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# 1 CIP: A Fourth Order System and Its Transfer Function

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Contourlet Transform Based Feature Extraction Method …

411

The Contourlet transform can also be enhanced to support different scales,

directions, and aspect ratio. This further allows Contourlet to efﬁciently approximate a smooth contour at multiple resolutions.

3.3 Principle Component Analysis

Principal component analysis is the linear dimensionality reduction technique based

on the mean-square error. It is also a second-order method that computes the

covariance matrix of the variables.

The obtained contourlet coefﬁcients are reduced to a lower dimension by

identifying the orthogonal linear combinations with greater variance exists among

the coefﬁcients. The ﬁrst principle component is the linear combination with largest

variance. The second principle component is the linear combination with second

largest variance and orthogonal to ﬁrst principle component.

Then, the computation of covariance matrix for the obtained contourlet coefﬁcients is obtained through the following steps

(1) Calculate the algorithmic means of all the feature information vectors viz.,

F1 ; F2 ; F3 ; . . .; Fn containing contourlet coefcients through (1)

vẳ

n

1X

Fj

n jẳ1

1ị

(2) The difference between each feature information vector and the calculated

mean is computed through (2)

rj ẳ Fj v

2ị

(3) The covariance matrix is computed through (3)

uẳ

n

1X

rj rTj

n jẳ1

3ị

(4) The Eigen value viz., f1 ; f2; f3 . . .; fn from the obtained covariance matrix is

derived through (4)

fj ¼

n 

2

1X

vTj rTj

n jẳ1

4ị

In this context, Principal Component analysis are used for the following two

main reasons. Firstly, it is used to reduce the dimensions of the obtained contourlet

coefﬁcients to the lower dimension which enables computationally easier for further

412

K. Usha and M. Ezhilarasan

processing. Secondly, even the reduced contourlet coefﬁcients could able to represents most reliable feature information for identiﬁcation.

3.4 Feature Extraction and Matching Process

From the captured ﬁnger knuckle print image, the feature extraction using the

proposed CTBFEM approach is achieved by the following steps:

1. If the obtained image is an RGB image, it is converted to gray scale image and

the original size of the image, 120 × 270 is retained

2. The obtained FKP image is subjected to Multidimensional ﬁltering and sharpening techniques for preprocessing.

3. The preprocessed FKP image is subjected to Discrete Contourlet Transform

which results with the coefﬁcients of lower and higher frequencies with different

scales and multiple directions.

4. Decompose the obtained coefﬁcients with the same size as C1 ; C2À2 . . .; CnÀd , in

which d represents the number of directions

5. The contourlet coefﬁcients are incorporated to construct image vector Fi, by

column values are reordered with the coefﬁcient values.

6. The obtained feature vector is transformed to lower dimensional sub-band using

Principle Component Analysis.

7. Matching between test image and registered image is performed by calculating

Euclidean distance between test image vector information and registered image

vector information.

3.5 Fusion Process

Matching Score level fusion scheme is adopted to consolidate the matching scores

produced by the knuckle surfaces of the four different ﬁngers. In the matching score

level, different rules can be used to combine scores obtained by from each of the

ﬁnger knuckle. All these approaches provide signiﬁcant performance improvement.

In this paper, weighted rule has been used.

In the weighted rule, say that S1, S2, S3 and S4 represents the normalized score

obtained from ﬁnger back knuckle surface of index ﬁnger, middle ﬁnger, ring ﬁnger

and little ﬁnger respectively. The ﬁnal score SF is computed using (5).

SF ẳ S1 w1 ỵ S2 w2 ỵ S3 w3 þ S4 w4

ð5Þ

where w1, w2, w3 and w4 are the weights associated with each unit given by (6).

Contourlet Transform Based Feature Extraction Method

w i ẳ Pi

413

EERi

kẳ1

6ị

EERk

4 Experimental Analysis and Results Discussion

The performance of the proposed ﬁnger knuckle print recognition system was

examined by means of the PolyU Finger Knuckle Print Database [19]. The PolyU

FKP database consists of ﬁnger knuckle images collected from 165 individual in a

peg environment. This database consists of knuckle images collected from four

different knuckle surface of a person viz, left index, right index, left middle and right

middle ﬁnger knuckle surfaces. Totally, this database consists of 7,920 images with

the resolution of 140 × 200. In this experimental analysis, images collected from 100

different subjects are used to train the proposed ﬁnger knuckle print recognition and

images collected from 65 different subjects are used to test the system.

The extensive experiments were conducted to assess the performance of the

proposed ﬁnger knuckle print recognition system. The genuine acceptance rate is

determined by calculation the ratio of the number of genuine matches and imposter

matches obtained to the total number of matches made with the system. False

acceptance rate and False Rejection rates are computed by tracking the number of

invalid matches and invalid rejections made by the system. The equal error rate is

Table 1 Performance of the proposed personal authentication system in terms of GAR values

obtained from the corresponding FAR values

FPK features

Left index ﬁnger knuckle (LIFK)

Left middle ﬁnger knuckle (LMFK)

Right index ﬁnger knuckle (RIFK)

Right middle ﬁnger knuckle (RMFK)

LIFK + LMFK

LIFK + RIFK

LIFK + RMFK

LMFK + RIFK

LMFK + RMFK

RIFK + RMFK

LIFK + LMFK + RIFK

LIFK + LMFK + RMFK

LIFK + RIFK + RMFK

LMFK + RIFK + RMFK

All four ﬁnger knuckles

Genuine acceptance rate

FAR = 0.5 %

FAR = 1 %

FAR = 2 %

74

75

76

72

82.5

83.4

84.8

85.2

86.1

87.1

91.5

92.6

91.8

93.5

97.4

79

74

78

75

86.3

86.5

86.3

89.7

89.3

89.6

96.5

96.7

95.9

96.9

98.7

76

73

73

74

84.5

84.7

85.9

87.3

88.2

88.5

94.7

94.8

93.7

95.6

98.2

414

K. Usha and M. Ezhilarasan

computed based on the point at which the false acceptance rate and false rejection

rate become equal and the decidability threshold is computed by ﬁnding the distributions of genuine and imposters matching scores. The following Table 1

illustrates the values of the genuine acceptance rate obtained for the different values

of false acceptance rate from the individual ﬁnger knuckle print feature and also

from their various combinations using PolyU dataset.

The tabulated results prove that the combined performance of all the four ﬁnger

knuckle print features using sum-weighted rule of matching score level fusion

shows higher GAR of 98.72 % for the lower FAR values.

The ROCs illustrating the individual performance of FKP features, combined

performance of two, three and all four FKP features are shown in Fig. 2a–d

respectively. The ROC shown in Fig. 2a, illustrates that the performance of the

system is considerably good even when features of single FKP image is used.

Further, the performance gets increases as when fusion of two, three ﬁnger knuckle

print image features are used as shown in Fig. 2b, c respectively. The best performance 98.7 % of GAR is achieved by fusing the entire four ﬁngers knuckle print

features as shown in Fig. 2d.

(a)

(b)

(c)

(d)

Fig. 2 Performance of the proposed system when experimented with a individual FKP features,

b fusion of two FKP features, c fusion of three FKP features, d fusion of all four FKP features

Contourlet Transform Based Feature Extraction Method …

415

Table 2 Comparative analysis of proposed method with some of the existing feature extraction

methods in hand based biometrics

Reference

Data set

Feature extraction methodology

Results

obtained

(EER %)

Meraoumia

et al. [12]

PolyU database for palm

print. PolyU database

for knuckle print

PolyU FKP Database

with 165 subjects and

7,440 images

Generation of phase correlation

function based on discrete fourier

transform

Measurement of average gray scale

pixel values and frequency values of

the block subjected to 2D DCT and

matching using correlation method

Computation of Eigen values by

subjecting the FKP image to random

transform and matching by calculating the minimal distance value

Contourlet transform based feature

extraction method

1.35

Saigaa et al.

[15]

Hedge et al.

[14]

PolyU FKP Database

with 165 subjects and

7,440 images

This paper

PolyU FKP Database

with 165 subjects and

7,440 images

1.35

1.28

0.82

The proposed ﬁnger knuckle recognition system is compared with the existing

personal recognition systems based on texture analysis methods which has been

implemented on various hand based biometric traits such as ﬁnger knuckle print,

palm print, hand vein structure and ﬁnger prints. The following Table 2 illustrates

the summary of reported results of existing systems and comparative analysis of

those results with the performance of proposed system.

In the comparative analysis as shown in the Table 2, it has been found that, the

existing ﬁnger knuckle print authentication system based on coding method and

appearance based method produces accuracy which is purely dependent upon the

correctness of the segmentation techniques and quality of the image captured

respectively. But in the case of the proposed Contourlet Transform based Feature

Extraction Method which is based on texture analysis produces the lower equal

error rate (EER) of 0.82 % with less computational complexity.

5 Conclusion

This paper has presented a robust approach for feature extraction from ﬁnger

knuckle print using Contourlet transform. The proposed CTFEM approach extracts

reliable feature information from ﬁnger knuckle print images is very effective in

achieving high accuracy rate of 99.12 %. From the results analysis presented in the

paper, it is obvious that the ﬁnger back knuckle print offers more features for

personal authentication. In addition, it requires less processing steps as compared to

the other hand traits used for personal authentication and hence it is suitable for all

types of access control applications. As a future work, ﬁrst we plan to incorporate

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