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Modeling and Analysis of Local ComprehensiveMinutia Relation for Fingerprint Matching

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Xiaoguang He, Jie Tian, Senior Member, IEEE, Liang Li, Yuliang He, and Xin Yang3

Abstract—This paper introduces a robust fingerprint matching4scheme based on the comprehensive minutia and the binary re-5lation between minutiae. In the method, a fingerprint is repre-6sented as a graph, of which the comprehensive minutiae act as7the vertex set and the local binary minutia relations provide the8edge set. Then, the transformation-invariant and transformation-9variant features are extracted from the binary relation. The10transformation-invariant features are suitable to estimate the11local matching probability, whereas the transformation-variant12features are used to model the fingerprint rotation transforma-13tion with the adaptive Parzen window. Finally, the fingerprint14matching is conducted with the variable bounded box method15and iterative strategy. The experiments demonstrate that the pro-16posed scheme is effective and robust in fingerprint alignment and17matching.18

Index Terms—Adaptive Parzen window, binary minutia rela-19tion, fingerprint identification, transformation-invariant feature,20transformation-variant feature.21

I. INTRODUCTION22

A T PRESENT, fingerprint identification is much more re-23

liable than most other biometric identification methods24

such as signature, face, and speech [1]. Various algorithms25

and techniques have been developed rapidly for fingerprint26

identification systems in the past decade. In fact, a fingerprint is27

the identity card that people carry for a lifetime. The classical28

fingerprint identification was applied in security systems like29

prison and criminal identification [1]. Recently, with the devel-30

opment of the technology, it is increasingly used for civilian31

daily life, such as access control, financial security, verification32

of firearm purchaser [2], etc.33

A fingerprint is a pattern of ridges and valleys on skin34

surface. The uniqueness of a fingerprint can be determined35

with an overall pattern of ridges and valleys as well as local36

ridge anomalies, such as ridge endings and bifurcations, i.e.,37

minutiae. Many experts have designed fingerprint represen-38

tation schemes under the strong assumption that the input39

Manuscript received April 29, 2006; revised October 10, 2006. This workwas supported in part by the Project of National Science Foundation for Dis-tinguished Young Scholars of China under Grant 60225008, by the Key Projectof National Natural Science Foundation of China under Grants 60332010 and60575007, by the Project for Young Scientists’ Foundation of National NaturalScience of China under Grant 60303022, and by the Project of Natural ScienceFoundation of Beijing under Grant 4052026. This paper was recommended byAssociate Editor N. Ratha.

The authors are with the Key Laboratory of Complex Systems andIntelligence Science, Institute of Automation, Chinese Academy of Sci-ences, Beijing 100080, China (e-mail: xiaoguang.he@ia.ac.cn; tian@ieee.org;Liang.Li@ia.ac.cn; yuliang.he@ia.ac.cn; xin.yang@ia.ac.cn).

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

Digital Object Identifier 10.1109/TSMCB.2006.890285

fingerprint and template fingerprint are acquired by the same 40

sensor. Therefore, those schemes usually characterize the same 41

intensity range and admit a certain type of noise. In current 42

years, techniques [3]–[8] are developed to recover geometric 43

distortion and misalignment of fingerprints. However, these 44

methods are time and memory consuming since they usually 45

align all minutiae one by one with the local transformation 46

information. 47

In this paper, a robust fingerprint matching scheme is de- 48

signed to explore comprehensive information of minutiae and 49

ridges and the relations between minutiae. The method intro- 50

duces a graph in fingerprint representation. In the graph, the 51

vertex set is the comprehensive minutiae, and the edge set is 52

the local binary minutia structures. Local structure is subject 53

to the positional constraints, and it helps to represent a local 54

fingerprint region and prevent false matching caused by insuffi- 55

cient minutiae. Compared with the ternary minutia structure as 56

other researchers adopted [3]–[8], [19], binary structure makes 57

a proper tradeoff between the performance and computational 58

expense. The proposed feature representation is inexpensive in 59

time and memory cost. 60

Two types of features are extracted from the binary compre- 61

hensive minutia structure. One is the transformation-invariant 62

features, which are used for the local matching probabil- 63

ity measurement between local structures. Another is the 64

transformation-variant features, and they are used to model 65

the rotation transformation with the adaptive Parzen window, 66

which statistically explores the transformation information 67

from local structures and admits the periodic property of ro- 68

tation angle. Finally, the variable bounded box method [9] 69

and iterative strategy are used for rechecking local matching 70

probability. Both the variable bounded box method and iterative 71

strategy globally reduce the influence of deformation on match- 72

ing. Experimental results on the database of the International 73

Fingerprint Verification Competition (FVC) 2002 [17] have 74

proven that our technique is efficient in terms of fingerprint 75

alignment and matching. 76

The rest of this paper is organized as follows: Section II in- 77

troduces and analyses the representation of fingerprint feature. 78

Section III describes the measurement of transformation para- 79

meter. Section IV presents the scheme of fingerprint matching. 80

Section V provides the experimental results. The final section 81

concludes our work with future perspectives. 82

II. REPRESENTATION OF FINGERPRINT FEATURE 83

Many popular fingerprint representation schemes, based on 84

image analysis, can be classified into three types. The first type 85

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2 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART B: CYBERNETICS, VOL. 37, NO. 4, AUGUST 2007

is the minutia-based technologies, which are predominantly86

dependent on local landmarks [1], [3], [10], i.e., ridge endings87

and bifurcates. This is widely used for its time saving and less88

memory consumption. However, a minutia set cannot charac-89

terize overall patterns of a fingerprint, and it is hard to further90

improve the performance. The second type is the exclusive91

global feature-based approaches [11]. With these methods,92

the holistic patterns of fingerprint texture are used to calcu-93

late the maximum mutual information between two finger-94

prints. The approaches are employed not only in identification95

[11], [12] but also in indexing [13], [14]. However, these96

methods require the exact determination of central point, and it97

is difficult to deal with distortion in the fingerprints. Moreover,98

the exclusive global information-based method needs much99

memory to store a fingerprint template. The third type is100

technologies based on comprehensive feature [12], [15]. In101

these schemes, fingerprints are matched by fusing minutiae,102

local features, and global features with a hybrid method. Local103

features accelerate the alignment of the input minutia pat-104

terns in different sizes, and the global features are used to105

overcome the shortage of minutiae and local features in low-106

quality fingerprints. In addition, these methods may combine107

various technologies, such as bounding box method and mutual108

information method. These approaches are popular for their109

robust performance with acceptable memory expense in recent110

years. However, these methods are not omnipotent for some111

special conditions with large deformation.112

This paper introduces a comprehensive feature-based tech-113

nique with two novel aspects: 1) A fingerprint pattern is114

characterized by the comprehensive minutiae and the binary115

relations between minutiae; and 2) as an improvement of our116

previous work [9] in alignment, the adaptive Parzen window is117

proposed to model the relationship between the local matching118

probability and the fingerprint transformation.119

A. Comprehensive Minutia120

A poor-quality fingerprint may be too dry or too wet, or the121

foreground area may be narrow with insufficient reliable minu-122

tiae. In some cases, even two fingerprints from the same finger123

fail to match for lack of common minutiae. Therefore, associ-124

ated ridge information is combined to improve the fingerprint125

representation. As demonstrated in Fig. 1, a comprehensive126

minutia Mn includes a minutia and the associated ridge feature,127

formally128

Mn = {xn, yn, θn, βn} ∪ {ϕnm|m = 1, 2, . . . , L} (1)

where (xn, yn) is the coordinate, and θn is the tangent direction.129

βn is the local gray variance of an area centered on (xn, yn).130

ϕnm is the direction from (xn, yn) to Rnm, which is a point131

sampled on the ridge derived from the minutia. {ϕnm|m =132

1, 2, . . . , L} embodies the information of the ridge curvature133

and the local shape, and L is the number of sampled points on134

the associated ridge. Here, the type information of the minutiae,135

e.g., ending or bifurcate, is not employed since it usually makes136

false matching in our experiments.137

Fig. 1. Comprehensive minutiae and binary comprehensive minutia structure.

In this paper, the comprehensive minutia set of a finger- 138

print F is denoted as MF = {Mn|n = 1, 2, . . . ,m(F )}, where 139

m(F ) is the minutia number of F . MF contains the compre- 140

hensive information of all minutiae. 141

B. Binary Comprehensive Minutia Structure 142

In fingerprint representation, minutia is a unary property. 143

There is the binary or higher order relation that conveys the 144

contextual constraints, which are crucial in fingerprint match- 145

ing. In this algorithm, binary structure between minutiae is 146

introduced. For each pair of comprehensive minutia points 147

Mi and Mj , where Mi,Mj ∈ MF and Mi �= Mj , if their 148

Euclidean distance d(Mi,Mj) =√

(xi − xj)2 + (yi − yj)2 149

satisfies dl ≤ d(Mi,Mj) ≤ dh, then Mi and Mj are connected 150

as a local binary structure Ek, formally 151

Ek = {sk, ek} ∪ {υk, θsk, θ

ek,Ψ

sk,Ψ

ek} ∪ {dk, β

sk, β

ek, α

sk, α

ek}(2)

where sk and ek denote the serial numbers of the binary minu- 152

tiae in minutia set MF . As shown in Fig. 1, sk = i and ek = j. 153

{vk, θsk, θ

ek,Ψ

sk,Ψ

ek} stands for the transformation-variant fea- 154

tures; it describes the information that is affected by fin- 155

gerprint transformation, where vk = arctan((yi − yj)/(xi − 156

xj)), θsk = θi, θe

k = θj , Ψsk = {ϕim|m = 1, 2, . . . , L}, and 157

Ψek = {ϕjm|m = 1, 2, . . . , L}. {dk, β

sk, β

ek, α

sk, α

ek} is the 158

transformation-invariant features; it represents the unchanged 159

information under transformation, where dk = d(Mi,Mj), 160

βsk = βi, βe

k = βj , αsk = θi − vk, and αe

k = θj − vk. 161

The binary comprehensive minutia structure set is formally 162

EF = {Ek|k = 1, 2, . . . , e(F )}, where e(F ) is the number of 163

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HE et al.: MODELING AND ANALYSIS OF COMPREHENSIVE MINUTIA RELATION FOR FINGERPRINT MATCHING 3

structures. e(F ) is much smaller than m(F )(m(F ) − 1)/2164

because the Euclidean distance d of most minutia pair do not165

satisfy dl ≤ d ≤ dh. The size of EF can be controlled by166

modifying the values of dl and dh. The minutia set MF and167

the binary structure set EF represent fingerprint F as a graph168

GF = (MF , EF ), where MF acts as the vertex set, and EF169

provides the edge set. GF explores the first- and second-order170

minutia relations of fingerprint F , and the higher order relations171

behave as the connected subgraphs of GF .172

III. MEASUREMENT OF TRANSFORMATION PARAMETER173

It is important to align the input minutiae with the template174

during matching. The alignment generally includes rotation,175

translation, and shearing. This matching algorithm is designed176

assuming that the input and template fingerprints are captured177

by the same device in the same condition but with little scaling178

deformation. Since the fingerprint matching performs well in179

polar coordinate, the translation of the input features to the180

template is not concerned if the central point is set in advance.181

One of the most important tasks in alignment is to find the182

optimal rotation parameter.183

A. Matching Probability of Binary Comprehensive184

Minutia Structure185

Since the transformation-invariant features remain un-186

changed under fingerprint transformation, they are ideal for187

the matching probability estimation of local comprehensive188

minutia structures. For each pair of local structures Ei and Et,189

where Ei ∈ EI , Et ∈ ET , and EI and ET denote the local190

structure sets of input fingerprint I and template fingerprint T ,191

respectively, then similarity Sit between Ei and Et is estimated,192

formally193

Sit =

{0, eit > ε and e′it > ε

1 − min(eit,e′it)

ε , otherwise(3)

eit =((di − dt)2 + (βs

i − βst )2 + (βe

i − βet )2

+ (αsi − αs

t )2 + (αe

i − αet )

2) 1

2(4)

e′it =((di − dt)2 + (βs

i − βet )2 + (βe

i − βst )2

+ (αsi − αe

t − 180)2 + (αei − αs

t − 180)2) 1

2(5)

where ε is the matching threshold of transformation-invariant194

feature. If Sit = 0, Mi and Mt are not matched; otherwise195

they are. The more similar the Ei and Et are, the larger the196

Sit is. However, two local structures, which are not from the197

same location of the same fingerprint, can be false matched198

accidentally. The false-matching cases can be excluded with199

the variable bounded box method, and the detail is presented in200

Section IV. All of the matching probability values construct a201

similarity matrix S = [Sit]1≤i≤e(I),1≤t≤e(T ), which represents202

the local comprehensive similarity between fingerprints I and203

T . In the next section, the rotation parameter is statistically204

analyzed with S, and in Section IV, S is used for adjusting 205

translation transformation with iterative strategy. 206

B. Adaptive Parzen Window for Modeling Rotation 207

Transformation 208

The transformation-variant feature is useful for the rotation 209

parameter estimation since it reflects the rotation transforma- 210

tion of a fingerprint. The local rotation parameter between local 211

structures Ei and Et is denoted as δit, and it is estimated as 212

follows: 213

δit =∆υit + ∆θit + ∆Ψit

3(6)

∆υit = υi − υt (7)

∆θit =θs

i + θei − θs

t − θet

2(8)

∆Ψit =1

2L((ϕsi1 + ϕsi2 + · · · + ϕsiL)

+ (ϕei1 + ϕei2 + · · · + ϕeiL)

− (ϕst1 + ϕst2 + · · · + ϕstL)

−(ϕet1 + ϕet2 + · · · + ϕetL)) . (9)

Then, Parzen Window is an effective method for estimating 214

the probability density. When Gaussian function is chosen as 215

the smooth kernel, the probability density f(δ) of rotation 216

parameters δ is formally 217

f(δ,∆x,∆y) =

∑1≤i≤e(I)

∑1≤t≤e(T )

K(δ − δit)

e(I) · e(T )(10)

K(δ − δit) =1√

2πσ2exp

(− (δ−δit)

2

2σ2

)(11)

where σ controls the size of the Parzen window. However, 218

the Parzen window is not appropriate for the estimation since 219

f(δ) is a periodic function and the similarity information of 220

local binary structures is very important for the estimation. 221

Therefore, the adaptive Parzen window is proposed as follows: 222

f(δ) =

∑1≤i≤e(I)

∑1≤t≤e(T )

K(δ − δit)

e(I) · e(T )(12)

K(δ − δit)=

+∞∑

n=−∞1√

2πσ2it

exp

(− (δ−δit+360n)2

2σ2it

), Sit �= 0

1360 , Sit = 0

(13)

where σ2it = 1/2π(aSit)2, and a is an experiential value. 223

Compared with Parzen window, the window size of every 224

sample’s smooth kernel is flexible, and it is determined by 225

the corresponding similarity. Given a rotation angle δit of a 226

local structure, the probability density function conditioned 227

on δit is formally f(δ|δit) = exp(−(δ − δit)2/2σ2it)/

√2πσ2

it. 228

The more similar the local structures are, the more crucial the 229

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corresponding rotation angle estimation is. When it is assumed230

that the probabilistic certainty is in proportion to the sim-231

ilarity, i.e., f(δ|δit)|δ=δit= 1/

√2πσ2

it = a · Sit, then σ2it =232

1/(2π(aSit)2). The larger the Sit is, the sharper the f(δ|δit) is.233

In other words, the larger the similarity of two local structures234

is, the more definite the fingerprint rotation angle equals to δit.235

When two local structures are not matched, i.e., Sit = 0, the236

corresponding angle δit cannot make any contribution to the237

final estimation. In this case, f(δ|δit) = 1/360. In (13), it does238

not need to sum the periodic responses from −∞ to +∞; the239

sum from −3 to +3 can yield a satisfying approach.240

To accurately calculate the transformation parameters,241

a confidence interval [δmax − σδ, δmax + σδ] is defined,242

where δmax satisfies f(δmax) = maxδ{f(δ)}, and σδ satis-243

fies σ2δ =

∑it(Sit · (δit − δ)2)/

∑it Sit, where δ =

∑it(Sit ·244

δit)/∑

it Sit. The confidence interval can reduce the effect245

of false matching of local binary structures because the false-246

matching contribution to f(δ) mainly concentrates on the out-247

side of the confidence interval. Moreover, as denoted in (14),248

it is effective to use the barycenter of δ on the interval as the249

optimal estimation δopt rather than δmax, which is sensitive to250

noises, i.e.,251

δopt =

δmax+σδ∫δmax−σδ

δ · f(δ)dδ. (14)

IV. FINGERPRINT MATCHING252

The task of fingerprint matching is to obtain the minimal253

difference between input fingerprint I and template T by254

an optimal alignment. In this paper, however, deformation in255

fingerprints may bring false matching of local structures and256

therefore affects the final result. Thus, the global fingerprint257

matching is essential after the coarse local matching if the258

transformation model is known. In this process, the variable259

bounded box [9] is used to recheck all local matched structures260

to reduce the influence of deformation in fingerprints. The261

matching steps are listed as follows:262

Step 1. For each comprehensive minutia pair Mi and Mt,263

where Mi ∈ M I and Mt ∈ MT , calculate the con-264

nected subgraph similarity Sit, formally265

Sit =∑

n∈RI(n)

∑m∈RT (m)

Snm (15)

where RI(n) = {k|Ek ∈ EI , sk = n, or ek = n},266

and RT (m) = {k|Ek ∈ ET , sk = m, or ek = m}.267

Sit is the similarity between the starlike subgraph268

centered at Mi in GI and the starlike subgraph269

centered at Mt in GT .270

Step 2. Set the iterative number c = 1.271

Step 3. Find the cth maximum connected subgraph similar-272

ity Sci ct and define the corresponding minutia pair273

Mci and Mct as the reference minutia pair.274

Step 4. Use the reference minutiae Mci and Mct as the275

original points of the two graphs GI and GT , re-276

spectively. All minutiae are aligned into their new 277

polar systems and rotated with the statistical pa- 278

rameter δopt. 279

Step 5. For each pair of matched local structures Ei and 280

Et, where Ei ∈ EI , Et ∈ ET , and Sit �= 0, if the 281

two minutiae of Ei are located within the variable 282

bounded boxes [9] centered at the two minutiae of 283

Et, respectively, then Ei and Et are true match; 284

otherwise, they are false match. 285

Step 6. Calculate the similarities of two fingerprints I and T 286

as follows: 287

Sc = fGLM(nc;nth1, nth2)

·fGLM(mc;mth1,mth2) (16)

where nc and mc denote the number and the 288

similarity mean of true-matching local structures, 289

respectively; nth1, nth2, mth1, and mth2 are 290

four empirical values; and fGLM(x; th1, th2) is 291

borrowed from the nonlinear matching technique, 292

formally 293

fGLM(x; th1, th2) =

{ 0, x < th2x−th2

th1−th2 , th2 ≤ x < th11, th1 ≤ x.

(17)

Step 7. If c < C, go back to Step 3, where C is the maxi- 294

mum iterative number and C > 1. 295

Step 8. max1≤c<C{Sc} is the optimal matching value of 296

fingerprints I and T ; the larger the value is, the 297

more similar the two fingerprints are. If the optimal 298

matching value is more than the threshold Sth, the 299

two fingerprints are considered from the same finger. 300

In our method, the thresholds, i.e., ε and Sth, are estimated 301

with the iterated conditional mode, which selects threshold by 302

maximum entropy criterion [16]. The other empirical values, 303

such as C, L, dl, and dh, are predetermined with many experi- 304

ments on a training set. 305

V. EXPERIMENTS 306

We evaluate our algorithm on the fingerprint databases pro- 307

vided by FVC in 2002 [17], which are appropriate for test- 308

ing online fingerprint systems. Our experiments analyzed the 309

character of adaptive Parzen window, checked the validity of 310

rotation parameter estimation, and evaluated the final matching 311

performance. 312

A. Character of the Probability Density Curve 313

In this section, an experiment is performed to analyze the 314

character of the probability density curve estimated by the 315

adaptive Parzen window. The curve from the same fingerprint 316

pair has been compared with that from different fingerprint 317

pairs. 318

Three probability density curves are estimated, as shown in 319

Fig. 2. The first curve is calculated with images A and B, which 320

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Fig. 2. Probability density curves of rotation parameter estimated by the adaptive Parzen window.

Fig. 3. Probability density curves under different global rotation parameters.

are acquired from the same finger. The second is estimated321

with images C and D, which come from two similar fingers.322

The third is computed with images A and C, which come323

from two dissimilar fingers. Among these three experiments, 324

the curve of the same fingerprints is very sharp because there 325

are many true-match local structure pairs, which contribute to 326

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TABLE IADAPTIVE PARZEN WINDOW VERSUS PARZEN WINDOW AND HISTOGRAM

the density around the true rotation angle. The curve of similar327

fingerprints is more convex than that of dissimilar fingerprints328

since several local structure pairs with the same rotation angle329

are accidentally matched. The experiment shows that the more330

similar the two fingerprints are, the sharper their probability331

density curve is. It is meaningful for quick rejection of impostor332

in practical recognition application. A simple way is to use333

the curve’s peak value as the match value of two fingerprints,334

and if the value is under a threshold, the two fingerprints are335

considered from different fingers.336

B. Performance of the Adaptive Parzen Window337

Two experiments are conducted to evaluate the accuracy338

of the rotation parameter estimation with the adaptive Parzen339

window because the parameter plays a very important role in340

the fingerprint alignment and final matching.341

In the first experiment, a fingerprint is selected randomly342

from FVC2002 database as the template T . Then, the finger-343

print image is transformed with the angles 5◦, 10◦, and 15◦,344

respectively, as the input fingerprint I . Finally, the rotation345

parameter δk between T and I is estimated with the adaptive346

Parzen window, as illuminated in Fig. 3.347

In the experiment, the adaptive Parzen window method is348

compared with the original method and the histogram method.349

As shown in Table I, the average error of our algorithm is below350

half of the Parzen window, and it is about one-third of the351

histogram estimation.352

In the second experiment, a randomly selected fingerprint353

is rotated from 14◦ to −14◦, and in total, 29 estimations are354

conducted, as illuminated in Table II and Fig. 4. The mean and355

standard deviation of the absolute errors are 0.420 and 0.242,356

respectively.357

C. Matching Results on FVC2002358

To evaluate the overall matching performance of our method,359

a series of experiments are conducted over the four fingerprint360

databases of FVC2002. To judge whether the binary compre-361

hensive minutia structure is helpful, the method without the362

binary structure [9], i.e., Alg_1, is compared with the proposed363

method, named Alg_2. The receiving operating curves (ROCs)364

[18] illustrate the overall performance, as shown in Fig. 5.365

Among the four data sets, the fingerprint quality of DB2_a is366

the best, whereas that of DB3_a is the worst [17]. As indicated367

by the ROCs, the proposed method outperforms the algorithm368

that does not involve the binary comprehensive minutia struc-369

tures on FVC2002 databases. The equal error rates (EER) of370

our method are 1.6%, 0.9%, 3.4%, and 1.8% in DB1_a, DB2_a,371

TABLE IIESTIMATED PARAMETER δk VERSUS REAL PARAMETER K

Fig. 4. Trend of the precision of estimated rotation angles.

DB3_a, and DB4_a, respectively, and the results are better 372

than the best academic participants, i.e., PA24 and PA21, in 373

FVC2002 [17]. With Pentium-III 933-MHz central processing 374

unit, the average matching times are 0.37, 0.55, 0.27, and 375

0.29 s in the four databases, respectively, which are much faster 376

than the best industry participants, i.e., PA15 and PA27, in 377

FVC2002 [17]. The better performance is contributed by two 378

aspects: 1) Minutia is replaced by binary minutia structure, 379

and the structure has many effective features to represent a 380

fingerprint; 2) the rotation parameter is accurately measured 381

with the adaptive Parzen Window, and it makes satisfactory 382

fingerprint alignment. 383

Additional experiment is conducted to compare the perfor- 384

mance of binary minutia structure and ternary minutia structure 385

in DB1_a and DB4_a of FVC2002. As illuminated in Table III, 386

the EER of Chen’s algorithm [19] with ternary minutia struc- 387

ture is about two-thirds of the proposed method, but in terms 388

of the resource consumption, the proposed method is very 389

competitive. By employing the binary minutia structure, our 390

method makes a proper tradeoff between the performance and 391

computational expense. This is important for applications that 392

have limited computational resources. 393

VI. CONCLUSION AND FUTURE WORK 394

This paper introduces a robust fingerprint matching method 395

based on the comprehensive features of fingerprint, and it 396

employs two novel technologies: 1) The binary comprehen- 397

sive minutia structure with the transformation-variant and 398

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Fig. 5. ROCs of the matching experimental results over the four fingerprint databases of FVC2002.

TABLE IIIBINARY STRUCTURE VERSUS TERNARY STRUCTURE. MMC DENOTES

MAXIMUM MEMORY CONSUMPTION, AND ATS STANDS FOR AVERAGE

TEMPLATE SIZE

transformation-invariant features is implemented to provide399

a comprehensive representation of fingerprint. Meanwhile, it400

results in a graph representation of fingerprint. 2) The adaptive401

Parzen window is proposed to measure the transformation para-402

meter. Compared with the traditional one, the adaptive Parzen403

window admits the periodic property, and it is more accurate404

by exploring the similarity information of local structure pairs.405

Moreover, it is more robust and needs fewer samples than the406

simple histogram estimation. By the way, the probability den-407

sity curve, which is estimated by the adaptive Parzen window,408

shows the potential ability for fast impostor rejection.409

Our method is based on the assumption that input fingerprint410

and the template are captured from the same sensor. In the case411

of different modal fingerprints [20], transformation invariants412

and variants of local structures will become invalid. Therefore,413

we will investigate the technique that employs a multiscale414

search strategy to address the issue. In addition, global pat-415

tern and features, as well as a hybrid matching technique,416

will be investigated to minimize false matching, which occa-417

sionally occurs with large deformation and very poor quality418

fingerprints.419

ACKNOWLEDGMENT 420

The authors would like to thank Dr. Y. He for his grand 421

contribution and crucial advice on this paper, as well as 422

Dr. Y. Liu for revising the English. 423

REFERENCES 424

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Xiaoguang He received the B.S. degree from the481Special Class for the Gifted Young, University of482Science and Technology of China, Beijing, China,483in 2002. He is currently working toward the Ph.D.484degree at the Key Laboratory of Complex Systems485and Intelligence Science, Institute of Automation,486Chinese Academy of Sciences, Beijing.487

His research interests include pattern recognition,488machine learning, and image processing and their489applications in biometrics.490

Jie Tian (M’03–SM’03) received the Ph.D. degree491(with honors) in artificial intelligence from the Insti-492tute of Automation, Chinese Academy of Sciences493(CAS), Beijing, China, in 1992.494

From 1994 to 1996, he was a Postdoctoral Fellow495with the Medical Image Processing Group, Univer-496sity of Pennsylvania, Philadelphia. Since 1997, he497has been a Professor with the Key Laboratory of498Complex Systems and Intelligence Science, Institute499of Automation, CAS. He has published more than50050 papers in academic journals and international501

conferences. His research interests include medical image process and analysis,502pattern recognition, etc.503

Prof. Tian received the Awards of National Scientific and Technological504Progress in 2003 and 2004, respectively. He is a specially invited reviewer for505Mathematical Reviews.506

Liang Li received the B.S. degree from Northwest- 507ern Polytechnical University, Xi’an, China, in 2002. 508He is currently working toward the Ph.D. degree at 509the Key Laboratory of Complex Systems and In- 510telligence Science, Institute of Automation, Chinese 511Academy of Sciences, Beijing, China. 512

His research interests include pattern recognition, 513machine learning, and image processing and their 514applications in biometrics. 515

Yuliang He received the B.S. degree in computer 516and system science from Nankai University, Tianjin, 517China, in 1997 and the M.S. and Ph.D. degrees from 518the Institute of Automation, Chinese Academy of 519Sciences (CAS), Beijing, China, in 2003 and 2006, 520respectively. 521

He is currently with the Key Laboratory of Com- 522plex Systems and Intelligence Science, Institute of 523Automation, CAS. His research interests include pat- 524tern recognition, machine learning, and information 525fusion and their applications in biometrics. 526

Dr. He received the CAS President Scholarship in 2005. 527

Xin Yang received the B.S., M.S., and Ph.D. degrees 528in intelligent instruments from Tianjin University, 529Tianjin, China, in 1994, 1997, and 2000, respec- 530tively. 531

From 2001 to 2003, she was a Postdoctoral Fellow 532with the Biometric Research Group, Key Labora- 533tory of Complex Systems and Intelligence Science, 534Institute of Automation, Chinese Academy of Sci- 535ences, Beijing, China. Since 2003, she has been 536an Associate Professor with the Laboratory. Her 537research interests include bioinformatics, pattern 538recognition, etc. 539

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