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1 CIP: A Fourth Order System and Its Transfer Function

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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