1-4244-1355-9/07/$25.00 @2007 IEEE

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Fast Search Methods for Biometric SignalProcessing

Snehal PatelMEngTech(Electrical and Electronic Engineering)

Abstract—The aim of this paper is to investigate some currentbiometric algorithms - which are basically statistical patternmatching and pattern database searching- and ways of speedingthem up. This will encompass both optimal (where the matchfound is identical to an exhaustive search) and suboptimal tech-niques. Implementation of the fast-search algorithms investigatedto determine both the computational complexity and optimalityof the search performance. The fast evolution and increasingcomplexity of computing platforms poses a major challengefor developers of fast algorithms for signal processing. Eventhough processor speeds have increased dramatically, the ever-increasing complexity of algorithms being investigated for signalprocessing applications still places constraints on processingtimes. This is particularly evident in the area of biometric signalprocessing. Airport security is a major issue after the event of9/11. Now countries have started issuing biometric passports or‘smart‘ passports[20], which are basically an embedded chip,containing information of the identity of the person. Thereare many biometric identification techniques currently underinvestigation, including voice, face, and iris, fingerprint, andsignature identification. Each technique has its strength andsome limitations. One problem with countries issuing biometricpassports or ‘smart‘ passports is that even if the algorithmswork well (which they don’t always), the speed of processing isa problem in many application domains (for example, Airportswhere large numbers of individuals need to be screened quicklybut with a high degree of accuracy). Code for vector quantizationand fast vector quantization search methods was developed usingMATLAB.

I. INTRODUCTION

Biometrics has started playing an important role in airportsecurity after the events of 9/11[20]. The term ”Biometrics”refers to a science involving the statistical analysis ofbiological characteristics basically for human identification.Biometrics is best defined as measurable physiological and/or behavioral characteristics that can be utilized to verifythe identity of a person [1]. The complexity of designinga biometric system based on three main factors (accuracy,scale or size of the database, and usability)[2]. Essentially,the science of biometrics aims to identify a person within adatabase. This study carried out to investigates fast algorithmsfor biometric signal processing. This defines statistical patternmatching for pattern matching. The main focus of this paperis the computational complexity related to signal processingapplication especially in biometric passports or ‘smart‘passports which is currently a major research area.

II. STATISTICAL PATTERN MATCHING

Statistical pattern matching is to compare pattern whichis represented in the terms of d features or measured andviewed as a point in d-dimensional space [14]. The goal isto choose those features that allow pattern vectors belongingto different categories to occupy compact and disjointregions in d-dimensional feature vectors[13]. There areseveral behavioral and physical characteristics of biometricidentification which are used for pattern matching purpose.In this input sample is to be match with feature samples andfind best possible match by finding minimum mean squarederror between given sample and features samples.

III. VECTOR QUANTIZATION (VQ) AND FAST VQSEARCH METHODS

A. Vector Quantization (VQ)

A vector quantization Q of dimension k and size N is amapping from a point in k- dimensional Euclidean space,Rk

into a finite set C containing N output or reproduction pointsthat exist in the same Euclidean space as the original point.These reproductions points are known as codeword and thesesets of codeword are called a codebook C with N distinctcodeword in the set. Thus the mapping function Q is denotedas,

Q : → Rk (1)

The representative codeword is determined to be the closestin Euclidean distance from the input vector. The Euclideandistance is defined by:

d(x, yi) =

√√√√ k∑j=1

(xj − yij)2 (2)

B. Fast VQ Search Methods

There are several techniques to reduce computationalcomplexity for statistical pattern matching. A directcalculation of the distance metric for each code vectorin the codebook for a given source vector is generally calledan exhaustive search [19]. There are several techniques to theVQ search algorithm to reduce the computational complexity.

Fast VQ search methods are in following categories:

(1) Partial-distance search techniques:

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Eliminate certain code vectors from the search before thefull distortion is calculated. The computational reductionattainable depends upon how early code vector may beeliminated as a candidate in the current search.

PDS method includes in [3], [10], [12] and [15].

(2) Algebraic simplifications:This approach uses a mathematical simplification of the

distortion metric to both pre-calculate certain constants andapply preliminary tests to remove certain code vectors fromcandidate.

Algebraic simplifications method includes in [5],[6] and[11].

(3) Region of Interest(ROI) partitioning:By considering the search process in Rk, a region of

interest may be used to prune the search to a much smallernumber of admissible candidate code vectors. This method isthe most powerful of all, but requires a very large memoryspace.

ROI method includes in [4], [7], [8] and [18].

C. Partial Distance Search

The main concept is to terminate the search if distortionexceeds the dmin which is defines the minimum distortion.The minimum distortion encoding of a test vector, using theconventional full-search algorithm for a codebook of size N(= 2kR ,k being vector dimension and R the bit rate) requiresN vector-distance computations [3].

The logic is as follows:

• Define minimum distortion dmin (Very large number)• Calculate D which is difference between image block and

codebook vector if D exceeds dmin , exit from the loop• Go to next index• Calculate D once again and check if D is exceeds dmin

or not• Large codebook required.

It can be observed that the partial-distance search algorithmgains computation saving over the full search algorithm be-cause of the provision for a premature exit from loop onsatisfying the condition D > dmin (called the exit conditionhenceforth) before the completion of distance computationd(X, ci)[3].

D. Rotated Partial Distance Search method

In this method, during calculation of distance sum, if thepartial distance exceeds the distance to the nearest neighborfound so far, the calculation is aborted [12]. It decreases thecomputational complexity.

IV. TESTING METHODOLOGY

All source code is executed within the MATLAB envi-ronment. For the scope of this paper, VQ, PDS and RPDSmethods are investigated.The code is tested on experimentalimages before being applied to the actual system. VQ isdeveloped and tested is structured in the format depicted infollowing steps:

• Original image is divided in blocks (4 x4, 8 x 8, and 16x 16).

• All the blocks of image stored in to row array.• Quantize codebook using training vectors.• Select random block of training vectors and compare

it with codebook vectors and calculate minimum mean-square error.

• Using that index, design a new codebook• Reconstruct image• Calculate number of floating point operations in order to

demonstrate computational complexity of VQ.• Calculate PSNR.

Fig. 1. Test images 256 x 256 dimension (bmp)

Fig. 2. Test image 512 x 512 in dimension

V. SIMULATION RESULTS

Simulation results based on PDS and RPDS methods, arebasically fast VQ search in order to reduce computationalcomplexity.

A. Floating point operations

The computational complexity is defined by the number offloating point operations. Table 1 and 2 show the comparisonof the number of floating point operations between VQ andfast VQ search methods.

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TABLE INO OF FLOATING POINT OPERATIONS BETWEEN VQ AND PDS

Block Floating Floating Bit RateSize Point Point (bbp)

operations operations(VQ) (PDS)

4 1225000 1176000 28 1254500 1204320 1.2516 1538000 1345750 1.0625

TABLE IINO OF FLOATING POINT OPERATIONS BETWEEN VQ AND RPDS

Block Floating Floating Bit RateSize Point Point (bbp)

operations operations(VQ) (RPDS)

4 1225000 1123521 28 1254500 1214163 1.2516 1538000 1381124 1.0625

Fig. 3. Comparison of number of floating point operations (VQ and PDS)

Fig. 4. Comparison of number of floating point operations (VQ and RPDS)

TABLE IIICOMPARISON OF COMPUTATIONAL COMPLEXITY IN PERCENTAGE

Block size VQ Vs PDS VQ Vs RPDS4 4 8.38 4 3.216 12.5 10.2

The computational complexity reduction in percentage isshown in w table III.

B. Peak Signal to Noise Ratio

The Peak signal to noise ratio is calculated base on theoriginal image and reconstructed image. Peak signal to noiseratio is the same for both VQ and PDS for same block sizeto verify algorithm. The formula to calculate PSNR is

20 log(origimage/recimage)dB (3)

PSNR compares mean values of original image and recon-structed image.Tables IV and V show the comparison of peak signal to noiseratio(PSNR).

TABLE IVCOMPARISON OF PEAK SIGNAL TO NOISE RATIO (VQ AND PDS)

Block size PSNR (VQ)in dB PSNR (PDS) in dB

4 10.15 10.158 6.14 6.1416 2.74 2.74

TABLE VCOMPARISON OF PEAK SIGNAL TO NOISE RATIO (VQ AND RPDS)

Block size PSNR (VQ)in dB PSNR (RPDS) in dB

4 10.15 10.158 6.14 6.14

16 2.74 2.74

C. Reconstruction of Image

Image would be reconstructed using new codebook whichis generated using codbook vectors and the image vectors.

VI. ACKNOWLEDGEMENT

The author would like to thanks organizers of ICIAS2007.

VII. CONCLUSION

This study carried out fast search methods for biometricsignal processing using statical pattern matching. vectorquantization is used for pattern matching and improveperformance using fast VQ search methods. The aboveresults reflect the fact that fast VQ search methods areable to reduce the computational complexity by a certainamount. It is reduced very less in percentage but still

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effective. There are also several other methods to reducecomputational complexity. If the codebook search reducesthen the computational complexity also reduces. The largerthe block size the greater the reduction in the computationalcomplexity. This research work will carry out to find optimalsolution for Biometrics.

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