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104 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 10, NO. 1, JANUARY 2015

Learning Fingerprint Reconstruction:From Minutiae to Image

Kai Cao and Anil K. Jain, Fellow, IEEE

Abstract— The set of minutia points is considered to be themost distinctive feature for fingerprint representation and iswidely used in fingerprint matching. It was believed that theminutiae set does not contain sufficient information to recon-struct the original fingerprint image from which minutiae wereextracted. However, recent studies have shown that it is indeedpossible to reconstruct fingerprint images from their minutiaerepresentations. Reconstruction techniques demonstrate the needfor securing fingerprint templates, improving the template inter-operability, and improving fingerprint synthesis. But, there is stilla large gap between the matching performance obtained fromoriginal fingerprint images and their corresponding reconstructedfingerprint images. In this paper, the prior knowledge aboutfingerprint ridge structures is encoded in terms of orientationpatch and continuous phase patch dictionaries to improve thefingerprint reconstruction. The orientation patch dictionary isused to reconstruct the orientation field from minutiae, while thecontinuous phase patch dictionary is used to reconstruct the ridgepattern. Experimental results on three public domain databases(FVC2002 DB1_A, FVC2002 DB2_A, and NIST SD4) demon-strate that the proposed reconstruction algorithm outperformsthe state-of-the-art reconstruction algorithms in terms of both:1) spurious minutiae and 2) matching performance with respectto type-I attack (matching the reconstructed fingerprint againstthe same impression from which minutiae set was extracted) andtype-II attack (matching the reconstructed fingerprint against adifferent impression of the same finger).

Index Terms— Fingerprint reconstruction, orientation patchdictionary, continuous phase patch dictionary, minutiae set,AM-FM model.

I. INTRODUCTION

F INGERPRINTS are ridge and valley patterns presenton the surface of human fingertips [1]. The purported

uniqueness of fingerprints is characterized by three levels offeatures [1] (see Fig. 1). Global features, such as pattern type,ridge orientation and frequency fields, and singular points,are called level-1 features. Level-2 features mainly refer tominutia points in a local region; ridge endings and ridge

Manuscript received July 7, 2014; revised October 9, 2014; acceptedOctober 15, 2014. Date of publication October 17, 2014; date ofcurrent version December 17, 2014. The work of K. Cao was supported in partby the National Natural Science Foundation of China under Grant 61101247and Grant 61473214. The associate editor coordinating the review of thismanuscript and approving it for publication was Prof. Patrizio Campisi.

K. Cao is with the Department of Computer Science and Engineering,Michigan State University, East Lansing, MI 48824 USA, and also with theSchool of Life Sciences and Technology, Xidian University, Xi’an 710071,China (e-mail: [email protected]).

A. K. Jain is with the Department of Computer Science and Engineering,Michigan State University, East Lansing, MI 48824 USA (e-mail:[email protected]).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIFS.2014.2363951

bifurcations are the two most prominent types of minutiae.Level 3 features include all dimensional attributes at a very-fine scale, such as width, shape, curvature and edge contoursof ridges, pores, incipient ridges, as well as other permanentdetails. Among these three types of features, the set of minutiapoints (called minutiae) is regarded as the most distinctivefeature and is most commonly used in fingerprint matchingsystems. An international standard ISO/IEC 19794-2 [2] hasbeen proposed for minutiae template representation forthe purpose of interoperability of matching algorithms.FVC-onGoing [3], a well-known web-based automated eval-uation platform for fingerprint recognition algorithms, has setup a benchmark to evaluate fingerprint matching algorithmsusing this standard minutiae template format.

It was believed that it is not possible to reconstruct afingerprint image given its extracted minutiae set. However, ithas been demonstrated that it is indeed possible to reconstructthe fingerprint image from the minutiae; the reconstructedimage can be matched to the original fingerprint image witha reasonable high accuracy [7]–[9]. There is still a roomfor improvement in the accuracies, particularly for type-IIattack. The aim of fingerprint reconstruction from a givenminutiae set is to make the reconstructed fingerprint resemblethe original fingerprint. A successful reconstruction techniquedemonstrates the need for securing fingerprint templates. Sucha technique would also be useful in improving the matchingperformance with ISO templates as well as addressing theissue of template interoperability [7]. It also could be used toimprove synthetic fingerprint reconstruction and restore latentfingerprint images [8].

Existing reconstruction algorithms essentially consist of twomain steps: i) orientation field reconstruction and ii) ridgepattern reconstruction. The orientation field, which determinesthe ridge flow, can be reconstructed from minutiae and/orsingular points. In [4], the orientation field was reconstructedfrom the singular points (core and delta) using the zero-pole model [5]. However, the orientation field in finger-prints cannot simply be accounted for by singular pointsonly. Cappelli et al. [7] proposed a variant of the zero-pole model with additional degrees of freedom to fit themodel to the minutiae directions. However, the orientation fieldreconstructed based on zero-pole model cannot be guaranteedwhen the singular points are not available. In [6], a setof minutiae triplets was proposed to reconstruct orientationfield in triangles without using singular points. The algorithmproposed by Feng and Jain [8] predicts an orientation valuefor each block by using the nearest minutia in each of theeight sectors. The approaches in [10] and [11] reconstructed

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CAO AND JAIN: LEARNING FINGERPRINT RECONSTRUCTION 105

Fig. 1. Illustration of fingerprint features at three different levels. (a) A gray-scale fingerprint image (NIST SD30, A002_01), (b) level 1 features: orientationfield and singular points (core shown as circle and delta shown as triangle), (c) level 2 features: ridge endings (red squares) and ridge bifurcations (blue circles)and (d) level 3 features: pores and dots.

orientation field from minutiae to improve the matching perfor-mance. However, these orientation reconstruction approaches,based on given minutiae, do not utilize any prior knowledgeof the fingerprint orientation pattern and may result in anon-fingerprint-like orientation field.

The other step in fingerprint reconstruction is ridge patternreconstruction based on the reconstructed orientation field. Theridge pattern reconstruction proposed in [4] only generatesa partial skeleton of the fingerprint, which is obtained bydrawing a sequence of splines passing through the minutiae.This method was further improved in [6] by using linearintegral convolution to impart texture-like appearance andlow-pass filtering to get wider ridges. However, it can onlygenerate a partial fingerprint, and the resulting ridge patternis quite different from that of the target fingerprint. Theapproach proposed by Cappelli et al. [7] is able to reconstructa full fingerprint image from minutiae points. An image isfirst initialized by local minutiae prototypes, followed byiterative Gabor filtering with the estimated orientation fieldand predefined ridge frequency to generate ridge pattern.However, this approach introduces many spurious minutiaearound the intersections of regions generated from differ-ent minutiae; these spurious minutiae cannot be controlled.Feng and Jain [8] utilized the amplitude and frequency modu-lated (AM-FM) model [13] to reconstruct fingerprints, wherethe phase, consisting of continuous phase and spiral phase(corresponding to minutiae), completely determines the ridgestructure and minutiae. Continuous phase reconstruction istherefore a critical step in the AM-FM model based fingerprintreconstruction. In [8], the continuous phase was obtained by apiecewise planar model. However, the piecewise planar modelintroduced many spurious minutiae and resulted in visibleblocking effects during the continuous phase reconstruction.Instead of using piecewise planar model, Li and Kot [9]reconstructed continuous phase from a binary ridge patterngenerated using Gabor filtering with the reconstructed orienta-tion field and predefined ridge frequency; the continuous phasewas obtained by subtracting spiral phase from the phase ofthe binary ridge pattern. While this approach ensures that nospirals will appear in the continuous phase, the continuousphase after removing all spirals may be quite different fromthe desired one in terms of ridge flow and ridge frequency,as shown in Fig. 3. Table I summarizes various fingerprint

reconstruction algorithms proposed in the literature and theirreported performance.

Although several fingerprint reconstruction algorithms havebeen proposed, the matching performance of the reconstructedfingerprints compared with the original fingerprint imagesis still not very satisfactory. That means the reconstructedfingerprint image is not very close to the original fingerprintimage that the minutiae were extracted from. An importantreason for this loss of matching performance is that noprior knowledge of fingerprint ridge structure was utilized inthese reconstruction approaches to reproduce the fingerprintcharacteristics. In the literature, such prior knowledge has beenrepresented in terms of using orientation patch dictionary [14]and ridge structure dictionary [15] for latent segmentationand enhancement. In this paper, our goal is to utilize asimilar dictionary-based approach to improve the fingerprintreconstruction from a given minutiae set. Two dictionariesare constructed for fingerprint reconstruction: 1) orientationpatch dictionary and 2) continuous phase patch dictionary.The orientation patch dictionary is used to reconstruct theorientation field from a minutiae set, while the continuousphase patch dictionary is used to reconstruct the ridge pattern.Instead of reconstructing continuous phase and spiral phaseglobally, we propose to reconstruct fingerprint patches usingcontinuous phase patch dictionary and minutiae belonging tothese patches; these patches are optimally selected to form afingerprint image. The spurious minutiae, which are detectedin the phase of the reconstructed fingerprint image but notincluded in the input minutiae template, are then removedusing the global AF-FM model. The proposed reconstructionalgorithm has been evaluated on three different public domaindatabases, namely, FVC2002 DB1_A, FVC2002 DB2_A andNIST SD4, in terms of minutiae set accuracy with respectto the given minutiae set and matching performance of thereconstructed fingerprint. Experimental results demonstratethat the proposed algorithm performs better than two state-of-the-art reconstruction algorithms [8] and [9], as shownin Fig. 2. The superior performance of the proposed algorithmover [8] and [9] can be attributed to:

1) Use of prior knowledge of orientation pattern, i.e.,orientation patch dictionary, which provides better ori-entation field reconstruction, especially around singularpoints.


TABLE I

A COMPARISON OF FINGERPRINT RECONSTRUCTION ALGORITHMS PROPOSED IN THE LITERATURE

2) The sequential process which consists of (i) reconstruct-ing locally based on continuous phase patch dictionary,(ii) stitching these patches to form a fingerprint imageand (iii) removing spurious minutiae. Instead of gener-ating a continuous phase and then adding spiral phaseto the continuous phase globally, this procedure is ableto better preserve the ridge structure.

3) Use of local ridge frequency around minutiae.

The rest of the paper is organized as follows. The pre-liminaries of the AM-FM fingerprint model are introduced insection II. The details of the proposed algorithm are presentedin section III. Experimental results are reported in section IV.Finally, conclusions and future research directions are reportedin section V.

II. AM-FM FINGERPRINT MODEL

The AM-FM fingerprint model proposed byLarkin and Fletcher [13] represents a fingerprint image I asa hologram, i.e., consisting of 2D amplitude and frequencymodulated fringe pattern:

I (x, y) = a(x, y)+ b(x, y) cos(ψ(x, y))+ n(x, y), (1)

where a(x, y), b(x, y) and n(x, y) are, respectively, the offset,amplitude and noise, which make the fingerprint realistic, andψ(x, y) is the phase which completely determines the ridgestructures and minutiae of the fingerprint. According to the

Helmholtz Decomposition Theorem [17], a phase ψ(x, y) canbe uniquely decomposed into a continuous phase ψC(x, y) anda spiral phase ψS(x, y), i.e., ψ(x, y) = ψC (x, y)+ ψS(x, y).For a fingerprint image I (x, y), its phase ψ(x, y) can beobtained by demodulation [13], [17]. Before the demodulation,the offset (or DC) term a(x, y), which can be estimated as themid-value in a local area, is removed from I (x, y). The offsetremoved image I ′(x, y) is

I ′(x, y) = I (x, y)− a(x, y) ≈ b(x, y) cos(ψ(x, y)). (2)

With the application of demodulation operator R, which isdefined as

R[I ′(x, y)] ∼= F−1{eiφ(u,v)F{I ′(x, y)}}, (3)

where eiφ(u,v) = (u + iv)/√(u2 + v2) is a spiral Fourier

multiplier, F(·) and F−1(·) are the Fourier transform andinverse Fourier transform, respectively, the cosine term in (2)can be converted to a sine term (in quadrature to the cosine),

−ie−iβ(x,y)R[I ′(x, y)] = b(x, y) sin(ψ(x, y)), (4)

where β(x, y) is the directional map (in the range (−π, π])which is normal to local ridge orientation (in the range(−π

2 ,π2 ]). There are several methods to convert orientation

field to directional map ([8] and [9]). Based on Eqs. (2) and (4),the phase is obtained by

ψ(x, y) = tan−1(−ie−iβ(x,y)R[I ′(x, y)], I ′(x, y)). (5)


Fig. 2. A comparison of fingerprint images reconstructed using four different reconstruction algorithms. (a) and (b) are two impressions from the same finger,(c) minutiae points extracted from (a), and its reconstructed fingerprint images using: (d) algorithm by Feng and Jain [8], (e) algorithm by Li and Kot [9],(f) proposed algorithm with a fixed ridge frequency and (g) proposed algorithm with adaptive ridge frequency around each minutiae. The matching scores,S(·, ·), between the two impressions (F1 and F2) and the reconstructed images (R1, R2, R3 and R4) using Verifinger SDK 6.3 [12] are shown around the twoimpressions.

Fig. 3. Phase analysis of a gray-scale fingerprint image. (a) A gray-scale fingerprint image (NIST SD4, S0005.bmp), (b) enhancement of (a) using Gaborfiltering in [16], (c) unwrapped orientation field based on the approach proposed in [9], (d) phase image ψ , (e) cos(ψ), (f) cos(ψS), where ψS is the spiralphase, and (g) cos(ψC ), where ψC is the continuous phase. Note that after removing the spirals (minutiae), the ridge flow and ridge frequency may change.

To get a smooth phase, directional filtering, such asGabor filtering [16], is applied to enhance the gray-scalefingerprint image before demodulation. Figs. 3(b) and (d) showthe enhanced fingerprint image and the phase of fingerprintimage in Fig. 3(a). With the phase ψ(x, y), its ideal fingerprintrepresentation is

I (x, y) = cos(ψ(x, y)). (6)

The spirals in the phase image (i.e., minutiae ina fingerprint) can be detected by the clockwise phasedifference [9], [18]. Let ψ0, ψ1, ψ2 and ψ3 denote the phasevalues at positions (x, y), (x + 1, y), (x + 1, y + 1) and(x, y+1), respectively. The clockwise phase difference ε(x, y)at location (x, y) is defined as

ε(x, y) =3∑

i=0

dθ(ψ(i+1) mod 4, ψi ), (7)


Fig. 4. Flowchart of the proposed reconstruction algorithm.

where mod is the modulo operator, and dθ(ψa, ψb) is thephase difference between ψa and ψb

dθ(ψa, ψb) =

⎧⎪⎨

⎪⎩

ψa − ψb + 2π, if ψa − ψb ≤ −π,ψa − ψb − 2π, if ψa − ψb > π,

ψa − ψb, otherwise. (8)

The value of ε(x, y) can be used as an indication ofnon-spiral (0), negative spiral (−π) and positive spiral (π).Minutiae set with n minutiae points can be removed fromcos(ψ(x, y)) by subtracting a spiral phase ψS(x, y), whichconsists of a set of n spirals:

ψS(x, y) =n∑

i

pi tan−1(y − yi

x − xi), (9)

where (xi , yi ) denotes the coordinates of the i th spiral andpi ∈ {−1, 1} is its polarity determined by the sign ofε(xi , yi ). After removing all the minutiae points or spiralsfrom ψ(x, y), the continuous phase ψC (x, y), the integralof whose gradient around any simple close path is zero, isretained. Figs. 3(f) and (g) show the cosines of spiral phaseand continuous phase, respectively. Note that after removingthe spirals (minutiae), the ridge flow and ridge frequency ofthe continuous phase may be quite different from those of thegray-scale fingerprint image.

III. PROPOSED RECONSTRUCTION ALGORITHM

The goal of fingerprint reconstruction is to reconstructa gray-scale fingerprint image based on an input set

of n minutiae M = {mi = (xi , yi , αi )}ni=1, where (xi , yi )

and αi (−π < αi ≤ π) denote the location and direction ofthe i th minutia, respectively. In this paper, a dictionary-basedfingerprint reconstruction method is proposed. Two kinds ofdictionaries are learnt off-line as prior knowledge: 1) orienta-tion patch dictionary and 2) continuous phase patch dictionary.For an input fingerprint minutiae set, the orientation patchdictionary is used to reconstruct the orientation field from theminutiae set, while the continuous phase dictionary is used toreconstruct the ridge pattern. In addition, the spurious minutiaeintroduced in the reconstructed fingerprint are removed usingthe global AM-FM model. The flowchart of the proposedalgorithm is illustrated in Fig. 4.

A. Dictionary Construction

1) Orientation Patch Dictionary: The orientation patchdictionary proposed by Feng et al. [14] for latent enhance-ment is directly utilized as prior knowledge of ridge flowfor orientation field reconstruction. The orientation patchdictionary DO , consisting of a number of orientation patches,is constructed from a set of high quality fingerprints(50 rolled fingerprint images). An orientation patch consistsof 10 × 10 orientation elements with each orientation elementreferring to the dominant orientation in a block of size16 × 16 pixels. Fig. 5 shows some examples of orientationpatches from DO .

2) Continuous Phase Patch Dictionary: The continuousphase patch dictionary, which includes a number of continuous


Fig. 5. Some example elements from the orientation patch dictionary.

Fig. 6. Orientation field of 24 orientation patch centers.

phase patches (without spirals), is constructed through thefollowing steps:

i) Fingerprint selection and processing: High quality fin-gerprints in NIST SD4 [19], whose NIST FingerprintImage Quality (NFIQ) [20] index1 is less than 3, areselected for dictionary construction. For each selectedfingerprint, the orientation field and the quality mapwith a block size of 8 × 8 pixels are obtained byMINDTCT [21], and the frequency field is computedby the method proposed in [16]. Gabor filtering [16]is utilized to enhance the selected fingerprints. This isfollowed by the demodulation in Eq. (5) to get the idealrepresentation using Eq. (6).

ii) Orientation patch clustering: A set of orientation patchesof size 6×6 blocks (with each block being 8×8 pixels)is then selected by sliding a window over the orientationfield with a step size of 1 block; if the average qualityvalue of a patch is larger than a predefined threshold T(T is set to 3.75), the patch is included in the training set.Each orientation patch is converted to an 18-dimensionalvector by down sampling by a factor of 2 (convertingthe block size from 8 × 8 pixels to 16 × 16 pixels) andrepresenting an orientation element θ in an orientationpatch as a 2-dimensional vector (cos 2θ, sin 2θ) to dealwith the ambiguity between −π

2 and π2 . The k-means

clustering method [22] is then adopted to find 24 clustercenters among the set of orientation patches. Fig. 6displays the orientation fields of the 24 orientation patchcluster centers.

1NFIQ ranges from 1 (the highest quality) to 5 (the lowest qualityfingerprint).

Fig. 7. Same examples from the continuous phase patch dictionary. Thecontinuous phase patches in a specific row are from the same orientationpatch cluster center. Each patch is of size 48 × 48 pixels.

iii) Fingerprint patch clustering: For each orientationpatch center, a set of fingerprint patches of size48 × 48 pixels (100,000 patches in our experiments)are selected by sliding a window over the ideal rep-resentation of selected fingerprint images with a stepsize of 8 pixels. A fingerprint patch is selected for thei th orientation patch center if it satisfies the qualityrequirement in step ii) and its closest orientation patchcenter is the i th one. A total of 1,024 fingerprint patchcluster centers are constructed by the k-means clusteringmethod [23] for each orientation patch center. The minu-tiae points in each cluster are removed using the methodin section II to get its continuous phase which formsthe continuous phase patch dictionary; a 24 × 1, 024dictionary is constructed. Fig. 7 shows some examplesfrom the continuous phase patch dictionary.

iv) Orientation and frequency fields estimation: The methodin [16] is adopted to compute the orientation field andaverage ridge frequency for each dictionary element,which is used for dictionary lookup. Its unwrappedpixel-wise orientation field, which is used for addinginput minutiae (spiral phase) to the continuous phase, iscomputed using the approach proposed in [9].

B. Orientation Field Reconstruction

The orientation field is considered only in the foregroundregion of a fingerprint which is determined by dilating theconvex hull of the input minutiae points with a disk-shapemask with a radius of 32 pixels. The image is divided intonon-overlapping blocks of size 16 × 16 pixels. For the blockscontaining minutiae, their orientations are simply replaced


Fig. 8. Illustration of orientation field interpolation methods. (a) Minutiaeshown on the gray-scale fingerprint image, (b) orientation field obtained fromminutiae, (c) interpolated orientation field, (d) and (e) are the orientationdensity maps of (b) and (c), respectively.

by the directions of their corresponding minutiae (modulatedby π), as shown in Fig. 8(b). Since the minutiae pointsare usually non-uniformly distributed (sparsely distributed insome regions), it is difficult to select representative orientationpatches from DO in the region without minutiae or with one ortwo minutiae. Orientation patch dictionary, therefore, cannotbe used to reconstruct the orientation field directly. In order toaddress this problem, orientation density is introduced, and theorientations of blocks with low orientation density values areinterpolated iteratively using Delaunay triangulation. Supposethat B = {(xi , yi )}Nb

i=1 is the set of Nb blocks with orientationsinitialized by minutiae directions (modulated by π) and DTB

is the Delaunay triangulation of B . The orientation density Dat block (x, y) is defined as

D(x, y) =Nb∑

i=1

exp(− (x − xi )2 + (y − yi )

2

2σ 2 ) (10)

where σ is a parameter which controls the neighborhoodinfluence. Fig. 8(d) shows the density map of orientationfield in Fig. 8(b). Note that the orientation density values insome of the blocks are very small. Suppose the orientationdensity value D(xb, yb) at block b = (xb, yb) is the minimumvalue in the foreground and D(xb, yb) is less than the densitythreshold TD . The orientation θb at block b is then interpolatedby blocks b1, b2 and b3, where �b1b2b3 ∈ DTB and b is in�b1b2b3, as shown in Fig. 9. Let θi denote the orientation ofblock bi and di be the Euclidean distance between bi and b(1 ≤ i ≤ 3). The cosine and sine components (u, v) of 2θb

are computed as

u = d2d3 cos 2θ1 + d1d3 cos 2θ2 + d1d2 cos 2θ3

d2d3 + d1d3 + d1d2(11)

v = d2d3 sin 2θ1 + d1d3 sin 2θ2 + d1d2 sin 2θ3

d2d3 + d1d3 + d1d2(12)

The orientation θb at block b is obtained by

θb = tan−1(v, u)/2. (13)

Fig. 9. Orientation interpolation in a triplet; b1, b2 and b3 are three blocksshown with their orientations.

The block b is then added into the set B and the triangle�b1b2b3 ∈ DTB is replaced by three triangles �bb2b3,�b1bb3 and �b1b2b. The orientation density D(x, y) isupdated using Eq. (10). The interpolation process continuestill the orientation density values in all the blocks in theforeground are larger than TD . Figs. 8(c) and (e) show theinterpolated orientation field and its corresponding orientationdensity map, respectively.

The orientation patch dictionary and context-based opti-mization [24] are then adopted to reconstruct the whole ori-entation field. The orientation field of blocks in B is regardedas the initial orientation field. For an initial orientation patch(of size 10 × 10 blocks), 6 reference orientation patches fromDO are retrieved based on the similarity between the initialorientation patch and the reference orientation patches. Theorientation similarity SO (,�) between an initial orientationpatch and an orientation patch � from DO is defined as

SO (,�) = (1 − λ)s(m,�m)+ λs(v,�v), (14)

where m and �m are the sets of orientations at the blockscontaining minutiae (shown in blue in Fig. 8(c)) of the twoorientation patches, v and �v are the sets of orientations atthe blocks without minutiae (shown in red in Fig. 8(c)) of thetwo orientation patches, λ is a weight parameter (λ = 2

3 inthis paper to preserve the orientations obtained from minutiaebetter) and s({αi }n

i=1, {βi }ni=1) is the similarity between two

orientation sets {α}ni=1 and {β}n

i=1, defined as

s({αi }ni=1, {βi }n

i=1) = 1

n

n∑

i=1

cos(αi − βi ). (15)

Let r Oi be the selected reference orientation patch candidate

for the initial orientation patch i . The selection of r Oi is

affected not only by its fitness to the orientation field patch ibut also by its neighboring selections. The optimal indicesvector rO = {r O

1 , rO2 , . . . , r

ONO

} of all the NO orientationpatches in the foreground can be selected by minimizing thefollowing energy function E(ro):

E O(rO ) = E Os (r

O)+ E Oc (r

O ), (16)

where E Os (r

O ) is the dissimilarity term and E Oc (r

O) is thecompatibility term. The dissimilarity term is determined by thedissimilarity between the set of initial foreground patches V O

and their corresponding selected reference orientation patches:

E Os (r

O) =∑

i∈V O

(1 − SO (i ,�i,r Oi)), (17)


Fig. 10. A comparison of orientation field reconstruction. (a) Minutiae shown on the gray-scale fingerprint image, (b) orientation field reconstructed by themethod in [8] and (c) orientation field reconstructed by the proposed method. Note that the proposed method provides better reconstruction results near thesingular points (marked as yellow circles).

where �i,r Oi

is the ri th candidate reference orientation patch

for initial orientation patch i and SO (·, ·) is defined in Eq. (14).The compatibility term is defined as

E Oc (r) =

∑

(i, j )∈N O

(1 − C O (�i,r Oi,� j,r O

j)), (18)

where N O is the set of four-connected neighboring orientationpatches. The compatibility C O (�i,r O

i,� j,r O

j) between two

neighboring reference orientation patches �i,r Oi

and � j,r Oj

is measured by their orientations φi,r Oi

and φ j,r Oj

in theoverlapping blocks, defined as

C O (�i,r Oi,� j,r O

j) = s(φi,r O

i, φ j,r O

j). (19)

The loopy belief propagation algorithm [24], which has beenshown to perform well on graphs with closed loops, is adoptedto find the optimal reference orientation patches.

The orientation field reconstructed by the orientation patchdictionary may also change the orientations in the blockscontaining minutiae. A modified Gaussian filtering is proposedto preserve the orientation around minutiae:

i) The orientations at the blocks with minutiae are replacedby the directions of minutiae (modulated by π).

ii) The cosine and sine components of the double valuesof the orientations at the blocks without minutiae aresmoothed using a Gaussian mask (with standard devia-tion value of 2).

iii) Repeat Step ii) 3 times.

Fig. 10 compares the reconstructed orientation field fromthe algorithm in [8] and the proposed algorithm. It showsthat the proposed algorithm is able to obtain better orientationapproximation, especially in the regions near singular points.This is achieved because of our use prior knowledge of localorientation pattern.

If the ridge frequency associated with minutiae is available,the Delaunay triangulation can be used to interpolate the ridgefrequency field. Suppose that B is the set of Nb blocks withminutiae and DTB is the Delaunay triangulation of B . The

ridge frequency fb at block b is interpolated by the triangle�b1b2b3 ∈ DTB covering b:

fb = d2d3 f1 + d1d3 f2 + d1d2 f3

d2d3 + d1d3 + d1d2, (20)

where fi denotes the ridge frequency of block bi which isobtained from the ridge frequency associated with the minutiacontained in block bi , di is the Euclidean distance betweenbi and b (1 ≤ i ≤ 3). The ridge frequency at the blocks thatare not in the convex hull of the block set B is estimatedas the median frequency value within the convex hull of theblock set B . Otherwise, a constant frequency value 0.12, assuggested in [8], is used for the whole image.

C. Fingerprint Reconstruction

The continuous phase patch dictionary is used to recon-struct fingerprint image patches based on the reconstructedorientation field and ridge frequency field in section III-B.Global optimization is then adopted to obtain the reconstructedfingerprint image.

1) Fingerprint Patch Reconstruction: For a patch p of size48 × 48 pixels in the initial image (only the reconstructedorientation field and ridge frequency field are available), itsorientation field θp with 3 × 3 blocks and average frequencyf p are obtained from the reconstructed orientation field andfrequency field. The closest subdictionary, among the 24 con-tinuous phase patch subdictionaries, is selected based on theorientation similarity (defined in Eq.(15)) between θp and theorientation patch centers in Fig. 6. A set of Np continuous

phase patches {ψ jC}Np

j=1 in the selected subdictionary areselected according to their similarity with θp and f p . Thesimilarity between an initial image patch and a continuousphase patch (with orientation field θ and average ridgefrequency f ) is defined as

SI ({θp, f p}, {θ, f }) = s(θp, θ) · e−( 1

f p− 1

f )2/(2σ 2

f ), (21)

where s(·, ·) is defined in (15) and σ f is a parameter control-ling the frequency similarity (σ f = 3 in this paper).


Fig. 11. Fingerprint patch reconstruction.

The minutiae can be added by combining the continuousphase patch and the spiral phase computed from the minutiaein a patch. Let M p = {m p

i = (x pi , y p

i , αpi )}

n pi=1 denote the

set of n p minutiae in the patch p, where (x pi , y p

i ) and α pi are

the coordinates and direction of the i th minutia, respectively.The polarity p j

i of the i th minutiae on the j th selectedcontinuous phase patch ψ j

C is determined by the differencebetween α

pi and its unwrapped pixel-wise orientation field

β j (xpi , y p

i ) which is obtained in III-A.2 as

p ji =

{1, if cos(α p

i − β j (xpi , y p

i )) > 0,

−1, if cos(α pi − β j (x

pi , y p

i )) ≤ 0.(22)

Then the spiral phase ψ jS of M p , corresponding to ψ j

C , canbe obtained by using Eq. (9). The j th phase ψ j with minutiaeis the combination of ψ j

S and ψj

C and the reconstructedfingerprint patch I j is cos(ψ j ). Fig. 11 illustrates this process.

2) Fingerprint Image Reconstruction: The fingerprint imagereconstruction can now be viewed as a combinatorial optimiza-tion problem similar to fingerprint orientation reconstructionin section III-B. For an initial fingerprint patch, a list offingerprint patch candidates can be constructed using theapproach in previous steps. The optimal candidates selectionr I = {r I

1 , rI2 , . . . , r

INI

} for all NI foreground initial fingerprintpatches is performed by minimizing the following energyfunction,

E I (rI ) = E Is (r

I )+ ωc E Ic (r

I ), (23)

where E Is (r

I ) is the dissimilarity term, E Ic (r

I ) is the compat-ibility term and ωc is the weight parameter. The dissimilar-ity term measures the dissimilarity of orientation field andfrequency field between an initial fingerprint patch and itsselected reconstructed fingerprint patch

E Is (r

I ) =∑

i∈V I

(1 − SI ({θi , fi }, {θi,r Ii, fi,r I

i})), (24)

where V I is the set of foreground fingerprint patches andSI (·, ·) is defined in Eq. (21). The compatibility C I (Ii,r I

i, I j,r I

j)

between two neighboring reconstructed fingerprint patchesIi,r I

iand I j,r I

jis measured by the difference of gray values

at overlapping pixels. Let {xi }ni=1 and {yi }n

i=1 denote the setof coordinates for Ii,r I

iand I j,r I

jat the n overlapping pixels,

respectively. The C I (Ii,r Ii, I j,r I

j) is computed as

C I (Ii,r Ii, I j,r I

j) = 1

n

n∑

i=1

(Ii,r Ii(xi )− I j,r I

j(yi ))

2. (25)

The compatibility term E Ic (r

I ) is defined as

E Ic (r

I ) =∑

(i, j )∈N I

(1 − C I (Ii,r Ii, I j,r I

j)), (26)

where N I is the set of four-connected neighboring patches.The fingerprint patch selection is performed via the loopybelief propagation algorithm [24].

In order to alleviate the blocking effect when composing thefingerprint image using the selection of the reconstructed fin-gerprint patches, a weighting strategy [25] is used. Fig. 12(a)shows a reconstructed fingerprint image and the minutiaedetected in its phase image. There are no missing minutiaein this example. However, there may be a few spuriousminutiae in the reconstructed fingerprints that are introducedin the overlapping regions because suboptimal selection maybe obtained in minimizing the energy function (23).

D. Fingerprint Image Refinement

We adopt the global AM-FM model to remove the spu-rious minutiae from the reconstructed image I . The block-wise orientation field is expanded to pixel-wise orientationfield. The orientation unwrapping method proposed in [9] isadopted to obtain the unwrapped orientation field Ou . Fororientation field with singular points, there are horizontaldiscontinuity segments, which will introduce discontinuity inthe unwrapped orientation field and then in the phase image.A discontinuity segment D(x1, x2, y) from pixel (x1, y) topixel (x2, y) can be identified using the following two con-ditions [9]: 1) |Ou(x, y) − Ou(x, y − 1)| ≥ π/2 whenx ∈ [x1, x2], and 2) |Ou(x, y) − Ou(x, y − 1)| < π/2when x ∈ [x1, x2]. The position of a discontinuity segmentD(x1, x2, y = a) can be changed to the other side byadding sign(Ou(x1, a)− Ou(x1, a − 1))π for all rows y < aor subtracting sign(Ou(x1, a) − Ou(x1, a − 1))π for allrows y ≥ a.

In order to alleviate the effect of the discontinuity, the i th(i ≥ 2) segment (according to the y coordinate in increasingorder) is changed, if necessary, to reduce the overlappingx coordinates with (i − 1)th segment. We still use Ou todenote the optimized unwrapped orientation field. The phaseimage ψ of I is obtained by applying demodulation with theunwrapped orientation field Ou . Spurious minutiae (shouldnot overlap with the input minutiae and the discontinuitysegments), which are detected in ψ using the method insection II, can be removed by subtracting the spirals formed bythe spurious minutiae. However, due to the discontinuity in thephase image, spirals are also introduced at the discontinuitysegments. The spirals at the i th discontinuity segment areremoved using the following two steps:

i) A complementary unwrapped orientation field Oiu is

computed by (1) changing the i th discontinuity segmentto the other side by adding or subtracting π and (2)


Fig. 12. Illustration of spurious minutiae removal. (a) Fingerprint reconstructed using continuous phase patch dictionary, where red squares refer to inputminutiae and blue circles refer to spurious minutiae, (b) unwrapped orientation field Ou , (c) and (d) complementary unwrapped orientation fields O1

u and O2u ,

respectively, (e) cos(ψ0), where ψ0 is the phase image after removing spurious minutiae, (f) cos(ψ1), where ψ1 is the phase image after removing spiralsaround the top discontinuity segment, (g) cos(ψ2), where ψ2 is the phase image after removing spirals around the discontinuity segment in the lower leftregion of the image, and (h) the final reconstruction image. The red squares in (e) and (f) are spirals around discontinuity segments.

changing other discontinuity segments, if necessary,to reduce the overlapping x coordinates with the i thdiscontinuity segment.

ii) cos(ψi−1), where ψi−1 is the phase image obtained byremoving the spirals around the (i − 1)th segment, isdemodulated to get ψi with Oi

u . The spirals around thei th segment in ψi are detected and removed.

After all discontinuity segments have been considered,Gabor filtering is used to smooth the fingerprint region aroundthese discontinuity segments, and demodulation is used againto obtain the final phase image and then final reconstruction.Fig. 12 illustrates this process, where Fig. 12(h) shows removalof the discontinuity.

IV. EXPERIMENTAL RESULTS

The proposed fingerprint reconstruction algorithm is eval-uated on two plain fingerprint databases (FVC2002 DB1_Aand FVC2002 DB2_A), each of which contains 800 plainfingerprint images from 100 fingers, and one rolled fingerprintdatabase (NIST SD4) which contains 4,000 rolled finger-print images from 2,000 fingers (for each finger there aretwo impressions: a file fingerprint and a search fingerprint).Verifinger SDK 6.3 [12] is used for minutiae extraction andfingerprint matching. The minutiae template includes coordi-nates (x, y), direction (θ) and ridge frequency ( f ) for eachminutia point. For each fingerprint minutiae template, wereconstruct a fingerprint image using the proposed algorithmbased on the following two types of inputs: 1) Minutiae:minutiae coordinates, minutiae directions and a fixed ridge fre-quency, and 2) Minutiae + Frequency: minutiae coordinates,

minutiae directions and ridge frequency around each minutiae.The two reconstructed images for each template are com-pared with two other state-of-the-art approaches proposed byFeng and Jain [8] and Li and Kot [9]. The codes for [8] and [9]were provided by the authors. Fig. 13 shows somereconstructed fingerprint images from different algorithms.The reconstruction performance is evaluated in terms ofreconstructed minutiae2 accuracy with respect to inputminutiae and matching performance in both verificationand identification modes. The algorithm was implementedin MATLAB and run on a machine with Intel Core i7 Q7201.60GHz, 4GB RAM and 64-bit Windows 7 operating system.The average computation time for FVC2002 DB1, FVC200DB2 and NIST SD4 is 20.55, 26.93 and 31.41 seconds,respectively, after loading all the dictionaries.

A. Reconstructed Minutiae Accuracy

Minutiae play a critical role in fingerprint recognition.Missing and spurious minutiae in the reconstructed fingerprintimage may deteriorate the matching performance betweenthe reconstructed image and the original fingerprint image.An input minutia p (input to the reconstruction algorithm)is regarded as missing if there are no minutiae in thereconstructed fingerprint within 10 pixels and 30 degrees ofp’s location and direction. A minutia q in the reconstructedfingerprint is regarded as spurious if there are no inputminutiae within 10 pixels and 30 degrees of q’s location anddirection. The reconstructed minutiae accuracy is evaluated

2The reconstructed minutiae refer to the minutiae extracted by VerifingerSDK 6.3 from the reconstructed fingerprint image.


Fig. 13. Examples of reconstructed fingerprint images. (a) Original fingerprint images (f1519.bmp (top, NFIQ3=3) and f0669 (bottom, NFIQ=4) fromNIST SD4), (b) reconstructed fingerprint images by the algorithm in [8], (c) reconstructed fingerprint images by the algorithm in [9], (d) reconstructedfingerprint images by the proposed algorithm with a fixed ridge frequency and (e) reconstructed fingerprint images by the proposed algorithm with ridgefrequency around each minutiae. The true mate of the top fingerprint in (a) is retrieved at rank 64, 18, 2 and 1 for (b), (c), (d) and (e), respectively, and thetrue mate of the bottom fingerprint in (a) is retrieved at rank 1,470, 335, 182 and 1 for (b), (c), (d) and (e), respectively, in type-II attack.

TABLE II

COMPARISON OF AVERAGE MISSING MINUTIAE RATE (MMR) (%)

TABLE III

COMPARISON OF AVERAGE SPURIOUS MINUTIAE RATE (SMR) (%)

based on two measures: Missing Minutiae Rate (MMR) andSpurious Minutiae Rate (SMR), where MMR refers to thepercentage of missing minutiae and SMR refers to the per-centage of spurious minutiae. As shown in Tables II and III,the proposed reconstruction algorithm outperforms two state-of-the-art algorithms, [8] and [9], in terms of MMR andis comparable with [9] in terms of SMR for all threedatabases.

B. Fingerprint Verification

The verification experiments are conducted on theFVC2002 DB1_A and FVC2002 DB2_A databases. In orderto evaluate the verification performance, type-I and type-IIattacks, proposed in [8], are considered. In type-I attack,each reconstructed fingerprint is matched against the sameimpression from which the minutiae template was extracted,

3NFIQ [20] assigns a quality value of 1 (highest quality) - 5 (lowest quality)to a fingerprint image.

while in type-II attack, each reconstructed fingerprint ismatched against the other 7 impressions of the same finger,which is more challenging than type-I attack. Therefore,there are 800 type-I attacks and 5,600 type-II attacks foreach database that can be launched against the fingerprintverification system. The match scores from type-I or type-IIattacks are regarded as genuine match scores. A total numberof 4,950 imposter match scores are obtained by crossmatching the first impression of each finger following theFVC2002 protocol [26]. The thresholds at different falseaccept rate (FAR) are calculated based on the imposter matchscores. The Receiver Operating Characteristic (ROC) curvesof the four reconstructions for each image in FVC2002DB1_A and FVC2002 DB2_A are plotted in Figs. 14 and 15,respectively. The matching performance of the proposedreconstruction algorithm is significantly better than that ofthe two state-of-the-art reconstruction algorithms. In otherwords, given a minutiae template, the proposed reconstructionalgorithm is better than the other two algorithms [8], [9] interms of preserving the original fingerprint characteristics.

In the type-I attack, the ROC curves of the proposedreconstruction are quite close to the original image on bothdatabases. With a fixed ridge frequency, the true acceptrates (TAR) at a FAR=0.01% of the proposed reconstructionare 99.38% and 99.88% on FVC2002 DB1_A and FVC2002DB2_A, respectively. In the type-II attack, TAR at the sameFAR of the proposed reconstruction is at least 24% higheron FVC2002 DB1_A and at least 19% higher on FVC2002DB2_A than the methods in [8] and [9], respectively.

Ridge frequency is an important feature that helps improvethe reconstruction performance. Given the ridge frequencyaround each minutia, the TAR (at FAR=0.01% ) of type-Iattack based on our reconstructed fingerprints is furtherimproved to 100% on both FVC2002 DB1_A and FVC2002DB2_A. The TAR (at FAR=0.01% ) of type-II attack is further


Fig. 14. ROC curves of different reconstruction algorithms on FVC2002 DB1_A under (a) type-I attack and (b) type-II attack.

Fig. 15. ROC curves of different reconstruction algorithms on FVC2002 DB2_A under (a) type-I attack and (b) type-II attack.

Fig. 16. CMC curves of different reconstruction algorithms on NIST SD4 under (a) type-I attack and (b) type-II attack.

improved to 85.23% and 90.29% on FVC2002 DB1_A andFVC2002 DB2_A, respectively.

C. Fingerprint Identification

The minutiae templates of 2,000 file fingerprintsfrom NIST SD4 are used to reconstruct fingerprints for

fingerprint identification experiments. Each reconstructedfingerprint is matched against 2,000 file fingerprints as thegallery to obtain 2,000 type-I attacks and against 2,000search fingerprints as the gallery to obtain 2,000 type-IIattacks. The Cumulative Match Characteristic (CMC) curvesof type-I and type-II attacks for four reconstructions, as wellas original fingerprints, are compared in Fig. 16. Similar to


TABLE IV

RANK-1 IDENTIFICATION PERFORMANCE OF TYPE-I ATTACK

ON NIST SD4 FOR DIFFERENT NFIQ VALUES (%)

TABLE V

RANK-1 IDENTIFICATION PERFORMANCE OF TYPE-II ATTACK

ON NIST SD4 FOR DIFFERENT NFIQ VALUES (%)

the verification experiments, the identification performance oftype-I attack is very high. The rank-1 identification rate of theproposed algorithm with a fixed ridge frequency is 99.05%.When the ridge frequency around minutiae is utilized inreconstruction, the rank-1 identification rate is improved to99.95%, which indicates that the features in the reconstructedfingerprint images are very close to the features in the originalimages.

In terms of type-II attack, the rank-1 identification rate ofthe proposed algorithm with a fixed ridge frequency is 71.00%,which is 28.20% higher than the algorithm in [9] and 18.50%higher than the algorithm in [8]. With the ridge frequencyaround minutiae, the rank-1 identification rate is improvedto 82.45%. The comparative results confirm that the proposedreconstruction algorithm performs better than the two state-of-the-art reconstruction algorithms of [8] and [9].

We also investigate the attack performance (both type-I andtype-II attacks) of the reconstructed fingerprint images withrespect to the quality of fingerprints from which minutiaetemplates are extracted. NFIQ [20] is used as a quality index.Tables IV and V compare the identification performance ofthe three reconstruction algorithms for type-I and type-IIattacks, respectively. These results show that, as expected,the identification performance of all three algorithms dropswhen fingerprint quality decreases, especially for type-IIattack.

Fig. 13 compares the four reconstructions of a fingerprintimage shown in Fig. 13(a). Given the prior knowledge oforientation pattern (i.e., orientation patch dictionary), the ori-entation field reconstructed from the proposed algorithm isbetter than the method proposed in [8]; the singular pointsobtained from the proposed algorithm are very close to theoriginal ones. Although a fixed ridge frequency was usedin [9], variations in ridge frequency are visible in the recon-structed image shown in Fig. 13(c). As shown in section II,the main reason is that the ridge structure does change after

editing the minutiae (removing or adding minutiae). Whilethe ridge frequency in Fig. 13(b) is preserved well, thereis a noticeable blocking effect. Based on these experimentalresults, we conclude that the proposed phase patch dictionarybased reconstruction algorithm is able to preserve the ridgestructure compared to published methods.

V. CONCLUSIONS AND FUTURE WORK

The goal of fingerprint reconstruction is to reproduce theoriginal fingerprint image from an input minutiae set. Thereare essentially three main reasons for studying the problemof fingerprint image reconstruction from a given minutiae set:(i) to demonstrate the need for securing minutiae template,(ii) to improve the interoperability of fingerprint templatesgenerated by different combinations of sensors and algorithms,(iii) to improve fingerprint synthesis. Despite a significantimprovement in the performance of reconstruction algorithmsover the past ten years, there is still a discrepancy between thereconstructed fingerprint image and original fingerprint image(from which the minutiae template was extracted) in termsof matching performance. In this paper, we propose a recon-struction algorithm that utilizes prior knowledge of finger-print ridge structure to improve the reconstructed fingerprintimage. The prior knowledge is represented in terms of twokinds of dictionaries, orientation patch and continuous phasepatch dictionaries. The orientation patch dictionary is used toreconstruct the orientation field from the given minutiae set,while the continuous phase patch dictionary is used to recon-struct the ridge pattern. Experimental results on three publicdomain fingerprint databases (FVC2002 DB1_A, FVC2002DB2_A and NIST SD4) show that the proposed reconstruc-tion algorithm outperforms two state-of-the-art reconstructionalgorithms [8] and [9] in terms of reconstructed minutiaeaccuracy and matching performance for both type-I and type-IIattacks.

Although the reconstructed fingerprints, as shown in Fig. 13,are very close to the original fingerprints from which theminutiae were extracted in terms of orientation field, ridgefrequency field and minutiae distribution, it is still difficultto fool a human expert because the reconstructed finger-prints are ideal fingerprints (without any noise) and have thesynthetic appearance. Future work will investigate to makethe reconstructed fingerprints more realistic. The proposedmethod for orientation field reconstruction only considers thelocal orientation pattern. The use of global orientation priorknowledge as well as singular points may further improvethe ridge orientation reconstruction. The ridge frequency fieldused in this paper can be either a fixed priori or reconstructedfrom the ridge frequency around minutiae. Future work willinvestigate frequency field reconstruction directly from theminutiae position and direction.

ACKNOWLEDGMENT

The authors would like to thank Prof. Alex C. Kot andSheng Li for providing us their reconstruction code for ourcomparative analysis, and Sunpreet S. Arora for conductingsome of the initial experiments.


REFERENCES

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Kai Cao received the Ph.D. degree from the KeyLaboratory of Complex Systems and IntelligenceScience, Institute of Automation, Chinese Academyof Sciences, Beijing, China, in 2010. He is currentlya Post-Doctoral Fellow with the Department ofComputer Science and Engineering, Michigan StateUniversity, East Lansing, MI, USA. He is also withXidian University, Xi’an, China, as an AssociateProfessor. His research interests include biometricrecognition, image processing, and machine learn-ing.

Anil K. Jain is currently a University DistinguishedProfessor with the Department of Computer Sci-ence and Engineering with Michigan State Univer-sity, East Lansing, MI, USA. His research interestsinclude pattern recognition, biometric authentica-tion, and computer vision. He served as the Editor-in-Chief of the IEEE TRANSACTIONS ON PAT-TERN ANALYSIS AND MACHINE INTELLIGENCE

(1991–1994). He holds eight patents in fingerprintmatching and face recognition. He has authored anumber of books, including Introduction to Biomet-

rics (2011), Handbook of Face Recognition (2011), Handbook of FingerprintRecognition (2009), Handbook of Biometrics (2009), Handbook of Multibio-metrics (2006), BIOMETRICS: Personal Identification in Networked Society(1999), and Algorithms for Clustering Data (1988). He served as a memberof the Defense Science Board, and the National Academies Committees onWhither Biometrics and Improvised Explosive Devices. He was a recipientof the IEEE TRANSACTIONS ON NEURAL NETWORKS Outstanding PaperAward (1996) and the Pattern Recognition Society Best Paper Awards (1987,1991, and 2005). He is a fellow of the American Association for the Advance-ment of Science, the Association for Computing Machinery, the InternationalAssociation for Pattern Recognition (IAPR), and the International Society forOptics and Photonics. He has received the Fulbright Award, the GuggenheimAward, the Alexander von Humboldt Award, the IEEE Computer SocietyTechnical Achievement Award, the IEEE Wallace McDowell Award, theInternational Conference on Data Mining Research Contributions Award, andthe IAPR King-Sun Fu Award.

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