2009 IEEE International Advance Computing Conference (IACC 2009)Patiala, India, 6-7 March 2009

A new Wavelet based Edge detectionTechnique for Iris Imagery

Avijit Sur Nilanjan PatraStudent, Instrumentation and Control Engineering Dept. Student, Instrumentation and Control Engineering Dept.

Academy Of Technology, Adisaptagram-712121 Academy Of Technology, Adisaptagram-712121West Bengal, India West Bengal, India

sur avijit.ice(&rediffmail.com nilanj anaot(ggmail.comSantanu Chakraborty Indrajit Saha

Student, Instrumentation and Control Engineering Dept. Lecturer, Information Technology Dept.Academy Of Technology, Adisaptagram-712121 Academy Of Technology, Adisaptagram-712121

West Bengal, India West Bengal, Indiasantanuaot ailcom indra rajugyahoo.conn

Abstract-In this paper, we present a novel design of a wavelet as a "window" function, and then calculated the Fourierbased edge detection technique. Edge detection is an important transform of a function in the "sliding window". The Gabortask in image processing. Edges in images can be mathematically transform is useful for time-frequency analysis. The Gabordefined as local singularities. Until recently, the Fourier transform was later generalized to the windowed Fouriertransforms was the main mathematical tool for analyzing transform in which g is replaced by a "timelocal" functionsingularities. However, the Fourier transform is global and not called the "window" function. However, this analyzingwell adapted to local singularities. It is hard to find the location functis nt thesolutiniand spatial distribution of singularities with Fourier transforms. function has the disadvantage that the spatial resolution isWavelet analysis is a local analysis; it is especially suitable for limited by the fixed size of the Gaussian envelope [2].Thetime frequency analysis, which is essential for singularity most preeminent books on wavelets are those ofMeyer [4], [5]detection. The fact motivated us to develop a technique using and Daubechies [6]. Meyer focuses on mathematicalHaar wavelet to find an edge from an image. The proposed applications of wavelet theory in harmonic analysis.technique has been demonstrated for iris imagery and the Daubechies gives a thorough presentation of techniques forreported results have been compared with Daubechies D4 constructing wavelet bases with desired properties, along withwavelet based edge detection technique. a variety of methods for mathematical signal analysis [7]. A

Index Terms-Haar wavelet, Daubechies D4 wavelet, Edge particular example of an orthonormal wavelet system was

detection, Iris Imagery. introduced by Alfred Haar [8]. However, the Haar waveletsare discontinuous and therefore poorly localized in frequency.

I. INTRODUCTION St'ephane Mallat [9], [10] made a decisive step in the theoryof wavelets in 1987 when he proposed a fast algorithm for the

The concept of wavelet analysis has been developed since computation of wavelet coefficients. He proposed thethe late 1980's. However, its idea can be traced back to the pyramidal schemes that decompose signals into sub bands.Littlewood.Pale techniqueandCalder'on-Zygmund theory These techniques can be traced back to the 1970s when theyLittlewood-Paley technique.an were developed to reduce quantization noise [1 1]. The

[1] in harmonic analysis. Wavelet analysis is a powerful toolfor time-frequency analysis. Fourier analysis is also a good framework that unifies these algorithms and the theory oftool for frequency analysis, but it can only provide global wavelets is the concept of a multi-resolution analysis (MRA).frequency information, which is independent of time. Hence, In 1997, Chui and Wang [12] further discussed thewith Fourier analysis, it is impossible to describe the local asymptotically optimal time frequency localization by scalingproperties of functions in terms of their spectral properties, functions and wavelets. In their paper they proved thewhich can be viewed as an expression of the Heisenberg convergence of the time-frequency window sizes of cardinaluncertainty principle [2]. In many applied areas like digital polynomial B-wavelets, which are used in Mallat's algorithmsignal processing, time-frequency analysis is critical. That is, and are important in many other wavelet applications.

An edge in an image is a contour across which thewe want to know the frequency properties of a function in a br1ghtness of the image changes abruptly. In magelocal time interval. Engineers and mathematicians developedanalytic methods that were adapted to these problems, prcsig.neg i fe nepee asne.las.otherefore avoiding the inherent diffitculties in classical Fourier siglrte. In a....fucin iglrtescnb hrceieanalysis. For this purpose, Dsennis Gabor [3 introduceda eaiyaaicniute hr h rdetapoce1- 1- * 1 r*TT * . 1~~~~~~nfinity. However, image data iS discrete, SO edges in an imageslidng-wndowtehniqe. H use a aussan fnctin g often are defined as the local maxima of the gradient. Edge iS978-1-4244-1888-6/08/f$25.00 Q 2008 IEEE 120

a main tool in pattern recognition, image segmentation, and W -2scene analysis. An edge detector is basically a high pass tfilter that can be applied to extract the edge points in an g LL HLimage. This topic has attracted many researchers and many Sachievements have been made [7], [13], [14], [15], [16], [17], hi[18]. In this paper, we will explain the mechanism of edgedetectors from the point of view of wavelets and develop a LH 11way to construct edge detector using wavelet transforms.

The rest of the article is organized as follows: Section IIand III briefly describe popular edge detector as well as some Xwavelet functions. In section IV describes the propose Figure 1. Wavelet multiresolution property of an image: (a) represents originaltechnique. Section V presents the experimental results image, (b) a one-level decomposition produces 4 sub-bands, namely LL, LH,conducted on several iris imagery. Finally, Section VI HH and HL.concludes the article. B. The Daubechies D4 Wavelet Transform

II. POPULAR EDGE DETECTOR The Daubechies wavelet transform is named as themathematician Ingrid Daubechies. The Daubechies wavelet isconceptually more complex and has a slightly higher

Many classical edge detectors have been developed over compual ore The aubehis D transfor hastime. They are based on the principle of matching local image fomur alionga wavelet.fun ecies. the salsegments with specific edge patters. The edge detection is. functin r unction coeffichents. The scaligrealized by the convolution with a set of directional derivative ' 'masks [19]. The popular edge detection operators are Roberts, I d 7Sobel, Prewitt, Frei-Chen, and Laplacian operators [15], [16], h, (3)[19], [4]. They are all defined on a 3 by 3 pattern grid, so theyare efficient and easy to apply. In certain situations where the 3 +edges are highly directional, some edge detector works h(especially well because their patterns fit the edges better.

h4 3-4 (III. WAVELET TRANSFORM 41

Wavelets are composed of two bases, a scaling and a 40wavelet basis. The scaling basis deals with how the waveletrepresents a signal over a given frequency band. The wavelet The wavelet function coefficients of the Daubechies D4basis shows how the wavelet sees the transients in a signal on wave- let transform are go, g1, g2, g3. Each step of the waveleta given frequency band. Two popular wavelets are described trans- form applies the scaling and wavelet functions to thein below. data input. The derivation for the coefficient values can be

found in Ingrid Daubechies work [6], [20].A. The Haar Wavelet Transform

P - {+Ue ....I h . (7)The Haar wavelet has the advantage of being simple to

compute and easy to understand [8], [20]. Each step in the I9 1(2 (S)Haar wavelet transform calculates a set of scaling coefficients

972 (+ve) h1and a set of wavelet coefficients. If a data set do, dl, ,dn (9)contains n elements; there will be n/2 scaling coefficients and Xue)N (1O)n/2 wavelet coefficient values. The scaling coefficients arestored in the lower half of the n element array and the wavelet The scaling values, s,, and the wavelet values, w, arecoefficients are stored in the upper half. For two dimensional calculated by taking the inner product of the hj and gjmatrixes the wavelet transform has performed both horizon- coefficients (0 < j < 3) and the signal. Note that, it alsotally and vertically. It creates four different subbands named works same as Haar wave let for two dimensional matrixes toas LL, HL, LH and HH as shown in Fig. 1. The Haar wavelet create different sub-bands. Daubechies D4 wavelet is creatingto calculate an scaling coefficients (se) and a wavelet co- a problem for the edge of the image. The problem has solvedefficient (w,) from an odd and even element in the data set are any one of these three methods:shown below: * Treat the data set as if it is periodic. The beginning of

X+ d n ( the data sequence repeats falling the end of thesequence.

a .~~~~~~~~~~~~~Treat the data set as if it is mirrored at the ends. Thisx 9 8 t~~~~~(2 means that the data is reflected from each end, as if

a mirror were held up to each end of the datasequence.

2009 IEEE Internlationlal Advance Computing Conference (IACC 2009) 12:1

Figure 2. Block Diagram of Propose Technique.

* Gram-Schmidt orthogonalization. Gram-Schmidt image. If an element in the LH sub-band is Vm,n, an element inorthoganalization calculates special scaling and the HH sub-band is dm,n and an element in the HL sub-band iswavelet functions that are applied at the start and end hmn, then the corresponding element em,n in the edge image isof the data set. given by Eqn. 11.

IV. PROPOSED WAVELET BESED EDGE DETECTION C = + d + h (11)TECHNIQUE

Let w and h be the width and height, respectively, of the LH,The proposed technique has composed with four different HH and HL sub-bands. Where I .m . wand I .n .h. Fig.

blocks as shown in Fig. 2. Each of these blocks is described indetail in next. 3.(b)/(c) shows the constructed edge image from the LH, HH

and HL sub-bands of Fig. 4.(a) using Eqn 11. In our system,we use the LH, HH and HL sub-bands of the one-level

A. Input Image decomposition because they have more detailed information ofthe dominant edges in the original image. Note that, here in

The images are used in this paper in the form of grey this method we consider the threshold as to make the edgecolour model'. The size of the images is considered here is very prominent which is shown in Fig. 4.512 x 512 pixel where each pixel contains different intensityvalues of grey from 0 to 255. The input image is processed D. Output Imageand set to forward for the next block.

The edge image of that given image has stored in the LLB. Wavelet Transform sub-band which is the desired output as we want get. It shown

in Fig. 3. (b)/(c).The image which is come from the previous block is used

here for the wavelet transform. The different wavelets aredescribed in section III are applied on the processed image V. EXPERIMENTAL RESULTwhich creates different sub-bands like LL, LH, HH and HL.Note that, when the Daubechies D4 wavelet transform is The result is reported by Fig. 3. The proposed techniqueapplied on the image, edge problem has to be taken in to has found the edges from the images which are very evidentconsideration and one of the technique as described in section and clear by the visualization. The Haar wavelet transformIII is used to solve it. produces the better result over the Daubechies D4 wavelet

transform. For example of third image of Fig. 3, the edgesC. Edge Detector found by the Haar wavelet transform is very clear than the

edges found by the Daubechies D4 wavelet transform. SimilarThis is the main block where the detection of the edge results are also found for the rest of the images. However the

from the image has to be performed. From a signal processing different sub-bands are used to get the edge from the imagepoint of view, the wavelet transform is basically a convolution where Haar wavelet sub-bands contains the more edgeoperation, which is equivalent to passing an image through information of the original image rather than the Daubechieslow-pass and high-pass filters. Let the original image be I(w, h), D4 wavelet.then the LH sub-band represents the vertical edges, HL sub-band represents the horizontal edges and HH sub-band VI. CONCLUSIONrepresents the diagonal edges of I(w, h). Using these propertiesof the LH, HH and HL sub-bands, we construct an edge In this article a novel edge detection technique using

wavelet has been developed. The developed technique has1CUHK Iris Image Dataset Date of Generation: 13 March 2003. Authored by: performed over six iris imagery and produces very promisingCHUN, Chun Nam Ben (e-mail: cnchun@acae.cuhk.edu.hk). Copyright: result. It also compared with Daubechies D4 waveletComputer Vision Laboratory, Department of Automation & Computer-Aided transform where Haar wavelet transform produces betterEngr., The Chinese University of Hong Kong, Hong Kong. Important: The result. Haar wavelet transform analysis is essential fordata set can be freely used for non-profit making education or research . .. .purpose provided that the source of the dataset is cited fully; any other use sigularity detecton which results as an edge of the origialhowever must first obtain prior agreement from the Computer vision image. Good performance of this technique for such imageryLaboratory, Department of Automation & Computer-Aided Engr., The shows that it may be motivating to use this algorithm in otherChinese university of Hong Kong, Hong Kong. contact: Prof Chung, Chi Kit Imagery applications also.Ronald (e-mail: rchung@acae.cuhk.edu.hk, Tel: (852)26098339, Fax:(852)26036002) As a scope of further research this technique can also be

extended for clustering, indexing and retrieval of image.

1122 2009 IEEE Internlationlal Advance Computing Conference (IACC 2009)

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using Haar~~~~~~~~ an Daubechis D4aveets

20IEEItrainlAvneCmuing Cofrec (IC 2009) 12

int edge_detector(int *LH[AJ4XCOLS], int *HH[MAXCOLS], int *HL[MAXCOLS], int cols, int rows){int ij, *EG[MAXCOLSI, *LLfMAXCOLSI, Threshold=2, /* Variable delaration *7for(i=0, i<rows, i++){

EGfi]=(int *)malloc(cols *sizeof(int)). /* Dynamic matrix allocation *7LLfih=(int *)malloc(cols*sizeof(int)),.

Vfor(i=0, i<rows, i++)fori=0,j<colsj+ +)

*(*(EG+i) +j)=sqrt(pow(*(*(LH+i) +j),2)+pow(*(*(HH+i) +j),2) +pow(*(*(HL+i)+j),2)),l/* Edge Computaion *7

for(i=0, i<rows, i++)fori=0,j<cols,j++)if('*(*(EG+i) +j)< =Threshold)

*(*(LL+i) +j) =255,else

*(*(LL+i) +j)=0, /* Making Edge to Prominent*7return (*LLfcols]), / Returning Edge Matrix *7

L}IFigure 4. 'C' code of Edge Detector.

ACKNOWLEDGMENT [14] B. K. P. Horn, The Binford-Horn line-finder, Artificial Intell. Lab.,Mass. Inst. Technol., Cambridge, Al Memo 285, 1971.

The work has been partially helped by the producer of this [15] L. Mero, "A simplified and fast version of the hueckel operator forgiven imagery. Wewol*asthis inding optimal edges in pictures," Pric. IJCAI, pp. 650-655, 1975.

given Imagery. We would also thankful to the CEO Of thlS [16] R. Nevatia, "Evaluation of simplified hueckel edge-line detector,"college for producing such a good platform of work and also Comput., Graph., Image Process., vol. 6, no. 6, pp. 582-588, 1977.thankful to the sponsor of this conference for giving us an [17] Y. Y. Tang, L.H. Yang, and L. Feng, "Characterization and detection ofopportunity to produce our article. edges by lipschitz exponent and MASW wavelet transform," Proc. 14th

Int. Conf. Pattern Recognit.,Brisbane, Australia, pp. 1572-1574, 1998.[18] K. A. Stevens, "Surface perception from local analysis of texture and

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1124 2009 IEEE Internlationlal Advance Computing Conference (IACC 2009)