Evolutionary Optimization Approach for
Fingerprint Classification
Jing-Wein Wang, Member, IEEE
1 Abstract—To test the effectiveness of GHM multiwavelets
in fingerprint classification with respect to scalar Daubechies wavelets, we study the evolutionary-based algorithm to evaluate the performance of each subset of selected feature. Comparatively studies suggest that the former transform features apparently contain more fingerprint information for discrimination than the latter.
Index Terms—GHM multiwavelt, Daubechies wavelet,
fingerprint classification, evolutionary-based algorithm
I. INTRODUCTION
ULTIWAVELETS have recently attracted a lot of theoretical attention and provided a good indication of a potential impact on signal processing [1]. In this paper, a novel fingerprint classification scheme is proposed both to extend the experimentation made in [1] and to test the effectiveness of the Geronimo-Hardin-Massopust (GHM) discrete multiwavelet transform (DMWT) [2] with respect to the scalar Daubechies wavelet [3]. Moreover, a point in genetic wavelet fingerprint analysis is that the chromosomes interact only with the fitness function, but not with each other. This method precludes the evolution of collective solutions to problems, which can be very powerful [4]. We further present an evolutionary framework for feature selection in which successive generations adaptively develop behavior in accordance with their natural needs. In the following sections, we give details of the propose fingerprint classification approach. The performance of the proposed method has been validated through experiments on the NIST special fingerprint database 4 (NIST-4) [5].
In the following sections, we give details of the propose fingerprint classification approach. Section II presents the example transformations for a fingerprint image. Section III describes the proposed coevolutionary feature selection scheme for classification. In section IV, we present our experimental results tested on the NIST-4. Section V concludes the paper.
1 Manuscript received Mar 06, 2011; revised Apr 07, 2011. This
work was supported in part by Taiwan, ROC, National Science Council under Grant NSC 99-2221-E-151 -057.
J. W. Wang is with the Institute of Photonics and Communications, National Kaohsiung University of Applied Sciences, Kaohsiung 807, Taiwan, ROC (phone: +886-930-943-143; fax: +886-7-383-2771; e-mail: jwwang@ cc.kuas.edu.tw).
II. DISCRETE MULTIWAVELET TRANSFORMS
For a multiresolution analysis of multiplicity r > 1, (MRA), an orthonormal compact support multiwavelet system consists one multiscaling function vector Φ(x)(1(x),...,r(x))T and one
multiwavelet function vector )) ( ..., ), ( ( ) (x 1 x x
Ψ r T. Both Φand Ψsatisfy the following two-scale relations:
) 2 ( 2 ) (x H Φ x k Φ k k
Z (1) ) 2 ( 2 ) (x GΦ x k Ψ k k
Z . (2)Note that multifilters {Hk} and {Gk} are finite sequences of r × r matrices for each integer k. Let Vj, j Z, be the closure of the linear span of
) 2 ( 2 /2 , ,jk j l jx k l , l = 1, 2,…, r. By exploiting the properties of the MRA, as in the scalar case, any continuous-time signal f(x) V0 can be expanded as
) ( ) ( 1 0, , x k c x f r l k l k l
Z 2 (2 ) 1 2 / J, , x k c J r l k J l k l
Z 2 (2 ) 1 0 2 / , , x k d j r l J j k j l k j l
Z , (3) where
c jk cr j k
T k j , 1 , , ,..., , , c (4)
d jk dr jk
T k j , 1 , , ,..., , , d (5) and dx k x x f cl ,j ,k
( )2j/2l(2j ) (6) dx k x x f dl ,j ,k
( )2j/2l(2j ) . (7) For the two-dimensional discrete multiwavelet transform, a 2-D MRA of multiplicity N for L2(R2)M
Proceedings of the World Congress on Engineering 2011 Vol II WCE 2011, July 6 - 8, 2011, London, U.K.
ISBN: 978-988-19251-4-5
chromosomes are combined by the following proposed combinative crossover criterion so as to toward the chromosomes of two offspring individuals. If the i-th genes of the inter and intra individuals are the same, then the i-th gene of the offspring individual is set as either individual. If not, the i-th gene of the offspring individual will be set as either individual at random. The size of each of the population remains constant during evolution. The mutation operation randomly changes a bit of the chromosome.
V. EXPERIMENTS RESULTS AND DISCUSSIONS
The reported results have the following parameter settings: population size = 20, number of generation = 1000, and the probability of crossover = 0.5. A mutation probability value starts with a value of 0.9 and then varied as a step function of the number of iterations until it reaches a value of 0.01. Due to the curse of dimensionality, one hundred 256 × 256 overlapping subimages each class as training samples are used for the D4 wavelet and one thousand samples are used for the GHM multiwavelet. Textural features are given by the extrema number of wavelet coefficients [8], which can be used as a measure of coarseness of the fingerprint at multiple resolutions. Then, fingerprint classifications with feature selection were performed using the simplified Mahalanobis distance measure [9] to discriminate fingerprint textures and to optimize classification by searching for near-optimal feature subsets. The mean and variance of the decomposed subbands are calculated with the leave-one-out algorithm [9] in classification.
The performance of the classifier was evaluated with three different randomly chosen training and test sets. Algorithms based on the two types of wavelets have been shown to work well in fingerprint discrimination. The classification errors in Tables 1 and 2 mostly decrease when the used features are selectively removed from all the features at the decomposed levels 4 and 3, respectively. This decrease is due to the fact that less parameter used in place of the true value of the class conditional probability density functions need to be estimated from the same number of samples. The smaller the number of the parameters that need to be estimated, the less severe the curse of dimensionality can become. In the meanwhile, we also noticed that the multiwavelet outperforms the scalar wavelet with the packet-tree feature selection. This is because the extracted features in the former are more discriminative than the latter and, therefore, the selection of a subband for discrimination is not only dependent on the wavelet bases, wavelet decompositions, and decomposed levels but also the fitness function.
To explore the performance of the proposed system, we report classification results on NIST-4 database with seven categories: right loop (437
images), left loop (484 images), tented (149 images), arch (530 images), S-type (twin loop) (110 images), whorl (241 images), and eddy (49 images). We compare our method to a few modern techniques as shown in Table 3. Our method not only achieves more accuracy in 4 and 5 classes than referred methods [10]-[13] with lower rejection rate, 7-class offers new report in classifying whorl, S-type, and eddy types, as well. On the other hand, we notice that there are some failures occurred in the experiments and the reasons can be summarized as the following. The indistinct ridges and valleys due to bad quality of the fingerprint image may lead to the fatal errors of wavelet extrema detection.
VI.CONCLUSIONS
This paper introduces a promising evolutionary algorithm approach for solving the fingerprint classification problem with the coevolving concept. While much of the researches are fighting to work out on the classification of four or five categories, even one or two seven classes, we have not joined the drive instead of reporting a new result on whorl, S-type, and eddy classes except general arch, tented arch, right and left loops.
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Proceedings of the World Congress on Engineering 2011 Vol II WCE 2011, July 6 - 8, 2011, London, U.K.
ISBN: 978-988-19251-4-5
