced five image-compositing schemes to synthesize rolled fingerprint image sequences. This

method assumes that finger rolling is equivalent to the rolling of a cylindrical surface and that images are perfectly matched in the overlapped area among image sequences. The method consists of several steps including foreground estimation of the fingerprint, pixel-wise confidence estimation using the foreground of each image, and image composition using a confidence measure. Zhou et al. [5] proposed a rolled fingerprint construction method that estimated the local affine transformations between two neighboring image sequences. Their method assumed that the main body of the finger can be modeled as a cylinder and that the tip of the finger can be modeled as a cone. The method has several steps including computation of the spatial shift, detection of the mosaicking point, partitioning of the tip part, and removal of the seams on the tip. In this paper, we mainly compare the proposed method with these two previous methods. A novel feature of the proposed method is that we do not assume the 3-D finger shape has a simple model such as a cylinder or a cylinder with a cone. III. OVERALL PROCEDURE In this paper, it is assumed that the finger is rolled from nail to nail on the scanning plane. Given image frames acquired from rolling of the finger on a live scanner, the proposed method initially determines a reference frame referred to as . The reference frame is defined as a frame containing a fingerprint positioned at the center of the fingerprint locations of the image frames (a more detailed explanation is given in Section III-B. Fig. 1 shows an example of the rolling sequence and marks its reference frame. Next, to construct a rolled fingerprint , every frame except the reference frame is registered and synthesized to the reference frame in the order of closest to farthest of the finger location for each frame. In a left-to-right or right-to-left rolling process, the closeness order is divided into two sequences: reference to the left-most frame and reference to the right-most frame. Fig. 2 describes the overall procedure. In this algorithm, lines (5–10) and lines (11–16) describe the roll synthesis procedures for the reference to the left-most frame and the right-most frame, respectively. Fig. 3 shows an example of the rolled fingerprint construction using the proposed method for the image sequence in Fig. 1. A. Comparison of Rolled Fingerprint Construction Methods Using a Simplified Finger Model The roll synthesis order of the proposed method differs greatly from ink-based rolled finger impressions or other previous rolled fingerprint construction methods using a live scanner. To understand these differences clearly, the 3-D shape of the finger tip is assumed to be a cylinder with a truncated cone, as shown in Fig. 4(a). Rolled fingerprint construction for this simplified finger model can be approximated by creating

KWON et al.: ROLLED FINGERPRINT CONSTRUCTION USING MRF-BASED NONRIGID IMAGE REGISTRATION

Fig. 2. Algorithm for constructing a rolled fingerprint S from images I

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;...;I

.

Fig. 3. Rolled fingerprint construction example using the proposed method for the image sequence in Fig. 1. Starting from a reference frame fI ; . . . ; I g are registered and synthesized towards I , and then, frames fI ; . . . ; I g are registered and synthesized towards I .

I

, frames

Fig. 4. Simplified finger model (a) with its various unfolded figures (b)–(d). (b) is an approximated unfolded figure for half side of (a). (c) is a synthesized figure to remove cracks of (b) using a previous method and (d) is a synthesized figure to remove cracks of (b) using the proposed method.

a development figure of a half-side of the model. As the cone part cannot be spread along the cylinder part, the surface of the half-side of the model is spread after slicing the cone into four parts, as shown in Fig. 4(b).1 Alternatively, this figure can be considered as a rolled fingerprint for the four impressions of the model obtained at the center position of the sliced cone parts. In the figures, the cylinder is divided into four parts representing individual impressions; a sliced cone part connected to a divided cylinder part is considered as a single impression. Using this simplified finger model and its unfolded figures, the characteristics of rolled fingerprint constructing methods can be distinguished. Rolled fingerprints are constructed using 1This is an approximation of the exact development figure. We assume the cone part can be slightly stretched.

the method of Ratha et al. [4] and the ink-based method corresponding to Fig. 4(b), which is simply the accumulated impressions of the rolled sequence without considering the transformations between the impressions. In the figure, cracks exist between the cone parts; therefore, the geometric properties between the cone parts are not preserved. Moreover, if many overlapping impressions accumulate during a practical rolling sequence, the results of the constructed rolled fingerprint are poor in the overlapped areas of the unmatched parts between impressions. To remove the cracks in Fig. 4(b) using transformations, neighboring sides can simply be stretched until they are joined. This scheme corresponds to the method of Zhou et al. [5] which applies affine transformations locally on overlapped areas of

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Fig. 5. Algorithm for finding a reference frame index c from images (I ; . . . ; I ).

impressions to remove the blur on this region. However, geometric properties (such as the length and angle) of the stretched regions are not preserved. The rolled fingerprints constructed by the method of Zhou et al. [5] correspond to Fig. 4(c). The dotted lines in this figure show the transformed locations of the dotted lines in Fig. 4(b). It is clear that the spacings between neighboring dotted lines are not preserved. Unlike these previous methods, the proposed method removes cracks using nonrigid transformations of the entire region. As nonrigid transformations are obtained while maintaining surface smoothness, the resulting deformation tends to preserve the geometric properties of the surface. Rolled fingerprints constructed by the proposed method correspond to Fig. 4(d). In this figure, spacings between neighboring dotted lines are preserved. Although the 3-D shape of the finger is greatly simplified in the explanations shown previously, similar analysis can be applied for more complex shapes. Moreover, the proposed method is flexible, as the shape of the finger is not explicitly assumed. B. Finding a Reference Frame We define a reference frame as a frame containing a fingerprint positioned at the center of the fingerprint locations of the image frames. As we assume nail-to-nail rolling sequences, the finger is moving along the -axis on the scanning plane. Therefore we define the position of a fingerprint in a frame as an -coordinate of a vertical center line of a foreground image . The foreground image is obtained by applying binarization with a fixed threshold value th to the smoothed image to reof . We apply the connected component analysis on move noisy foreground parts if any. Then the vertical center is computed as an -coordinate of the center-of-mass line is closest for . A reference frame is chosen such that its , where and are the minto imum and maximum values of , respectively. Fig. 5 shows the entire procedure of determining a reference frame. In Fig. 1, the reference frame is marked with a box determined by this algorithm.

As we register and synthesize image frames towards the reference frame, the proposed method may produce different synthesized images whenever we apply different reference frames. Therefore, finding a reliable reference frame is an important issue. Although high-level information such as the locations of the singular points (core or delta) and the directional ridge flow can be incorporated into this scheme, a simple method using the vertical center line of each segmented foreground of the fingerprint is used instead, as this approach is efficient and shows good empirical performances. Actually, the performance of the rolled fingerprint is not very sensitive to the exact reference frame. In Section V-E, we will show that the proposed method performs well when we use an alternative reference frame.

IV. NONRIGID IMAGE REGISTRATION OF TWO IMAGES FROM A ROLLED FINGERPRINT SEQUENCE Nonrigid image registration is the process of determining the geometric transformation between two images which are not related by simple rigid or affine transformations. In the literature, many relevant techniques have been proposed thus far [15]–[20]. However, not every previous registration method is suitable for the proposed rolled fingerprint construction framework. Specifically, the registration method has to satisfy the following requirements: • since the quality of rolled fingerprints depends directly upon results of registrations, the method has to generate accurate registration results for various nonlinear distortions; • since there exist occluded areas between two fingerprints from a rolled fingerprint sequence, the method has to handle occlusions naturally in its framework; • since the time complexity of constructing rolled fingerprints is a critical issue, the method has to be able to incorporate efficient optimization schemes. Considering these requirements, we applied the nonrigid registration method based upon a Markov random field (MRF) energy model where MRF energy models have been extensively researched in the computer vision area [21]. Recent studies [18],


Fig. 6. Algorithm for registering an image I

[19] show that MRF-based nonrigid registration methods incorporating discrete energy optimization greatly outperform existing registration methods. Also, MRF energy models can naturally incorporate occlusion handling [22]. Moreover, there exist various efficient discrete optimization methods for MRF energy models [23]–[26]. An MRF-based nonrigid registration method models the deformation pattern as a discrete label set in which the labels correspond to displacements of control points placed on a square mesh. An MRF energy model which defines control points as nodes is then constructed. The energy is optimized using discrete energy optimization methods such as the graph cut or belief propagation. Finding a label set minimizing MRF energy corresponds to the maximum a posteriori (MAP) estimation problem. In this section, we will propose an MRF-based nonrigid registration method for two images from a rolled fingerprint image sequence. In addition to the previously described elements, the proposed method incorporates the specialized properties of fingerprints and utilizes characteristics of rolled fingerprint sequences. Fig. 6 summarizes the entire registration procedure. A foreground image and an occlusion map are initially computed and a graph is constructed based upon this information. The unary and pairwise potentials of the MRF energy model are then computed on this graph and MAP labels are obtained after an optimization procedure using these potentials. The final transformation is computed using these labels. A. Notations Before proceeding, we introduce some of the notations used in this section. Let be an undirected graph where and are a set of nodes and edges, respectively. , let be a label taking values in some For each is defined for discrete set . If a function corremapping labels to 2-D displacements, each label sponds to a displacement vector . We assume each dimension of the displacements has a different set of values , where controls the displacement width. For a set and , a corresponding label set and is assigned, and then . In , a unary is defined for each node and a pairwise potential

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to an image I given transformation T .

is defined for each edge where potential . , and In the sequel, it is assumed that two images is given (assume and exist on the a transformation right of the reference frame ).2 is a transformation of calculated from its previous registration. is denoted is then registered as a transformed image of using , and to . B. Deformable Mesh , we construct a set which consists of For an image nodes placed in a grid with spacing . If the domain of the input image is denoted as , the size of the image covered by is . For a given , a displacement vector of an image pixel is assumed to be represented by a linear or nonlinear of nodes as combination of the displacement vectors follows [18] (1) where is a location of the node and is a weighting function measuring the contribution of the node to the dis. To define , we consider a convenplacement vector tional free-form deformation (FFD) model based upon cubic B-splines [27], [28]. The FFD is a powerful tool for modeling deformable objects. It has been researched extensively in the image morphing and registration areas [15], [29]. Using the FFD model, (1) is changed as follows: (2) where is the th node on the grid, and is the th basis function of the uniform cubic B-spline.3 The displacement is calculated using displacement vectors of vector its 4 4 neighboring nodes . 2For the registration of I frame, we simply change I

0

and I which exist on the left of the reference to I in this section.

3B (a) = (1 a) =6; B (a) = (3a 3a + 3a + 1)=6; B (a) = a =6.

0 6a

0

+ 4)=6; B (a) = ( 3a +

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+1

Fig. 7. Example of two frames registration. (a) an image I at time t, (b) an image I at time t which is the next frame of I , (c) the segmented foreground F of I (vertical center line described as a magenta-colored line), (d) the segmented foreground F of I (vertical center line described as a cyan-colored and the occluded region (red-colored area) O , (f) grid nodes V I for image I line), (e) the intersection of foregrounds (gray-colored area) F and F (green, red, blue, and gray-colored nodes denote foreground, occluded foreground, mesh region, and background nodes, respectively). (a) I , (b) I , (c) F , (d) F , (e) F \ F with O , (f) V I with I .

(

(

)

)

For the given nodes , a graph is constructed after the pairwise interactions between nodes are determined. In this paper, a set of 4-connected edges of a grid is used for . When the locations of each node are transformed, the transformed image is interpolated using (2). C. Node Coloring is divided into To generate an efficient graph , where denotes the foreground mesh nodes, derepresents the mesh region notes the occluded mesh nodes, nodes, and refers to the background mesh nodes.4 As the fingerprint area of generally does not cover the entire image area, it is not necessary to consider the movements of the mesh nodes, which have no effect on the image transformation. As shown in (2), the effective nodes for transforming a

pixel are the 4 4 neighboring nodes for . Therefore, for an image , it is not necessary to consider nodes outside of the 4 4 neighboring nodes for the foreground area . is a binarized image obtained using the method in Section III-B. It is also necessary to take into account the occluded area of . As some pixels of have no corresponding area in , these pixels must be excluded when calculating the correspondences. As the occluded area cannot be precisely known before estimating the exact transformation is approximated as in which is the foreground area of . From this description, different sets of mesh nodes are summarized as follows: (3) (4) (5)

4Schnabel

et al. [16] introduced active and inactive FFD control points to approximate nonuniform mesh nodes. Active and inactive control points represent whether nodes are moving or not (in a binary manner) in their iterative coarse-to-fine registration step. In each iterative step, this method uses an independent gradient-based continuous optimization method, which finds a local optimum from a given initial solution. In contrast, the proposed method is not an iterative approach and the importance of the nodes is directly controlled by the weights of the smoothness cost. The proposed method applies a discrete optimization method which finds a global optimum or a reasonably good suboptimum.

(6) where clude all 4

represents a set of nodes expanded from 4 neighboring nodes for .

to in-


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Fig. 8. Visual comparisons of corresponding patches for (a) I , (b) I , and (c) I . (d)–(f) show magnified views of boxed areas for (a)–(c). The centers of (d)–(f) is located on the same fingerprint ridge bifurcation. (g), (h), and (i) are overlapped images of (e) (red) and (d) (green), (d) (red) and (f) (green), and (e) (red) and (f) (green), respectively.

Fig. 7(a)–(e) shows the example frames and with the , and which is corresponding foreground and . Fig. 7(f) shows the mesh nodes on used for calculating in which the nodes in , and the example image are represented by green, red, blue and gray-colored dots, respectively.

and is indistinctive However, the potential between or less distinctive when involves a large amount of deformation.5 To make the potential more distinctive, the untransformed . If denotes an image is used directly to calculate inverse transformation of , a new dissimilarity measure is defined as follows:

D. MRF Energy Model with their color, we After defining the mesh nodes for constructed energy on graph . Here, energy is constructed using the pairwise MRF model, as follows: (7) where is a set of nodes defined on a grid and is a set of edges incorporating the neighborhood information of the nodes. In this , and model, is the data cost defined on each node is the smoothness cost defined on each edge . of (7) which mea1) Data Cost: The unary potential is defined as sures the cost when a node has a label

if if

, .

(10) In Fig. 8, we visually compare corresponding patches for , and . On the same physical locations, the difference be[Fig. 8(i)] is smaller than that tween patches from and from and [Fig. 8(h)]. As a larger difference between patches causes a higher SSD cost, the potential computed using (9) tends to lack distinctiveness. From these observations, we can infer that (10) is able to calculate more distinctive potentials than (9). of 2) Smoothness Cost: The pairwise potential (7) which measures the cost when nodes and have labels and is defined as (11)

(8)

For nodes , we assign a zero potential, which implies that nodes can move freely. For nodes , the potential is calculated by the dissimilarity measure using two image patches in image and centered on in transformed image , respectively. Although it is possible to incorporate various dissimilarity measures into , is used in the sum of squared difference (SSD) measure this paper, as follows:

is a regularization constant and is the threshold for where truncation. This is a conventional truncated linear spatial prior [23] and produces a high cost when the difference in the dis, difplacements between neighboring nodes is large. For ferent values are assigned for combinations of node colors, as follows: if if if (12)

(9) , and and where represent half of the block width and height, respectively.

and are constant and where stronger connectivity is set on the nodes in

, implying that . Addi-

5We suppose a potential is distinctive if its global minimum or strong local x) when x ^ is a true solution. We also suppose is more distinctive minimum is (^ ^ is steeper. when the shape of the potential around x

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Fig. 9. TRW message passing algorithm for optimizing (7).

tionally, the zero value for freely.6

indicates that the nodes can move

E. Optimization In this section, we will describe an optimization method to to each node such that the MRF assign a label . However, as energy (7) is minimized minimizing (7) is an NP-hard problem in general [25], approximate optimization methods have been extensively researched extensively [23]–[26], [30]. We selected tree-reweighted message passing (TRW) [25], [30] as this method can be applied to any function of the form given in (7) and the message passing procedure can be easily parallelized [31]. Moreover, TRW distinguished itself from the various discrete optimization methods in that it showed state-of-the-art performance in a recent comparative study [21]. The TRW method decomposes a graph into trees in which an exact MAP can be calculated by max-product belief propagation (BP) [24] on each tree. In this scheme, a lower bound for the energy is calculated from the energies of each tree. This lower bound can then be used as a measure of convergence. In particular, the sequential TRW (TRW-S) [25] adjusts the message updating schedule and yields a lower bound that is guaranteed not to decrease. Thus, this method is preferable to conventional BP methods, in which scheduling is heuristic and convergence is unknown. 6In the experiments, we do not create background nodes during optimization. As the data and smoothness costs for the background node are all zero, the background node does not affect the optimization procedure.

In this paper, we followed the TRW-S method and the optimization algorithm for (7) is described in Fig. 9. As we provide brief descriptions for implementing TRW-S, the reader is referred to [25] for more details. The input parameters of the algorithm are the unary potential (8) and the pairwise potential (11). This algorithm assumes that a graph is subdivided into monotonic chains ( trees) where each edge is covered by at least one chain. As is positioned on a 2-D grid, the ordering is used as the row-major node ordering of nodes scheme on the grid. The monotonic chains are constructed from this ordering; hence, each edge is covered by exactly one tree. The algorithm works by message passing similar to BP. For each , the message is updated as follows: edge

(13) where

and

where

which verifies each edge is covered by one tree. While passing messages, the lower bound is calculated by adding the and temporal beconstant subtracted from messages liefs . For one pass of the for-loop (lines 5–12) in Fig. 9, are computed; reverse messages only one-way messages are computed using the same loop after simply reversing . This procedure needs only half the memory the ordering required for BP. For the stopping condition, a fixed iteration number as well as a threshold of the change of the lower bound delta are used.7 7In the experiments, we use 50 for the maximum iteration number and 10 for the threshold of the lower bound delta.


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Fig. 10. Example of two frames registration (continued from Fig. 7). (a) the optimized grid nodes V (I ) = V (T (I )) on the image I (b) the optimized grid nodes V (I ) on the image I (c) the absolute difference image between I and I (d) the absolute difference image between I and I (e) the synthesized (f) synthesized image for I and I . In (f), blurred areas on upper and lower part in (e) are clear with better contrast. (a) V (I ) with image for I and I I , (b) V (I ) with I , (c) jI 0 I j, (d) jI 0 I j, (e) I + I , (f) I + I .

After optimizing (7) using this TRW message passing algorithm, a suboptimal (or almost optimal) labeling set is obtained. The displacement of each control point is obtained . Therefore, the pixel-wise transformation is calas . Fig. 10(a) and (b) show mesh culated using (2) with nodes transformed by the optimizaand , respectively. The tion process; they are overlaid on (the gray-colored nodes in the figure) do background nodes not move during the optimization process, as these nodes do not affect the transformation of the foreground areas. It is apparent that the mesh nodes are transformed while maintaining the smoothness. Fig. 10(c) and (d) show the absolute differand , respectively. The unence images matched areas of the upper and lower parts in Fig. 10(c) are well matched in Fig. 10(d). Fig. 10(e) and (f) show synthesized imand , respectively. The blurred areas on ages the upper and lower parts in Fig. 10(e) are clarified with better contrast in Fig. 10(f).

, bilinear interpolation is used to compute the pixel value of . Next, foreground images and are calculated from and , respectively, using the method in Section III-B. For , a minimum color of and each pixel in is then applied if . Since is aligned to by nonrigid transformation using photometric consistencies, this color minimization scheme improves the overall contrast , we copy image of the rolled image . When . As the boundary of is aligned, this helps ensure that the rolled image includes all available informa, we average tion of the image sequence. If and . As this region is generally backthe colors of ground, this reduces the background noise. Fig. 11 describes this process with pseudo-code. In Fig. 12, we show an example of frame synthesis. As can be [Fig. 12(b)] using seen in Fig. 12(c), a transformed image the proposed method is perfectly assembled into the existing synthesized image [Fig. 12(a)].

F. Frame Synthesis given , and in the previous After obtaining is synthesized to a rolled image using . First, step, is calculated as . a transformed image transforms a pixel of to a floating point position in As

V. EXPERIMENTS In this section, we designed various experiments to reveal the differences between the proposed method and previous methods. The experiments consisted of four different parts. In

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Fig. 11. Algorithm for synthesizing an image I

to a rolled image S given T

.

Fig. 12. Example of frame synthesis after registration (continued from Fig. 10). (a) is a synthesized image for fI ; . . . ; I g. (b) is a transformed image of I using T . (c) is a synthesized image of (a) and (b) using Fig. 11. (a) S, (b) I , (c) S + I .

the first two parts, as described in Sections V-A and V-B, experiments were done to illustrate the differences in image quality between the methods. In the next two parts, as described in Sections V-C and V-D, two matching tests were done including matching flat impressions with various areas of the finger to a rolled fingerprint, and matching using a flat fingerprint database against a rolled fingerprint database. For the proposed method, the following parameters were for making a foreground image, used: for a reference to the right registration, for a reference to the left registration,8 for a for a block size,9 and mesh spacing, for a smoothness cost. 8We allow larger movement on the x-axis as deformations are stronger in the direction of the x-axis in nail-to-nail rolling sequences. Additionally, we set D > D for reference to the right registration and D < D for reference to the left registration, as frames are registered towards the reference frame. 9We use an anisotropic block size for computing data costs, as we allow larger movement on the x-axis.

For efficient optimization of the MRF energy (7), we used the decomposed scheme proposed in [19]. By using this scheme, the complexity of the registration can be reduced from to . The proposed method is referred to as Kwon in the experiments. We used the methods of Ratha et al. [4] and Zhou et al. [5] as previous methods for comparison with Kwon. For Ratha et al. [4], we chose the Minimum, Foreground, and Smoothed compositing methods; they are referred to as Ratha , Ratha , and Ratha , respectively. The Naive and Center methods were excluded, as Naive results in rather poor visual quality, and Center generates a foreground area that is too small. For Zhou et al. [5], we used the vertical center line in the proposed method for their mosaicking line . For the removal of the seams on the tip, was used, and bilinear interpolation was applied for an affine transformation of the block. To synthesize image frames and , we used in area in area , and minimum colors of and in the overlapped area which improved the contrast. This method is referred to as Zhou in the experiments.


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Fig. 13. Example for a visual quality comparison. (a)–(e) are synthesized rolled fingerprints using each algorithm. (f) is a confidence image for (d) representing the overlapping ratio of image frames. (g)–(k) are magnified views of (a)–(e) on areas displayed in (f) as red-colored boxes. (l) is a magnified view of a selected frame from image sequences. (m) contains the upper and lower part of the overlapped image of Kwon (red) and Ratha (green).

Fig. 14. Another example for a visual quality comparison. Descriptions of the figure are same with Fig. 13.

For the rolled image sequences, databases of 290 independent fingers were created. For each finger, four rolled impressions were acquired under the following conditions: 1) a fast rolling speed (about 2 s) on device A; 2) a slow rolling speed (more than 3 s) on device A; 3) a fast rolling speed on device B; and 4) a slow rolling speed on device B. For devices A and B, two Suprema RealScan-10 [32] devices with large sensor areas were , used. These databases are referred to as in the experiments. and For the matching tests in Section V-C and V.D, our own implementations were used for the feature extraction and matching which are minutiae-based algorithms. For the feature extraction process, we applied smoothing, orientation field estimation, filtering, binarization, skeletonization, and minutiae extraction in sequence. For the feature matching process, we assumed a rigid transformation and applied a bounding box to determine corresponding pairs.10 10It is possible to increase the matching performance using matching algorithms considering a nonrigid transformation [33], [34]. However, we used the matching algorithm assuming a rigid transformation to carefully evaluate geometric properties of constructed rolled fingerprints.

A. Visual Quality To compare the visual quality, visual inspection was done on the synthesized rolled fingerprints. First, the rolled fingerprints constructed by Ratha typically contained blurred image areas, although the contrast is high due to the use of minimum color on the overlapped areas without compensating for distortions. Compared to this scheme, Ratha and Ratha alleviated the blurring effects on overlapped areas using pixel weights calculated by segmented foregrounds. However, these two schemes cannot completely eliminate blurring effects, as they do not compensate for distortions on overlapped areas either. For blurring effects on the overlapped areas, the Zhou and Kwon methods generated clearer images, as they compensated for distortions. However, Zhou frequently failed to estimate transformations when the distortions were large, because Zhou finds local affine transformations over limited ranges without optimizing transformations. On the contrary, Kwon generally did not fail to estimate transformations since this scheme uses the image information from all foreground areas and optimizes the transformation with smoothness spatial priors.

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TABLE I FINGERPRINT QUALITY STATISTICS ON ROLLED FINGERPRINT DBS

Fig. 15. Examples of various flat impressions used in Section V-C.

Figs. 13 and 14 show examples of synthesized rolled fingerprints, and they represent high and low quality fingerprints, respectively. Figs. 13(f) and 14(f) represent the confidences for Ratha which imply accumulated foreground images for the rolled image sequences. As described previously, Ratha , Ratha , and Ratha produced blurred images over a wide area. Among these methods, the images synthesized by Ratha show the best visual qualities. Compared to these schemes, Zhou and Kwon produced clearer images. However, as shown in Figs. 13(h) and 14(h), images synthesized by Zhou contain corrupted ridge structures caused by incorrect transformation estimations. To check whether the original fingerprint information is effectively conserved, we can compare the selected frames in Figs. 13(l) and 14(l) with the synthesized images. As Kwon registers images towards the reference image, the overall shapes of the rolled fingerprints constructed by Kwon differ from those of the other methods. To show these shape differences, the overlapped images between Kwon and Ratha are displayed in Figs. 13(m) and 14(m). In these figures, the upper part of the rolled fingerprint generated by Kwon has a smaller width than that produced by Ratha , and the lower part has significant differences as well. As there are limitations on showing a sufficient number of examples for visual quality comparisons, quality statistics are given in the next section. B. Statistics on Various Quality Measures For statistical verification of the visual inspection, three , and were defined. These quality quality measures

measures utilize the quality map of NIST biometric image software (NBIS) [35] which integrates the information of a direction map, a low contrast map, a low flow map, and a high curve map. The quality assigned to each block (8 8 in size) of the quality map is defined using five grades: A (good quality), B (good quality with low flow/high curve neighbor), C (low flow or high curve), D (low flow or high curve), and E (low contrast or no direction). NIST notes that the features in the blocks with A and B qualities are useful but those in the blocks with C and D qualities are not. Following this for , we counted the number of blocks having grade A to D on the measures the number foreground fingerprint area; that is, of all meaningful blocks. For , we counted the number of blocks having grade A or B on the foreground fingerprint area; measures the number of blocks having good quality. that is, , we counted the number of blocks having grade C or For D on the foreground fingerprint area and divided the number measures the ratio of poor-quality blocks on by ; that is, the foreground area. Table I shows the average values of these measures on the rolled fingerprint databases. The results demonstrate that Kwon and on outperforms the other methods for measures nearly every database. This implies that the rolled fingerprints generated by Kwon contain larger regions of good quality with a smaller ratio of poor-quality regions compared to the other methods. For , Ratha generated the largest fingerprint reand for gions compared to the other methods. However Ratha are exceedingly poor compared to the other methods.


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Fig. 16. Examples of matching results for flat (f) to rolled fingerprints (a)–(e). In (g)–(k), we show skeletons of the transformed flat fingerprint with the rolled ). (a) Kwon, fingerprint and display matched minutiae as squared boxes. Also, we represent the number of matched minutiae and the matching score as ( (b) Zhou, (c) Ratha , (d) Ratha , (e) Ratha , (f) flat, (g) Kwon (33, 2975), (h) Zhou (22, 1122), (i) Ratha (24, 861), (j) Ratha (25, 1118), (k) Ratha (18, 420).

m

s m;s

Fig. 17. Comparative FNMR curves for Section V-C. Fig. 18. Comparative DET curves for Section V-D.

Apart from Ratha was largest on Kwon. To summarize, the average rank of all the measures for all databases was calculated. It was concluded that Kwon shows the best performances on these quality measures. C. Matching Tests Using Various Flat Impressions With Synthesized Rolled Fingerprints As the purpose of rolled fingerprint acquisition is to increase the accuracy of fingerprint recognition, it is important to check the matching performance between various flat impressions and rolled fingerprints. In this section, for 10 fingers, 40 various flat impressions containing various areas on the finger surface were generated per finger. Examples of these flat impressions are shown in Fig. 15. These flat impressions were matched to the rolled fingerprints generated by each method. The matching test includes 1,600 genuine flat-to-rolled fingerprint matchings.11 Fig. 17 shows the comparative false non matched ratio (FNMR) 111,600 = 4

(rolled impressions)

2 40 (flat impressions) 2 10 (fingers).

curves.12 In these curves, Kwon had lower FNMR ratios in the low matching score region than the others. This suggests that Kwon produces relatively larger matching scores for the difficult genuine matchings. To analyze the matching performances in detail, an example of the genuine matchings are shown in Fig. 15. In the figure, the skeletons of flat and rolled fingerprints are shown to be better matched in Kwon. Moreover, matched minutiae are more evenly distributed and their numbers are larger in Kwon. And, the matching scores are larger in Kwon. The figures also show that the extracted ridge structures on Ratha , Ratha , and Ratha are corrupted in the blurred regions of the rolled fingerprints. Although the extracted ridges of Zhou are of better quality compared to those by Ratha , Ratha , and Ratha , the ridge correspondences between the rolled fingerprints and the flat fingerprints for Kwon are superior to those of Zhou. 12The matching algorithm used in the experiments produces matching scores between 0 and 10,000.

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Fig. 19. Differences between constructed rolled fingerprints with varying reference frames. We denote rolled fingerprints S with a reference frame I as S (I ). (a) shows the overlapped image of S (I ) (red) and S (I ) (green). (b) shows the overlapped image of S (I ) (red) and S (I ) (green). (c) shows the overlapped ) (green). image of S (I ) (red) and S (I

TABLE II RESULTS FOR SECTION V-D

TABLE III RESULTS FOR SECTION V-E

D. Matching Tests Using a Flat Impression Database With Synthesized Rolled Fingerprints In this section, the flat-to-rolled matching test was expanded to a larger database. A flat impression database was created from 220 independent fingers, in which every finger had a corresponding identity in the rolled image database. For each finger, eight flat impressions were acquired under the following conditions: 1) two normal flat impressions, 2) two impressions including the left part of the finger, 3) two impressions including the right part of the finger, and 4) two impressions including the upper part of the finger. A Suprema RealScan-D [32] device with a smaller sensor than that of RealScan-10 was used to compile the database. Using this flat impression database, the flat impressions were matched to the rolled fingerprints generated by each method. The matching test included 7,040 genuine and 96,360 imposter flat-to-rolled fingerprint matchings.13 It was expected that the scale of this matching test would show persuasive statistical results.14 In Fig. 18 and Table II, the comparative detection-error tradeoff (DET) curves15 and its numerical results are shown where the equal error rate (EER) represents the false non matched ratio (FNMR) value when the false matched ratio (FMR) is the same as FNMR. FMR100 indicates that the FNMR value at FMR is 1%, and FMR1000 indicates that the FNMR value at FMR is 0.1% [37]. In the results, Kwon significantly outperformed the other methods. It is surprising that the difference in the matching performance is quite large by changing the rolled fingerprint construction method only. 137,040 = 4

2

2

(rolled impressions) 8 (flat impressions) 220 (fingers). example, the number of matching tests here is larger than that of FVC2004 [36] which evaluates 2,800 genuine and 4,950 imposter matchings for 120 fingers. 15The DET curve is a plot of FMR against FNMR, while the receiver operating characteristic (ROC) curve is a plot of FMR against (1-FNMR) [3]. 14For

E. Effects of Changing a Reference Frame To analyze how a reference frame affects the constructed rolled fingerprints, we show the differences between the constructed rolled fingerprints with varying reference frames in Fig. 19. In the figure, we denote rolled fingerprints with a . The rolled fingerprint with reference frame as (which is found by Fig. 5) is an original reference frame , and . and compared with have a geometrical bias towards the left and right to in the upper parts, respectively, whereas the difference between and is small. In addition, we performed matching tests using Kwon , Kwon , and Kwon on the conditions of Section V-D where Kwon , Kwon , and Kwon construct rolled fingerprints using , and as their reference frames, respectively. The results are shown in Table III. The performances of Kwon and Kwon are better than that of Kwon , and they are comparable has with that of the original algorithm Kwon. As than , the results greater geometrical similarity to of the matching tests are consistent with the visual inspections. From these results, we can conclude that the performance of the proposed method is not sensitive to small perturbations of the reference frame, and the reference finding algorithm in Fig. 5 works well in practice. In addition, the performance decrease for Kwon (the worst case for finding a reference frame) is small and it even performs better than previous methods Zhou, Ratha , Ratha , and Ratha . F. Effects of Nonrigid Image Registration To analyze how the nonrigid image registration procedure affects the constructed rolled fingerprints, we show the constructed rolled fingerprints using the proposed method with and without the nonrigid registration procedure in Fig. 20. In the figure, we denote Kwon as a method which excludes the registration procedure (Fig. 6) from Kwon, that is, Kwon assumes


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Fig. 20. Comparisons between rolled fingerprints constructed by Kwon and Kwon . The method Kwon excludes the registration procedure from Kwon. (a) shows the rolled fingerprint constructed by Kwon. (b) shows the rolled fingerprint constructed by Kwon . (c) shows the overlapped image of Kwon (red) and Kwon (green).

TABLE IV RESULTS FOR SECTION V-F

TABLE V AVERAGE PROCESSING TIME FOR ONE FRAME

an identity transformation between image frames. As nonrigid distortions between frames are not compensated for, the constructed rolled fingerprints using Kwon contain many blurred fingerprint regions in Fig. 20(b). In Fig. 20(c), we show the difference between the rolled fingerprints constructed by Kwon and Kwon . In this figure, it can be seen that almost every area except the center region is different between the two rolled fingerprints. In addition, we performed matching tests using Kwon on the conditions of Section V-D. The results are shown in Table IV. The performance of Kwon is much worse than that of Kwon and comparable with Ratha in Table II. From these results, we can conclude that the registration and the synthesis procedures of the proposed method are closely related, implying that the registration step plays an important role in determining the quality of the rolled fingerprints and the matching performances. VI. CONCLUSION This paper describes a new rolled fingerprint construction approach, which incorporates a MRF-based nonrigid image registration method. Image registration is designed to find a set of discrete displacement vectors on a deformable mesh using the energy model defined by the label sets related to these vectors. As this method finds dense correspondences between image frames from rolled sequences, we register every image frame of the rolled sequence to the reference image which is defined as a frame containing a fingerprint positioned at the center. A rolled fingerprint is constructed by accumulating information from registered images. This process cannot be carried out unless the entire foreground area of the fingerprint

is registered. This approach produces a conceptually different rolled fingerprint compared to previous methods. In the experiments, the proposed method was compared with previous approaches in terms of the image quality and the matching performance. The experimental results showed that the proposed method produces rolled fingerprints with high quality. Moreover, the results demonstrated that the practical matching performance between the rolled fingerprints and various flat fingerprints is superior to that of the previous methods. However, the proposed method has a number of limitations. As this method synthesizes fingerprints after estimating a reference frame, it does not work in an online manner, as do previous methods. Of course, this is not a problem if additional processing time is allowed after obtaining the rolled sequences. Another limitation concerns the computational complexity involved with nonrigid image registration. This process uses a large size of label space, and its computational time is increased by the square of the label space. In the experiments, the proposed method requires a few seconds to register two frames which is somewhat slower than the previous methods, which can be executed in real time, as shown in Table V.16 To overcome this issue, it is possible to implement the registration process using a graphics processing unit (GPU) as the computations for the data cost of the MRF energy and the TRW message passing structure are highly parallel [31]. Lastly, we want to point out that using second-order spatial priors for the MRF energy rather than first-order spatial priors normally improves the registration accuracy [38]. Since the quality of registration was sufficient using the proposed method, we did not use second-order priors in this paper. REFERENCES [1] P. Komarinski, P. T. Higgins, K. M. Higgins, and L. K. Fox, Automated Fingerprint Identification Systems (AFIS). New York: Elsevier, 2005. [2] Taking Legible Fingerprints: V. Steps for Fingerprinting [Online]. Available: http://www.fbi.gov/hq/cjisd/takingfps.html [3] D. Maltoni, D. Maio, A. K. Jain, and S. Prabhakar, Handbook of Fingerprint Recognition, 2nd ed. New York: Springer-Verlag, 2009. [4] N. K. Ratha, J. H. Connell, and R. M. Bolle, “Image mosiacing for rolled fingerprint construction,” in Proc. Int. Conf. Pattern Recognit., 1998, pp. 1651–1653. 16The processing time for one frame is calculated as (total processing time for rolled fingerprint construction)/(number of frames). The time is measured on an Intel Xeon E5345 2.33 Ghz machine.

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[29] S. Lee, G. Wolberg, and S. Y. Shin, “Scattered data interpolation with multilevel B-splines,” IEEE Trans. Vis. Comput. Graphics, vol. 3, no. 3, pp. 228–244, Jul./Sep. 1997. [30] M. J. Wainwright, T. Jaakkola, and A. S. Willsky, “MAP estimation via agreement on trees: Message-passing and linear programming,” IEEE Trans. Inf. Theory, vol. 51, no. 11, pp. 3697–3717, Nov. 2005. [31] C.-K. Liang, C.-C. Cheng, Y.-C. Lai, L.-G. Chen, and H. H. Chen, “Hardware-efficient belief propagation,” in Proc. IEEE Conf. Comput. Vis. Pattern Recognit., 2009, pp. 80–87. [32] Suprema, Inc. [Online]. Available: http://www.supremainc.com [33] D. Kwon, I. D. Yun, D. H. Kim, and S. U. Lee, “Fingerprint matching method using minutiae clustering and warping,” in Proc. Int. Conf. Pattern Recognit., 2006, vol. 4, pp. 525–528. [34] D. Kwon, I. D. Yun, and S. U. Lee, “A robust warping method for fingerprint matching,” in Proc. IEEE Comput. Soc. Workshop Biometrics, 2007, pp. 1–6. [35] C. I. Watson, M. D. Garris, E. Tabassi, C. L. Wilson, R. M. McCabe, S. Janet, and K. Ko, User’s Guide to NIST Biometric Image Software (NBIS) National Institute of Standards and Technology, 2004. [36] D. Maio, D. Maltoni, R. Cappelli, J. L. Wayman, and A. K. Jain, “FVC2004: Third fingerprint verification competition,” in Proc. Int. Conf. Bioinf. Appl., 2004, pp. 1–7. [37] D. Maio, D. Maltoni, R. Cappelli, J. L. Wayman, and A. K. Jain, “FVC2000: Fingerprint verification competition,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 24, no. 3, pp. 402–412, Mar. 2002. [38] D. Kwon, K. J. Lee, I. D. Yun, and S. U. Lee, “Nonrigid image registration using dynamic higher-order MRF model,” in Proc. Eur. Conf. Comput. Vis., 2008. Dongjin Kwon was born in Seoul, Korea, in 1978. He received the B.S. degree in physics and computer science from Seoul National University, Seoul, Korea, in 2001, where he is currently working towards the Ph.D. degree in electrical engineering and computer science. His research interests include computer vision, fingerprint recognition, and medical image analysis.

Il Dong Yun received the B.S., M.S., and Ph.D. degrees from Seoul National University, Seoul, Korea, in 1989, 1991, and 1996, respectively. In 1996–1997, he was a Senior Researcher at Daewoo Electronics. He is currently a Professor at the Department of Digital Information Engineering, Hankuk University of F.S., Yongin, Korea. His current research interests are on object segmentation, nonlinear image registration, content-based image retrieving, and medical image analysis. Sang Uk Lee received the B.S. degree from Seoul National University, Seoul, Korea, in 1973, the M.S. degree from Iowa State University, Ames, in 1976, and the Ph.D. degree from University of Southern California, Los Angeles, in 1980, all in electrical engineering. From 1980 to 1981, he was with the General Electric Company, Lynchburg, VA, working on the development of the digital mobile radio. From 1981 to 1983, he was a Member of Technical Staff, M/A-COM Research Center, Rockville, MD. In 1983, he joined the Department of Control and Instrumentation Engineering, Seoul National University as an Assistant Professor, where he is now a Professor at the Department of Electrical Engineering and Computer Science. He is also affiliated with the Automation and Systems Research Institute and the Institute of New Media and Communications, both at Seoul National University. He was the President of the Korean Institute of Communication Science in 2005. His current research interests are in the areas of image and video signal processing, digital communication, and computer vision. Dr. Lee served as an Editor-in-Chief for the Transactions of the Korean Institute of Communication Science from 1994 to 1996. He was an Associate Editor for the IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY from 2002 to 2005, and was on the editorial board of the Journal of Applied Signal Processing from 2003 to 2004. He is currently on the editorial board of the Journal of Visual Communication and Image Representation. He is a member of Phi Kappa Phi.