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Fingerprint classification based on decision tree from singular points and

orientation field

Jing-Ming Guo a, Yun-Fu Liu a, Jla-Yu Chang a, Jiann-Der Lee a,b,

a Department of Electrical Engineering, National Taiwan University of Science and Technology, Taipei, Taiwanb Department of Electrical Engineering, Chang Gung University, Taipei, Taiwan

a r t i c l e i n f o

Keywords:

Fingerprint

Fingerprint identification

Fingerprint singularity

Decision tree classifier

Fingerprint analysis

a b s t r a c t

In this study, a high accuracy fingerprint classification method is proposed to enhancethe performance in

terms of efficiency for fingerprint recognition system. The recognition system has been considered as a

reliable mechanism for criminal identification and forensic for its invariance property, yet the huge data-

base is the key issue to make the system obtuse. In former works, the pre-classifying manner is an effec-

tive way to speed up the process, yet the accuracy of the classification dominates the further recognition

rate and processing speed. In this paper, a rule-based fingerprint classification method is proposed,

wherein the two features, including the types of singular points and the number of each type of point

are adopted to distinguish different fingerprints. Moreover, when fingerprints are indistinguishable,

the proposed Center-to-Delta Flow (CDF) and Balance Arm Flow (BAF) are catered for further classifica-

tion. As documented in the experimental results, a good accuracy rate can be achieved, which endorses

the effectiveness of the fingerprint classification scheme for the further fingerprint recognition system.

2013 Elsevier Ltd. All rights reserved.

1. Introduction

Fingerprint is widely used in individual identification, largely

due to the bio-invariant characteristic of human fingerprints,

which also provide more details for distinguishing various persons.

Former fingerprint verification methods normally demand users

to input their personal information through various means, such as

a name or an ID card. This kind of system verifies the correspon-

dence between the captured fingerprint and the users personal

information, yet the system is inefficient as the users have to oper-

ate the system. For example, keying in their name or directly

inserting an ID card is an additional operation for user identifica-

tion. To avoid this inconvenience, an alternative approach namely

fingerprint identification (Maltoni, Maio, Jain, & Parbnhankar,

2009) which does not require users interaction was presented,yet extensive processing complexity caused by its cross reference

of fingerprints in the database is required. To cope with this, for-

mer works (Ratha, Chen, Karu, & Jain, 1999; Tan, Bhanu, & Lin,

2003) used a strategy to pre-classify the fingerprints in database

into different categories. As a result, a fingerprint to be verified

simply needs to cross-reference the fingerprints in the category

which identical to the verified fingerprint. This manner effectively

reduces the number of fingerprints for further matching process.

The researches focusing on fingerprint classification are dis-

cussed as below. For instance, in Henrys work (Henry, 1900) the

fingerprints were separated into four classes (namely 4C): Arch

(A), Whorl (W), Left loop (L), and Right loop (R), some examples

are illustrated inFig. 1(a), (c)(e). Another classification approach

indicates that the category A can be further classified into A and

Tented arch (T) Watson & Wilson, 1992 (namely 5C), and

Fig. 1(b) shows an example of the additional Tented arch category.

Even more numbers of fingerprint categories are also employed

(Cappelli, Lumini, Maio, & Maltoni, 1999), but which also raise

other issues such as reduced accuracy (ambiguous categories even

cannot be classified by experts (Maltoni et al., 2009; Tan & Bhanu,

2005). Thus, in this work, the 4C system is adopted as the standard

for classification.

Feature extraction for fingerprint classification is anotherimportant issue. Several well-known types of methods have been

proposed, including orientation field (OF), singular point (SP), ridge

flow (RF), and Gabor filter (GF). Moreover, lots of classification

methods based on these features are established, such as rule-

based (RB), SYntactic (SY), STRuctural (STR), STAtistical (STA),

Neural Network (NN), and Multiple Classifiers (MC). Among these,

the RB approach is the most straightforward method than the oth-

ers. This method relies on the acquired number and positions of

the extracted singular points (Karu & Jain, 1996; Kawagoe & Tojo,

1984; Msiza, Leke-Betechuoh, Nelwamondo, & Msimang, 2009;

Wang & Dai, 2007; Zhang & Yan, 2004) to classify fingerprints.

Since the singular points cannot be extracted from a fingerprint

0957-4174/$ - see front matter 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.eswa.2013.07.099

Corresponding author. Tel.: +886 928856123.

E-mail addresses: [email protected] (J.-M. Guo), [email protected] (Y.-F.

Liu), [email protected](J.-Y. Chang),[email protected](J.-D. Lee).

Expert Systems with Applications 41 (2014) 752764

Contents lists available at ScienceDirect

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image directly, the SY classification approach (Chang & Fan, 2002)

adopted the global distribution of 10 basic ridge patterns, the anal-

ysis of the ridge shapes, and the sequence of ridge distributions to

achieve their work. The STR method (Cappelli et al., 1999) was pro-

posed to partition the orientation field of a fingerprint into differ-

ent orientation regions, and the related graphs of these regions

were employed to classify fingerprint. Meanwhile, the STA ap-

proaches were based on a different input features to determine

multi-dimensional regression equations. After that, the data fea-

tures are extracted directly and input into the classifier, and the

classified results can be obtained efficiently (Jung & Lee, 2009;Min, Hong, & Cho, 2006; Lia, Yau, & Wanga, 2008; Park & Park,

2005). The STA and NN approaches employed a special strategy

to classify fingerprints as they imitated human perception and

empirical model. These approaches require lots of training data

to yield the classifier, and sufficient data should be obtained to

yield a more effective classifier (Bernard, Boujemaa, Vitale, & Bri-

oct, 2001; Kristensen, Borthen, & Fyllingsnes, 2007; Senior & Boll,

2004). Conversely, insufficient training data will be a problem

since it significantly degrades the accuracy of a system. In all of

the classification methods, the two key issues always affect the

accuracy rate: (1) The quality of a fingerprint image, and (2) the

ambiguity of a classification scheme.

In this work, clear and explicit rules are established to re-

move ambiguous classes of fingerprints. The RB technique isthen applied since it is easy to implement, and which does not

require a training procedure for classifier, while the high accu-

racy still can be achieved. Moreover, two issues affecting the

accuracy rate indicated above are discussed. Finally, a decision

tree is designed to realize an automatic fingerprint classification

system.

The rest of this paper is organized as follows. Section2 intro-

duces the preprocessing and feature extraction steps. The results

of our analysis and the descriptions of decision trees are provided

in Section 3. Section 4 provides the experimental analyses and per-

formance comparisons. Finally, conclusions are drawn in Section 5.

2. Preprocessing and feature extraction

The quality of the captured fingerprint ridge is very important

since it dominates the singular point extraction. In an ideal case,

a captured fingerprint should include sharp ridges and valleys,

yet these are obstructed by other factors (Amengual et al.,

1997). Thus, to achieve a better performance, an image enhance-

ment process is highly demanded. In this study, the three public

fingerprint databases FVC datasets (Fingerprint database FVC,

2000, 2002, 2004) are adopted in this study for conducting

experiments, in which the fingerprints are captured from differ-

ent devices, thus perfect and imperfect fingerprints are involved.

The critical issues involved can be solved by the proposed finger-

print classification as shown inFig. 2, and the detail flows of the

preprocessing is shown in Fig. 3 which is discussed belowfirstly.

2.1. Preprocessing

2.1.1. Histogram equalization

To obtain an image with stable contrast distribution, due to the

foreground and background are simple, the global histogram equal-

ization is utilized. The transformation function is formulated as

below,

HEi;j 255

PImagei;jg0 Hg

PQ ; 1

whereH(g) denotes the histogram value at grayscalegand variableImage(i,j) denotes the grayscale value of the captured fingerprint

image of size P Qat location (i,j). Notably, in this study the full

black and white colors are defined at 0 and 255, respectively.

Fig. 4shows a series of results of each sub-function in the prepro-

cessing block, and the result corresponding to histogram equaliza-

tion is shown inFig. 4(b).

2.1.2. Grad field

The grad field represents the high-frequency energy distribu-

tion of the captured fingerprint image, and it can yield a mask to

assist the following segmentations process.

GHi;j @

@jImagei;j; 2

GVi;j @@i

Imagei;j; 3

Gradi;j 1

W2

XiroundW2 uiroundW

2

XjroundW2 vjroundW

2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiG2Hu;v

2 G2Vu; v

q ; 4

where the notations Hand Vdenote horizontal and vertical, respec-

tively; the constant W= 9 denotes the average filter size; the

round() denotes the round down operation. Fig. 4(c) shows two dif-

ferent examples of grad results.

2.1.3. Segmentation

TheHE(i,j) obtained by Eq.(1)is separated into foreground and

background by the variance thresholding method (Mehtre, 1993).

The processing steps are described as below:

AverageGrayScalei;j 255

Pr=2mr=2

Pr=2nr=2HEim;jn

r 12 ; 5

SegmentMapi;j AverageGrayScalei;j Gradi;j

2 ; 6

Mean 1

PQ

XPi1

XQj1

SegmentMapi;j; 7

Var

1

PQXPi1

XQj1 SegmentMapi;j Mean

2

; 8

(a) A (b) T (c) W (d) L (e) R

Fig. 1. Fingerprint categories. (a) Arch (A). (b) Tented arch (T). (c) Whorl (W). (d) Left loop (L). (e) Right loop (R).

J.-M. Guo et al. / Expert Systems with Applications 41 (2014) 752764 753
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ImageSegmenti;j 255; if SegmentMapi;j Var

HEi;j; if SegmentMapi;j> Var;

9

where the empirical parameter r= 6 which denotes the size of the

referenced average range. An example of the obtained ImageSegment(i,j) is shown in Fig. 5. Yet, in the casethat ImageSegment(i,j) obtained

from a brighter (causes low image contrast) captured fingerprint

image, partial fingerprints are wrongly classified to the background,

and which thus causes difficulty in detecting the singular points. An

instance is shown inFig. 6(b), in which the circle indicates a singu-

lar point. To deal with this, the ratio between the areas of the seg-

mented background and the whole fingerprint image is estimated,

and a parameter c, denoting the target ratio to be met, is used to ad-just the threshold Var for enlarging the area of segmented finger-

print The parameterc is defined as below,

cCovered gray background area

PQ 100%: 10

Fig. 6(c) shows an example of the improved segmented result.Although some fingerprint areas are wrongly segmented, the

singular point of interest is clear. Some results of the segmentation

are also shown inFig. 4(d).

2.1.4. Orientation field

To estimate the orientations of local fingerprint ridges, the ori-

entation field is obtained with the following steps, and which is

necessary for the next Gabor filtering process (Hong, Wan, & Jain,

1998).

VHi;j Xiround W2

uiround W2

Xjround W2 vjround W

2

2GHu; vGVu; v; 11

VVi;j XiroundW2

uiroundW2

XjroundW2 vjroundW

2

G2Hu; v G2Vu; vh i

; 12

Oi;j 1

2tan1

VHi;j

VVi;j

; 13

where variables GH(u, v) and GV(u, v) are obtained by Eqs. (2) and (3)

and the size Wis identical to that used in Eq. (4)for the proposed

algorithm.Fig. 4(e) shows the corresponding results of the obtained

O(i,j) images.

2.1.5. Simplified Gabor filtering

The traditional Gabor filter used inHong et al. (1998)is a filter

for enhancing the ridge at a specific frequency and angle. This filter

with various frequencies (f) and angles (h) can be obtained by thefollowing equation as

Preprocessing

Singular pointextraction

Bottom center point

Top center point

No

Delta point No

Method of

CDF(Node 1)

Method of

BAF(Node 2)

Delta pointposition(Node 3)

Yes

No

Asymmetric Flow

AQ

End

Classified fingerprint

image

LPLIP

RPRIP

Decision tree

WPWIP

AD LD RDAPAIP

Symmetric

FlowLeft

Asymmetric

Right

Asymmetric

>=-R and

=R


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Gx;y; h;f e1

2

x2h

r2x

y2h

r2y

cos2pfxh; 14

where the variable rx andry denote the standard deviations, andvariables xh andyh are defined as below,

xh

yh

cosh sinh

sinh cosh

x

y

: 15

Supposing that the support region of the obtained Gabor filter is

Mx My, every pixel requires Mx My computations. To speed up

the processing, a simplified Gabor filtering is proposed in this study.

The enhanced image can be obtained by

Imageenhancedi;j X3

u3

X3v3

filterMv ImagesegmentRoundi uh;Roundj vh; Ifv 0

filterOu Imagesegment Roundi uh90 ;Roundj vh90 ; Ifu 0

0; Otherwise

;

8>:

16

filterMv 1

7 1 1 1 1 1 1 1 ; where v2 3; 3; 17

filterOu 1

7 3 1 3 9 3 1 3 whereu2 3; 3;

18

The processed values forfilterO(u) are orthogonal with the values for

filterM(v), and it is achieved by rotating the coordinates uh and vhwith an angelh obtained from O(i,j) in the Cartesian plane. The cor-

responding definition is shown below,

uh

vh

cos h sin h

sin h cos h

u

v

: 19

An example is shown inFig. 7, where the gray lines represent the

flows of a fingerprint. In this figure, the pixels labeled with FH(x)

indicate that these pixels are processed byfilterM(v); FV(x) indicates

that these pixels are processed by filterO(v), and 0 indicates that

these pixels are not processed. The obtained results are shown in

Fig. 4(f). In otherwise case of Eq.(16), the process does not do any

calculation. Thus, this modification only requiresMx+ Mycomputa-

tions (suppose the sizes of the main and orthogonal filters are MxandMyrespectively for comparison). The obtainedImageenhanced(i,j)

image is used to acquire a more accurate orientation field O(i,j)

through the processes discussed in Section2.1.4. Notably, the vari-ables GH(u, v) andGV(u, v) are calculated fromImageenhanced(i,j).

(a) (b) (c) (d) (e) (f)

Fig. 4. Results of the preprocessing block. Two types of captured fingerprints are adopted. (a) Original image. (b) Histogram equalization. (c) Grad image. (d) Segment

image. (e) Orientation image. (e) Enhanced image.

(a) (b) (c)

Fig. 5. Example of the segmented result. (a) AverageGrayScale(i,j). (b) Segment-

Map(i,j). (c)ImageSegment(i,j).

(a) (b) (c)

Fig. 6. Example of over-segmented caused by a brighter captured fingerprint. (a)

Original fingerprint image. (b)ImageSegment(i,j). (c) Segmented image obtained with

an adjusted thresholdVar, wherec = 35%.

FV(3) 0 0 0 0 0 FH(3)

0 FV(2) 0 0 0 FH(2) 0

0 0 FV(1) 0 FH(1) 0 0

0 0 0 FV(0)

FH(0)0 0 0

0 0 FH(-1) 0 FV(-1) 0 0

0 FH(-2) 0 0 0 FV(-2) 0

FH(-3) 0 0 0 FV(-3)0 0

Fig. 7. Simplified Gabor filtering example, when (i,j) e37.552.5.

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2.2. Singular point extraction

To distinguish various types of fingerprint under unpredictable

image conditions, robust features are highly demanded. In this

study, the commonly used singular points including the center

and delta points as illustrated inFig. 8are used. To extract these

singular points, due to the dramatic variations on fingerprint tex-

ture, the orientation field obtained from Imageenhanced

(i,j

) is em-

ployed. Defining the Poincar index, which is a differential

summation related to each of the two neighboring pixels going

along a closed curve (Karu & Jain, 1996; Kawagoe & Tojo, 1984;

Maltoni et al., 2009), and it is directly proportional to the variation

of the orientation field. The mathematical definition is given below,

anglei;jjm; n Oi;j Om;n; 20

Pinternali;j X7k0

anglerkjrk1mod 8 ; 21

Pexternali;j X15k0

angleRkjRk1mod16 ; 22

Point type

Center point; if 180 r Pinternali;j 180 r

Center point; if 180 r Pexternali;j 180 r

Deltapoint; if 180 r Pinternali;j 180 r

Deltapoint; if 180 r Pexternali;j 180 r

non-singular point; Otherwise

;

8>>>>>>>>>>>:

23

where the function angle() denotes the difference between two ori-

entation field values; vectors rk and Rk denote the positions in the

inside and outside rings centered the current processing position

(i,j), a corresponding example is illustrated in Fig. 9, where the

notationx denotes the current processing position; the empirical

parameterr = 25 denotes a single-side error toleration. Two Poin-car indexes calculated by Eqs. (21) and (22)are used to represent

the summed angle differences of the internal and external rings,

respectively. In general, the Pinternal(i,j) calculated from an ideal cen-

ter singular point is close to 180, and the Pexternal(i,j) calculated

from an ideal delta singular point is close to 180. Based upon this

phenomenon, a decision rule is established as shown in Eq. (23)

with a toleration parameterrto distinguish different singular pointtypes.

Multiple candidates of center and delta points are obtained by

the above methods. In this study, the center points are further sep-

arated into top center point and bottom center point two classes

for the following fingerprint classification, in which the top center

point is defined when the neighboring flows down, an example is

shown inFig. 8(a); conversely, the bottom center point is defined

when the neighboring flows up. The decision rule to classify the

two center point types are described as below,

TPvalue jOi 1;j 1 45j jOi 1;j 1 135j; 24

BPvalue jOi 1;j 1 135j jOi 1;j 1 45j; 25

Center point type Top center point; if TPvalue BPvalue

Bottom center point; Otherwise

:

26

As a result, in total three types of singular points may appear on a

captured fingerprint image. According to the observation from

experiments, the candidates of each type of singular points are in

clustering and surrounding the real singular point. Consequently,

the averaged positions of the top and bottom center points are con-

sidered as the real top and bottom singular points. Yet, due to the

candidates of delta points are possible to have obvious differences

in distance (an example is shown in Fig. 1(c), which contains two

real delta points distributed on left- and right-side of the finger-

print), the averaged positions are only considered within a circle re-

gion centered the candidate itself with a radius of one-ten image

width. Since the number of the remained positions may be still

higher than two, thus two of these positions with the highest aver-aged from the candidates are considered as the real delta points in

this study.

3. Fingerprint classification

In this section, various types of fingerprints are further investi-

gated. From this analysis, a series of rules are introduced to assess

and define different fingerprint categories. The captured finger-

prints in the FVC database are adopted in this study to provide var-

ious quality levels. One of the critical cases is the Incomplete

fingerprint, in which the structures of the fingerprint are not en-

tirely captured. The fingerprints in this class have low image qual-

ity, yielding partially lost of the singular points. Thus, the proposed

method is discussed in terms of two fingerprint quality conditions:perfect and imperfect. At the end of this section, an overall fea-

ture analysis and a summary are specified. We will also show how

to apply this feature analysis scheme to classify fingerprint with

different methods. Moreover, two methods, namely Center-to-Del-

ta Flow (CDF) and Balance Arm Flow (BAF), are used to classify a

fingerprint when it cannot be classified by simply using the types

and the numbers of the singular point.

3.1. Symmetry estimation

Five different numbers of extracted singular points from zero to

four (at most two center points and two delta points) are possible

to appear in the previous feature extraction. Among these, the case

when the top center point is found and the bottom center point isnot found, the fingerprint classification employs the fingerprint

(a) (b)

Fig. 8. Two types of the singular points, (a) center point, and (b) delta point.

Fig. 9. Operational range matrix.

756 J.-M. Guo et al. / Expert Systems with Applications 41 (2014) 752764


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orientation symmetry characteristic to distinguish different fin-

gerprint types. An example is shown in Fig. 10for explaining this

characteristic, in which the regions A and B are reflexive symmetry,

and the line C used to divide the two regions is called balance line

in this study. This case exists when the values of the left-hand and

right-hand sides of the balance line are identical. A computation

concept is depicted inFig. 10(b), in which the reflexive symmetry

is demonstrated on the obtained orientation field. In the following,

two different estimation methods are proposed for estimating

whether the reflexive symmetry is existed.

3.1.1. Center-to-Delta Flow (CDF)

This method is performed when only one delta point is ex-

tracted from the classified fingerprint image. A corresponding

example is depicted in Fig. 11(a), where the hdenotes the angle be-

tween the horizontal line of the captured fingerprint image and the

line Center-to-Delta Line (CDL) connected the top center and the

delta point. To calculate every un of the points on the line CDL,an example is shown in Fig. 11(b), all of the orientation fields

O(i,j) contained in a one-pixel-width region of length R which is

perpendicular to the line CDL are averaged. The length Ris defined

at the quarter of the width of the captured image. According to the

above calculated h andun, the symmetric estimation of CDF isdefined as below,

CDF Symmetric; if 1

N

XNn1

/nh

rCDF

Asymmetric; Otherwise

;

8>: 27

where the constant N denotes the length of CDL, and parameter

rCDFis set at 15 in this study. The pseudo code of the CDF is orga-nized as below:

Pseudo code of the Center-to-Delta Flow (CDF)

Step 1. Determine whether only one top center point and one

delta point are extracted, if not, perform the BAF process

introduced in the following sub-section

Step 2. Connect the extracted center and delta points with the

line CDL, and calculate the angle h.

Step 3. Forn = 1 N, whereNdenotes the number of discrete

points which constructs the line CDL

Calculate averaged orientation fields unEnd For

Step 4. Determine whether the two regions at the two sides of

CDL are symmetric

3.1.2. Balance Arm Flow (BAF)This method is used to obtain a Balance Arm Line (BAL) which is

constructed by the calculated pivot points. The orientation fields of

the both sides of BAL are used to determine whether it is symmet-

ric.Fig. 12shows a corresponding example for better understand-

ing. The top center point is considered as the start pivot point. The

next pivot point is determined by Eq. (28),in which theun illus-trated inFig. 12(b) and (d) is calculated.

Px;y Px 4 cos/n;y 4 sin/n: 28

Subsequently, all of the orientation fields O(i,j) contained in the

one-pixel-width region of length R which is perpendicular to the

un1 or 90 are averaged at the current pivot point positionP(x,y). The length R is defined as that used in CDF. Afterward, all

of the orientation fields O(i,j) used to obtain un are adopted toaccumulate theLeftFlow andRightFlow as below.

LeftFlow LeftFlow 1; if Oi;j< 90

RightFlow RightFlow 1; if Oi;j> 90

None Otherwise

:

8>: 29According to these two variables, the symmetric estimation of the

BAF can be determined with the following criterion,

Left asymmetric; if LeftFlowRightFlow >1 rBAF

Right asymmetric; if RightFlowLeftFlow

>1 rBAF

Symmetric; Otherwise

;8>>>>>: 30

where the parameter rBAF is empirically set at 0.15 in this study.The pseudo code of the BAF is organized as below.

Pseudo code of the BAF

Step 1: Determine whether one top center point is extracted,

or the asymmetric is determined by CDF

Step 2: The initialLeftFlow andRightFlow are set at 0, and

consider the top center point as pivot pointP(x,y) which is

the starting point of the BAF as shown inFig. 12(a)

Step 3: Repeat the following steps IIII until the current P(x,y)

is beyond the areas of the fingerprint or the captured image

I. For the calculation in the first time:

Calculate the average orientation fieldu1,LeftFlow, andRightFlowwith both sides perpendicular as 90 of distance

Rto the current position P(x,y), whereLeftFlow, and

RightFloware updated by Eq. (29)

II. Otherwise

Calculate the average orientation fieldun,LeftFlow, andRightFlowwith both sides perpendicular toun1of distanceRto the current position P(x,y), whereLeftFlow, and

RightFloware updated by Eq. (29)

III. Move the pivot point to the next position by Eq.(28)

Step 4: Determine whether the regions on the two sides of the

line BAL symmetric or not by calculating Eq.(30)

3.2. Fingerprint analysis

The characteristics of the fingerprints in various categories is

introduced, and the discussion is separated into perfect and

imperfect two conditions because of the high variety of samples

in the database. Moreover, the classification manners for each class

are also explained.

3.2.1. Fingerprint definitionsThis analysis is provided toward the above three types of singu-

lar points (top center, bottom center, and delta), in which the types

and the amounts of them are utilized to construct the hierarchical

decision strategy, namely decision tree, as shown in Fig. 2(more

about the fingerprint classes will be revisited later). Each node in-

side this figure indicates that many fingerprint types are possible

to enter with identical judgment for classification. These selections

in the decision tree are feasible to choose a suited way to classify

various fingerprint types. In addition, Table 1also shows the de-

tails of each fingerprint type in perfect and imperfect condi-

tions. The perfect condition indicates that a captured fingerprint

image contains the entire fingerprint regions and all of the singular

points, while the imperfect condition indicates that a captured fin-

gerprint image losing part of the regions or singular points. More-over, the term Query inTable 1represents classifying a fingerprint

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according to its types or the numbers of the extracted singular

points.

Fig. 13 shows the fingerprint type AQ without any singular

points. Figs. 14 and 15 show the fingerprint types WP and WIPwhich have one top-center point, one bottom-center point, and

zero to two delta points. Since these two types both have a unique

bottom-center point feature, these two fingerprint types and AQcan be classified with the Query manner. For another three finger-

print types, AP, LP, RP, all of them have a top-center point and a del-

ta point, as some examples shown in Figs. 16 and 17. Since the

three cases have the same singular points, the Node 1s CDF is

adopted for symmetry estimation for further classification. If the

response of this decision is true, the fingerprint is determined as

AP; if not, for further classifying the fingerprints, BAF is adopted

for Node 2s BAF for symmetry estimation. According to the result

of the BAF, the left asymmetry result determines the fingerprint is

LP, otherwise it is determined as RP. Considering the imperfect con-

dition (AIP, LIP, and RIPas some examples shown in Figs. 18 and 19),

due to the delta point cannot be extracted or two delta points are

extracted, the Node 2s BAF is employed. If the result of this esti-

mation is symmetric, then the AIP is determined; type LIP for left

asymmetry, and RIPfor Right asymmetry.

Except for the above conditions, the incompletely captured fin-

gerprint images have only delta points extracted, as shown in

Fig. 20(a) and (b). In this situation, four classes, AI, WI, LI, and RI,

are considered; if two delta points are extracted, then WI is deter-

mined; if only one delta point are extracted, the Node 3s function

will be used. As it can be seen fromFig. 20(c) and (d), the width of

the extracted delta point, the center point DCP, and therRare ob-tained. If the delta point belongs to the right-side of the center

point, and which is greater than rR, then LI is determined. Other-wise, if the delta point belongs to the left-side of the center point,

and which is greater thanrR, thenRIis determined. Notably, in thisstudy the parameterrRis empirically set at 1/10 of the input imagewidth.

3.2.2. The description of singular point quadrantal diagram

The relationships among top center, bottom center, and delta

singular points are constructed in a 3-D space as shown in

Fig. 21, where the intersected point of these three axes is notated

as (0, 0, 0). To further define this space, the positive axis of each

point types denotes that the corresponding fingerprint category in-

cludes at least one singular point of the category, and negative axis

denotes that the corresponding fingerprint categories have no sin-

gular point. One more fingerprint category namely Undecided (U)

is additionally added. This class comprises three fingerprint cate-

gories, A, L, and R. The three categories have a common feature that

one center point and one delta point are included, thus the classi-

fier cannot rely on these information to distinguish the three fin-

gerprint categories. The CDF and BAF are used for distinguishing

these categories. In which, the distance between the extracted cen-

ter point and the delta point indicates that when the estimation of

the CDF and BAF have larger asymmetry value, the more likely the

fingerprints belong to L or R class, The estimation of the CDF and

BAF is an asymmetry result when the distance between the ex-

tracted center point and the delta point is larger, and an example

is shown inFig. 22. The corresponding distances are calculated as

below,

Dx xcenterxdelta; 31

Dy ycenterydelta: 32

4. Experimental results

Nowadays, the two databases, namely NIST (Watson & Wilson,

1992) and FVC (Fingerprint database FVC, 2000, 2002, 2004),

have been widely used on the related studies of fingerprint. In this

work, the FVC database is adopted in our experiments with the fol-

lowing two reasons: (1) The NIST database has about 17% captured

fingerprints which are difficultly classified even by an expert; (2)

comparing with the NIST database, containing ink-on-paper

(a) (b)

Fig. 10. Example of reflection symmetry. (a) Conceptual diagram. (b) Concept of

calculation.

(a) (b)

Fig. 11. Conceptual processing diagrams. (a) Center-to-Delta Line (CDL) and the

angleh. (b) Average orientationsun.

(a) (b) (c) (d)

Fig. 12. Conceptual diagrams of BAF. (a) The top center point regarded as the start pivot point. (b) Example the average orientations u1 calculation. (c) Calculating theposition of the next pivot point, and moving the pivot point. (d) Balance Arm Line (BAL) constructed by all of the pivot points.



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fingerprints, the images in FVC database are captured by optical

device has been widely used in practical applications. Thus, nine

various FVC databases are adopted, including three FVC2000 (Fin-

gerprint database FVC, 2000), three FVC2002 (Fingerprint data-

base FVC, 2002), and three FVC2004 (Fingerprint database

FVC, 2004). The numbers of the classified properties are organized

in Table 2, where the process is according to the prior knowledge of

singular point of each fingerprint type as arranged in Table 1.

In the Section2.1.3, the parameter c is used to determine thebackground ratio in segmentation.Fig. 23shows the Correct Clas-

sification Rates (CCRs) vs. variousc, and the empirical parametercis set at 35%. When 35% 6 c 6 60%, the CCRs are descending, sincesome of the error segmentations of the background cannot be de-

creased, which causes less ridge information obtained for finger-

print classification with the CDF and BAF. The CCR is defined as

below,

Table 1

Features of various singular point types and their corresponding classification methods.

Types Features

Top center point (\) Bottom center point ([) Delta point (N) Symmetry flow Classification method

Perfect AP U U Symmetric CDF

LP U U Left asymmetric CDF and BAF

RP U U Right asymmetric CDF and BAF

AQ Query

WP U U U Query

Imperfect AIP U Symmetric BAF

LIP U Left asymmetric BAF

RIP U Right asymmetric BAF

WIP U U Query

AI U Query

LI U Query

RI U Query

WI U Query

Fig. 13. Example of perfect Arch (A) fingerprint.

(a) (b)

Fig. 14. Examples of (a) perfect whorl class fingerprint. (b) Ridge appears around top center point and bottom center point.

Fig. 15. Example of imperfect whorl class.

(a) (b) (c)

Fig. 16. Example of (a) perfect tented arch class fingerprint. (b) The ridges appear

around the top center point and delta point. (c) Using CDF to determine the CDL,

and calculating the average orientations un.

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CCRNumCorrect classification

NumFingerprint classes ; 33

Table 3 shows the correct rate of singular points extraction (Correct

Extraction Rate, CER) of the above nine FVC databases, where the

CER is defined as below,

CERNumCorrect Extraction

NumFingerprint classes: 34

Notably, the positions of the singular points on fingerprint

images are marked before this estimation. According to the obser-

vation, the correct extraction of each singular points, including topcenter point, bottom center point, and delta point, are almost with

high quality. Yet, when the delta point is closer to the boundary of

the captured fingerprint, or when the image suffers from noise, the

corresponding CER is significantly degraded. The influence can be

seen from the CERs of L and R as shown in Table 3andFig. 24(a).

(a) (b)

(c) (d)

Fig. 17. Examples of (a) perfect loop class fingerprint. (b) Ridge appears around top center point. (c) Using CDF to determine the CDL. (d) Using BAF to determine the BAL.

(a) (b) (c)

Fig. 18. Examples of (a) imperfect tented arch class. (b) Ridge appears around thetop center point and delta point. (c) Using BAF to determine the balance line.

(a) (b) (c)

Fig. 19. Examples of (a) imperfect loop class fingerprint. (b) Ridge appears around top center point. (c) Using BAF to determine the balance line.



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Among these, the delta points in A type are not close to the bound-ary of fingerprint area, as shown in Fig. 24(b).

The CCRs of the four different fingerprint types (A, W, L, and R)

classified by the proposed method are organized in Table 4with

the confusion matrix form. Among these, the W, L, and R classes

yield good performance in terms of CCRs, yet the A type despite

in perfect or imperfect conditions leads to unsatisfactory perfor-

mance. Most of the errors occurred in A type classification is due

to the sensitivity of the calculated balance line affected by the local

fingerprint flow and incomplete fingerprint images, as an example

shown in Fig. 25. Nonetheless, the proposed scheme can achieve an

accuracy rate of 92.74% in average.

Fig. 26 and Table 5 show the CCR comparison among Msiza

et al.s method (Msiza et al., 2009), Jung-Lees method (Jung &

Lee, 2009), and the proposed method. The proposed method is sim-

ilar to that of Msiza et al.s method (Msiza et al., 2009), includingthe feature types and classifier. Yet, their classification rules can

hardly distinguish the ambiguous classes, such as the cases shown

in Fig. 22. The Jung-Lees study (Jung & Lee, 2009) adopted the

ridge as the features and considered the incomplete fingerprints

case. Nonetheless, the W fingerprint type is hardly classified in

their work due to various ridge orientations.

Since the proposed classification method cannot achieve 100%

in CCR, which causes an input fingerprint may not be found in

the classified fingerprint class. Hence, a fingerprint searching strat-

egy is required for searching for other fingerprint classes (except

the class which is firstly determined) with high efficiency. The

(a) (b) (c) (d)

Fig. 20. Examples of (a) incomplete class fingerprint with one delta point and (b) two delta points. (c) The dotted line surrounded the area is the ridge area, and the line DCL

width is the ridge area width in (a). (d) The threshold of classification for incomplete class in extracting one delta point.

Fig. 21. Singular points quadrantal diagram, in which the Whorl, Arch, Incomple-

tion, and Undecided are denoted by , , , , respectively.

Fig. 22. Relationships of the singular point positions among tented arch, left loop and right loop.

Table 2

Properties of the nine FVC databases.

Databases Types

Perfect Imperfect

A W L R A W L R

FVC 2000DB1 141 239 103 52 3 1 153 188

FVC 2000DB2 125 240 101 59 3 0 171 181FVC 2000DB4 55 262 100 73 9 2 228 151

FVC 2002DB1 53 205 134 130 3 3 162 190

FVC 2002DB2 68 222 138 155 4 2 166 125

FVC 2002DB4 27 192 87 69 5 8 257 235

FVC 2004DB1 112 213 125 82 0 3 163 182

FVC 2004DB2 66 272 59 75 6 8 173 221

FVC 2004DB4 64 190 117 130 0 10 195 174

Sub-total 4535 3385

Total 7920

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proposed searching strategy is illustrated in Fig. 27. An example is

adopted to explain this figure: In the case that when a fingerprint is

classified to A class but error occurs (the fingerprint cannot be

found in this class), both branches L and R classes are adopted to

compare theLeftFlowandRightFlow, Since the W has a unique fea-

ture and this category has a higher CER, the bottom center point

may not exist. The LeftFlow andRightFlow represent the numbers

of each flows, thus these two flows are directly compared. If the

LeftFlow is greater than RightFlow, the L type is considered as the

next searched class; conversely, when RightFlow is greater than

LeftFlow, then R type is considered as the next searched class.

Moreover, when a fingerprint is classified to L or R firstly, the

connected branch is class A since both L and R are similar to A,

and the W class is the last consideration because it has a unique

singular point and of higher CER. Given another case, when the fin-

gerprint is classified to W, and error is occurred, it will dismiss bot-

tom center point and then continue the classification by the CDF

and BAF. To compare the efficiency of the fingerprint recognition

system with and without the proposed fingerprint classification

method, the related analysis is provided as below,

EffectNC;NSTotal;SCS BranchNC;NSTotal;SCS; First calculation

MathcingNC;NSTotal;SCS; Otherwise

;

35

89%

90%

90%

91%

91%

92%

92%

93%

93%

0% 20% 40% 60% 80% 100%

CCR

Segmentation threshold ()

CCR vs. Segmentation threshold ()

Fig. 23. Relationship between Correct Classification Rate (CCR) andc.

Table 3

Correct Extraction Rates (CERs) of the nine databases.

Databases Classes

Arch (A) Whorl (W) Left (L) Right (R)

FVC 2000DB1 95.14% (137/144) 95.42% (229/240) 72.66% (186/256) 82.66% (205/248)

FVC 2000DB2 99.22% (127/128) 96.25% (231/240) 85.29% (232/272) 88.33% (212/240)

FVC 2000DB4 100.00% (64/64) 98.48% (260/264) 77.13% (253/328) 71.43% (160/224)

FVC 2002DB1 98.21% (55/56) 97.12% (202/208) 78.72% (233/296) 88.13% (282/320)

FVC 2002DB2 98.61% (71/72) 94.20% (211/224) 86.84% (264/304) 86.07% (241/280)

FVC 2002DB4 100.00% (32/32) 98.00% (196/200) 87.50% (301/344) 78.62% (239/304)

FVC 2004DB1 99.11% (111/112) 96.76% (209/216) 70.49% (203/288) 79.17% (209/264)

FVC 2004DB2 93.06%(67/72) 97.50% (273/280) 77.16% (179/232) 87.84% (260/296)

FVC 2004DB4 100.00% (64/64) 94.00% (188/200) 73.72% (230/312) 69.74% (212/304)

Average CER 98.12% 96.48% 79.07% 81.45%

(a) (b)

Fig. 24. Two examples of singular point locations in tented arch.

Table 4

Correct Classification Rates (CCRs) of the fingerprint types classified by the proposed method.

Types Results

Arch (A) Whorl (W) Left (L) Right (R) CCR (%)

Perfect Arch (A) 595 5 63 48 83.68

Whorl (W) 8 1988 21 18 97.69

Left (L) 67 3 888 6 92.12

Right (R) 58 2 4 761 92.24

Imperfect Arch (A) 15 0 5 13 45.45

Whorl (W) 4 33 0 0 89.19

Left (L) 79 15 1561 13 93.59

Right (R) 122 6 15 1504 91.32

Average CCR 92.74%



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MathcingNC;NSTotal;SCS XNCi1

CPCi NSCi 1 CPCif

NSCiXNB

j1

NBCj

NBSTotal Mathc NC 1;NSTotal NSCi;fSCS SCSig !#)X; 36

BranchNC; NSTotal; SCS XNCi1

NSCiNSTotal

fMathcingNC

1; NSTotalNSCi; fSCS SCSigg; 37

Efficience NSTotalX

EffectNC; NSTotal;SCS; 38

where NC denotes the number of classes; NSTotal denotes the total

number fingerprints in database; SCS denotes the current searching

fingerprint class; NSCi denotes the number of fingerprints in SCS;

CPCi denotes the correct probability of fingerprint class of SCS; NB

denotes the number of branches under SCS, for instance the W classshown in the second row ofFig. 27 has three branches, thenNB= 3;

NBCj denotes the number of fingerprints in the class ofjth branch;

NBSTotaldenotes the number of fingerprints in all branched classes;Xdenotes the consumed time for classifying a fingerprint image.

The calculated efficiency is 3.62 (this number will be explained be-

low) as shown in Fig. 29, which yields the CCRs as shown in Table 4.

For a fair comparison with other former methods, the numbers of

each type of fingerprints are supposed to be equivalent. Fig. 28

shows the relationship between the efficiency and CCR, and which

indicates the direct proportion between them. Fig. 29 shows the

classification efficiencies of various classification methods com-

pared to that of searching the entire database (for example, value

2 in this figure denotes that a method is faster than that of search-

ing the entire database by a factor of 2). Notably, the random rep-

resents a nave way that randomly selects a fingerprint class to be

the firstly searched class; the other three methods denote that the

strategy of Fig. 28 is used and various classification methods aregeared. According to this figure, the proposed method can yield a

good efficiency, and which is obviously superior to other methods.

(a) (b)

Fig. 25. Some fingerprint classification errors of the A type. (a) Caused by wrong

balance line, and (b) imperfect image.

50%55%60%65%70%75%80%85%90%95%

100%

Jung-Lee's method Msiza et al.'s

method

Proposed methodTheCorrectC

lassificationRate

Arch Whrol Left loop Right loop Average CCR

Comparison among various fingerprint classifications

Fig. 26. Comparison of various methods in terms of the Correct Classification Rate.

Table 5

CCR comparison on various fingerprint classification methods.

Methods Features Classifier CCRs Comments

Msiza et al.s method

(Msiza et al., 2009)

Orientation field,

singular point

Rule-

based

84.50%

(364/431)

Select only 431 samples from the database FVC2000 DB1_A (total has 800 samples). Notably,

rule-based method does not require training database

Jung-Lees method

Jung & Lee, 2009

Ridge flow Markov

model

80.01%

(650/812)

Entire samples of the FVC2000 DB1 and FVC2002 DB1 are adopted (each of them contains 880

samples). However, 136 unknown samples are excluded from their experiments. Half of the

remaining samples are adopted for training, and the others are for testing

Proposed method Orientation field,

singular point

Rule-

based

92.74%

(7345/

7920)

Entire samples of nine FVC databases are adopted (FVC2000 DB1, DB2, DB4; FVC2002 DB1,

DB2, DB4; FCV2004 DB1, DB2, DB4; each of the database contains 880 samples), and the

rule-based method does not require training database

A

W

L

R

L

R

R

LW

A

L

R

L

R W

W

L

R

R

L

A

R

L

Start

A

A

A

Fig. 27. Proposed fingerprint classification strategy.

0

1

2

3

4

5

0% 20% 40% 60% 80% 100%

Theefficiencyvalue

The average correct classification rate

The curve of relative benefit increase

Fig. 28. Relationship between classification efficiency and CCR.

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5. Conclusions

Fingerprint classification system is an effective manner for

further improving the correct recognition rate of the fingerprints,

and further reducing the average required cross-reference time be-

tween the test fingerprint and the fingerprints in existed database.

In this study, nine public FVC databases are adopted, and these

samples can be classified to perfect and imperfect fingerprints.To cope with these complex databases, a decision tree-based

scheme comprising query, CDF, and BAF methods is proposed. As

documented in the experimental results, the proposed method

can achieve a CCR of 92.74%, and which outperforms the two for-

mer works, Jung-Lees (Jung & Lee, 2009) and Msiza et al.s (Msiza

et al., 2009) methods. Moreover, the corresponding processing effi-

ciency is also significantly improved.

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1.4628

3.19573.385

3.6212

1

2

3

4

Im

provedefficiency

(times)

Classification efficiency

Random Jung-Lees method

Msiza et al.s method Proposed method

Fig. 29. The comparison of classification efficiency with different methods.

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Clasificación de huellas dactilares basada en el árbol de decisión de los puntos singulares y

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