Palmprint Linear Feature Extraction and Identification Based on

Palmprint Linear Feature Extraction and Identification Based on Ridgelet Transforms and Rough Sets Shanwen Zhang, Shulin Wang, and Xuelin Li Hefei Institute of Intelligent Machines, Chinese Academy of Science, Hefei, Anhui 230031, P.R. China [email protected]

Abstract. As one of the most important biometrics features, palmprint with many strong points has significant influence on research. In this paper, we propose a novel method of palmprint feature extraction and identification using ridgelet transforms and rough sets. Firstly, the palmprints are first converted into the time-frequency domain image by ridgelet transforms without any further preprocessing such as image enhancement and texture thinning, and then feature extraction vector is conducted. Different features are used to lead a detection table. Then rough set is applied to remove the redundancy of the detection table. By this way, the length of conduction attribute is much shorter than that by traditional algorithm. Finally, the effectiveness of the proposed method is evaluated by the classification accuracy of SVM classifier. The experimental results show that the method has higher recognition rate and faster processing speed. Keywords: Palmprint feature identification; Ridgelet transforms; Rough sets.

1 Introduction Personal identification is known as biometrics computing began in 1970s. At that time, fingerprint based automatic checking systems are widely used in law enforce. Retina and iris based systems were introduced in the mid 1980s. Today’s speaker identification biometrics have their roots in technological achievements of the 1970s; while signature identification and facial recognition are relative newcomers to the industry. Now worldwide, there are many applications of biometrics being used or considered. Most of the applications are still in the initializing stage of testing and are optional for end users. Any situation that allows an interaction between man and machine is capable of incorporating biometrics. The situations may fall into a range of application areas such as computer desktops, networks, banking, immigration, law enforcement, telecommunication networks and monitoring the time and attendance of staff. Fraud is an ever-increasing problem and security is becoming a necessity in many walks of life. palmprint based identification system has several special advantages such as stable line features, rich texture features, low-resolution imaging, low-cost capturing devices, easy self positioning, and user-friendly interface etc. For these reasons, nowadays the research related to this issue is becoming more active. So far, there have been many D.-S. Huang et al. (Eds.): ICIC 2008, LNAI 5227, pp. 1101–1108, 2008. © Springer-Verlag Berlin Heidelberg 2008

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S. Zhang, S. Wang, and X. Li

approaches proposed for palmprint recognition including verification and identification[1-3]. Zhang and Kong proposed PalmCode method, which employed one 2D Gabor filter to extract the texture feature of palmprint [4]. Zhang et al. used over-complete wavelet expansion and directional context modeling technique to extract principal lines-like features [5]. And in order to analyze the palmprint images in a multi-resolution-frequency representation, they also adopted wavelet transformation at the same time [6]. Ordinal Code proposed by Z.N. Sun et al. and Robust Line Orientation Code proposed by W. Jia were also using orientation feature for palmprint recognition [7-9]. A. Kumar proposed an approach combining hand shape and palmprint texture features [10]. Linear feature detection is a foremost problem in palmprint image processing and pattern recognition. The palmprint is composed of a number of points, lines and planes. Effective detections of these components play an important role in simplifying feature model in pattern recognition and pattern match. Ridgelet transforms, related to the wavelets and the Radon transform, offers a sound mathematical framework to organize linear information at different scales of resolution, and it performs very well for objects with point singularities two dimensions. However, in palmprint compression and image edge detection, both wavelets and Fourier transforms are far from efficient in extracting edges in images. Edges lie in the regions where the palmprint is discontinuous. So the palmprint data is regarded as a 2-D function, which is smooth away from line-like singularities and singular across edges. For a short straight line in the palmprint, we can use Radon transforms and Hough transforms to obtain it. But for a curve, the detection algorithm is very complicated. Ridgelet[11,12] is just a new analysis tool to get the efficient approximation of images by exhibiting some special sorts of higher-dimensional spatial in homogeneities, and it is developed on the basis of the concepts and methods of modern harmonic analysis and the group representations theory and wavelet analysis, which describes general functions as a superposition of ridge functions in a stable and concrete way. One interesting property of the ridgelet transforms is coefficient sparsely. Higher coefficients are concentrated around the angle θ and situation t corresponding to the longer lines in the image. Thus, the sparsity permits us to localize and to separate linear singularities into the parameter space. This is the main property that distinguishes this wavelet from usual separable wavelets. This paper presents a new method of palmprint identification using ridgelet transforms. Experimental results show that the method is more effective.

2 Relation between Ridgelet Transforms, Wavelet Transforms, and Radon Transforms The definition of ridgelet is as follows： Denoting a function ψ condition, 2

∫ ψˆ (ξ ) ξ

−2

: ℜ → ℜ , satisfying a

dξ < ∞

where, ψ is ridgelet base function, ψ a ,b ,θ in 2-D is defined from ψ ,

(1)

Palmprint Linear Feature Extraction and Identification

\ a ,b ,T ( x ) a 1 2\ (( x1 cos T x2 sin T b) a ) The continuous 2-D ridgelet transforms (CRT) of a signal

CRT f (a, b, T )

³\

( a ,b ,T )

1103

(2)

f ( x) can be written as

( x) f ( x)dx

(3)

The ridgelet inverse transforms as fellow

f (x )

2S

f

f

0

f

0

³ ³ ³

f (a, b, T )\ a ,b ,T ( x )

da dT db a3 4S

(4)

For comparison, the continuous 2-D wavelet transforms (CWT) of a signal f ( x ) can be written as

CWT f (a1 , a2 , b1 , b2 )

³

R2

\ a , a ,b , b ( x ) f ( x ) d x 1

2

1

2

(5)

where the wavelets in 2-D are tensor products

ψ

( a1 ,a2 ,b1 ,b2 ,θ )

( x) = ψ ( a ,b ,θ ) ( x1 ) ⋅ψ ( a ,b ,θ ) ( x2 ) 1 1

2 2

(6)

In 2-D, points and lines are related via radon transforms(RT), thus the wavelet and ridgelet transforms are linked via the radon transforms. More precisely, denote the Radon transforms as

RT f (θ , t ) = ∫ f ( x1 , x2 )δ ( x1 cos θ + x2 sin θ − t )dx1dx2 where

(7)

(θ , t ) ∈ [0, 2π ) × R .

As can be seen, the CRT is similar to the 2-D CWT except that the point parameters ( b1 , b2 ) are replaced by the line parameters( b, θ ). In other words, these 2-D multiscale transforms are related by Wavelets: ⇒ ψ scale, point− position ,

Ridgelets: ⇒ ψ scale,line− position (Seeing the Fig.1). The ridgelet transforms is the application of 1-D wavelet transforms to the slices of the Radon transforms, while the 2-D Fourier transforms is the application of 1-D Fourier transforms to those Radon slices. So in the two-dimensional case, the information provided by a ridgelet coefficient CRT f is just the one-dimensional wavelet coefficient of

CWT f , i.e. the radon transforms of RT f . Hence the ridgelet transforms is

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1D-Fourier transforms

Radon domain

1D-Wavelet transforms

Ridgelet domain

2D-Fourier domain

Fig. 1. Relations between transforms

precisely the application of a one-dimensional wavelet transforms to the slices of the Radon transforms of a function, where θ stands for the orientation of Radon transforms and t is a variable parameter. In fact, although it is an independent image transform, originated in the context of non-separable wavelets, the ridgelet transforms can also be explained as the combination of the Radon transform and the wavelet transforms. This particular point of view relates this work to other recent approaches for shape representation and retrieval based on the Radon/Hough transform application of wavelets to the Radon transform of an image. Therefore, as the Radon space corresponds to the parameters of the lines in the image, and applying wavelets allows to detect singularities, the ridgelet transforms will detect singularities in the Radon space, which will correspond to the parameters of relevant lines in the image. Therefore, the ridgelet transforms combines advantages from both transforms, the ability to detect lines, from the Radon transform, and the multiscale property of wavelets to work at several levels of detail.

3 Attribute Reducing Algorithm of Rough Set In a data table, it is well known that not all conditional attributes are necessary to depict the decision attribute before decision rules are generated. To acquire brief decision rules from decision systems, knowledge reduction is needed. Knowledge reduction for a database aims to search for some particular subsets of condition attributes that preserves the same properties as the condition attribute set. We denote

γ B (D) =

PosB (D) U

the dependency of decision attribute D to condition

attribute subset B ⊆ C , where PosB(D) is the subset of tumor samples whose neighborhoods consistently belong to one of the decision classes, and SIG(a, B, D) =γB(D) −γB−a (D) denotes the significance condition attribute a with respect to condition attribute subset B ⊆ C . The algorithm is described as follow:

Input: RD =< U , C , D > // RD is a rough decision table, U denotes tumor sample set // C is a condition attribute set, D is a attribute set


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red //reduction of condition attribute set C step1: red = ∅ ; //Initial red is set to empty set and is the

Output:

pool to contain the informative attribute. step 2:

∀ai ∈ C − red

For each Computing

// where, define

SIG (ai , red , C ) = γ (C , red ∪ ai ) − γ (C , red )

γ (C , ∅ ) = 0 , the dependency of subtype table

//the set C with respect to empty set is fixed to zero. step3: Selecting the informative gene ak satisfying

SIG ( ak , red , C ) = max( SIG (ai , red , C )) ; i

SIG (ak , red , C ) > 0

step4: if

red = red ∪ ak // Add the optimal gene ak to the reduction set red go to step2; else return red ; step5: Algorithm end;

4 A Method of Palmprint Identification by RT and RS The question about palmprint identification has complicated nature of incertitude. In many conditions, we always get cursory information in the beginning of investigation. So the key of the problem is how to engender the final rule using useful feature and original data. To deal with the decision information using ridgelet transforms gets feature vector. To express acquired rule uses the form of relation table and logic arithmetic. A method of plamprint identification is as follows: 1) To pretreatment the original plamprint images f ( m, n) (m, n = 0,1,2,…,

，

L −1) such as mending the miss data and uniting the repeated object.

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2) To select the ridgelet functionψ j , k ,i ( m, n) = a j ψ (2 −1

j

( L j ,i (m, n) − b j ,k )) ,

and to decompose ridgelet transforms for the pretreatment data, denoting the

α j , k , i = ψ j , k , i , f ( m, n ) . two thresholds λ , ε , for each k ,

coefficients 3) Ordering

plamprint images, Ak = {xi, j

defining two sets, toning up the

α j ,k ,i > λ} , Bk = ∪{xi, j α j,k,i −α j±1,k,i±1 > ε} . i, j

4) Calculate the ridgelet transforms energy of each k , get an eigenvector from the Ak , Bk , form the relation table consisting conditional attribute aggregate and decision attribute aggregate. 5) By above attribute reducing algorithm of rough set, to predigest the relation table, delete the redundant attribute and unite repeated object in turn, and predigest each object, delete redundant attribute. 6) To calculate the core valued and the possible predigesting of conditional attributes, and make relevant rule. For identification rules are not alone, we choose attribution table according to definite rule and get the excellent and brief rule finally.

5 Experimental Results and Analysis The objective of the experiments is to show the difference between attribute reduction with traditional rough set model and covering rough sets. As traditional model can just deal with discrete attributes, we employ two discretization techniques, equal-width, equal-frequency, to transform the numerical data into discrete one. There is a parameter to be specified in using covering rough sets to compute dependency, the size of the covering of an object. We try the size of covering delta at a step of 0.05. Before reduction, all of the numerical attributes are standardized at interval [0,1]. During the experiment, we employ radial basis function(RBF) kernel in support vector machine(SVM) learning algorithm to validate the selected features. The covering decision systems can be divided into consistent covering decision systems and inconsistent decision systems. The following experiments are designed for testing the accuracy and efficiency of the proposed method. The data collection process involves four steps: z z z z

Find 50 people of different ages, sexes and occupations. Capture six palmprint samples from each person. Randomly pick up one from the six samples to set up the database. Use the left 250 samples (each person has five) as the testing set.

All the palmprints are from right hand and are captured with the same palmprint capture device. Palmprint samples from the same palm may be with a little rotation and shift. The size of all the palmprint images is 240×240.


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To ridgletet transform for each palmprint image, obtaining coefficients. To give a threshold T, and order ⎧ 0 G i,k , j = ⎨ ⎩ 1

if if

c o e ffic ie n ts < T c o e ffic ie n ts

(8)

≥ T

Then, Gi , k , j is lines-image of the palmprint, seeing the Fig.3. The Fig.2 shows an example of palmprint-line-feature. Fig.2(b) is the palmprint-line-feature for k =54, Fig.2(c) is the fusion of palmprint-line-feature for k =54 and k =78, Fig.2(d) is the fusion of palmprint-line-feature for k =54, k =78, and k =126. From the figure2, all palm lines are represented clearly and accurately.

(a)

(b)

(c)

(d)

Fig. 2. Images appearing in feature extraction stage: (a) Original image; (b) line-feature image for k=54; (c) fusion line-feature image for k =54 and k =78; (d) fusion line-feature image for k =54, k =78 k =126.

We extract the feature vector from the coefficients, obtaining the relation table, every object in the table has 50 condition attributes. Basing on attribute reduction method of rough set, the number of condition attribute is reduced to 28. In this experiment, we use 30 samples as training data and the other 20 samples as testing data. We try the following two kinds of support vector machines: 1) Linear SVM (no kernel); 2) Radial basis function SVM (RBF kernel). Where, we select wavelet function Daubechies5. The results can be seen from table1. In order to compare, the palmprint identification based on other methods are given in table.1. Table 1. Results of palmprint identification rate Method Identification rate response time (s)

PCA and SVM 96% 12

ICA and SVM 95% 14

RT,RS and SVM 95% 8

The response time is recorded to evaluate the efficiency of the proposed method. From the table1, we can see the timing response is shorter using the method which is presented in this paper.

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6 Conclusions Mutual information has recently been proposed for feature selection. But it often contains redundancy in the feature set selected by this method. Attribute reduction in rough set theory provides a feasible way to deal with redundancy and does not reduce the contained information. In this paper, we introduce a method of feature extraction and identification for palmprint retrieval based on ridgelet transforms and rough set. First, the palmprints are first converted into the time-frequency domain image by ridgelet transforms, and then feature extraction vector is conducted. Different features are used to lead a detection table. Then rough set is applied to remove the redundancy of the detection table. Finally, the effectiveness of the proposed method is evaluated by the classification accuracy of SVM classifier. Experiments are carried out in order to measure the performance of the proposed method. Experimental results prove the efficiency of the proposed method. Acknowledgements. This work was supported by the grants of the National Science Foundation of China, Nos. 60705007 & 60772130.

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