A Study to Develop Human Face Recognition using PCA, Neural Networks and Wavelet

A Study to Develop Human Face Recognition using PCA, Neural Networks and Wavelet

Jaimin H Jani Dr. Subhash chandra Desai

Abstract-A method to improve the precision of the face recognition with the help of an integrating of WT, PCA and neural networks has been presented in this paper. The three main critical issues for face recognition are- preprocessing, feature extraction and classifying rules. A hybrid approach for employing the three issues has been presented in this paper. A combination of wavelet transform (WT) and PCA has been used for preprocessing and feature extraction. Neural Network is discussed for achieving a fast decision in the presenceofvarietyoffacialexpressions,intheclassificationstage.Ov erall,improvisationsintheproposed methods accuracy isdone.

INTRODUCTION

Theauthenticationofusershavebeenincreasinginthepastf ewyears,becausetherequirementofsecurity isomnipresent.originally,identificationcardsandpasswo rdswerepopularforprovingauthenticity,though security through these methods is not very reliable. The latest interest of the researchers are authentication technologies based on biology, such as the ones that use iris, fingerprint, face, print of the palm and voice. Face recognition has gained popularity, largely because the process of authentication is done in a hands free way, without interrupting the activity of the user in any way. also, it is economic due to the low cost of the cameras and computer. Psycho-physicists and neuroscientist have focused on issues like face uniqueness, organization of face memory and the perception of faces by infants in the past 20 years. At the same time, engineers have studied, developed and designed algorithms of face recognition in the last 20 years. This paper focusses on the work of the engineers. Content based approach and face based approach are the two approached of face recognition system done by the computers.

There lation ship between the face boundary and facial eatures like nose, eyes, mouth are used in the content based approach. A huge classification error can be committed in the process of derivation, since all the human faces have features that are similar.

Inthefacebasedapproach,thefaceiscapturedasawholean distreatedasa2Dpattern.Thefaceismatched with the statistical regularities. Principal Component Analysis (PCA) is a face based approach, which has been proven to beeffective.

Karhunen- Loeve (KL) transform was proposed the representation of human faces by Sirovich and Kirby. The faces are represented with the help of eigenfaces, which are the linear combinations of weighed

eigenvector, in this method. However, a system of face recognition that makes use of the PCA has been developed by Turk and Pentland. But, this method is not free from limitations. The two limitations of this methodsarelargeloadofcomputationandpoor powerofdiscrimination.Themeasuredsimilaritybetween 2 pictures of the same individual by using the PCA method is high. However, the measured similarity of 2 pictures of different people is also high. Therefore, the discrimination power of this PCA method is very poor.

This drawback of PCA was improved by addition of Linear Discriminant Analysis (LDA) by Swets and Weng. A different method for selection of eigenfaces was suggested by OToole et al. they stated that the eigenvectors which have large eigenvalues is not the best method to differentiate face image. It was also presented by them that the representations of low dimension are efficient in identification of physical features of the face, like race and gender even though they might not be the best way for the recognition of human faces.

Heavyloadofcomputationintheprocessoffindingeigenve ctorsisanotherprobleminPCAbasedmethod is the h. The typical value of computational complexity of O(d2) is 128×128, where d= number of pixels. The cost of computation is beyond many existing computers power. However, Matrix Theory tells us that if the number of training images (N) is smaller than the value of d, the complexity of computation will be decreased to O(N2). Then also if N will increase the load of the computation is increased in cubic order. A newapproachintheapplicationofPCAinthelightofthealre adyexistingPCAapproachhasbeenproposed here. It is proposed that in this method, the image is decayed into many sub bands using the wavelet transform with many frequencycomponents.

Theresultshaveshownthatthe3 levelwavelethasperformedwellinfacerecognition.Them ethodwhich hasbeenproposedinthispaperdoesntworkontheimagere solutionof128x128,butonalowerresolution of 16×16. Hence, the computational complexity is reduced significantly for many applications, where the training images are more than 16×16. increASed accuracy in the recognition and better discrimination power was observed when PCA was applied on wavelet transform (WT) than when PCA was applied on the entire of the

original image.

REVIEW OF PCA

resolution of 16×16 is enough for human face recognition. When compared to the original image having a resolution 128×128, it leads to a reduction

Some major details of PCA are as follows:

Let X = {Xn,n = 1,…, N} R be an ensemble of vectors. When dxd is the product of width and height of the image, the row concatenation of the data of the image is form in the applications of imaging.

1 N

Let be the average vector in the ensemble E( X) =X N n=1fter subtracting the average from each

off the sub image by 64 times, thus implying a reduction on the computational load of 64 times.

• Theimagesaredecomposedintosubbandswhichcorres

  pondtovariousfrequencyrangesundertheWTmethod. The computational overhead is minimized as the

  sub bands readily meet the input requirement in the system proposed in this paper.

• While the Fourier decomposition support only the

  global information in the frequency domain, the WTmethodofdecompositionofimagesprovideslocali

  elementof X, a

  elementof X, a

  nformationindomainsfor bothfrequencyandspace.

  In mthoidsifpieadper, we applied two well-known mother

  ensemble of vectors, X = {X n ,n = 1,…, N} with Xn = Xn E( X ) is received .

  covariance matrix M for the ensemble X is defined by M = cov(X ) = E( X X ) , Where M is d 2 xd

  2 matrix, with elements.

  It is a well-known fact of the matrix theory that matrix M is always positive and will only have eigenvaluesthatarenon-negative.ThematrixM oftheeigenvectorsformabasisforRdxd.Thisbasis is called K-L basis.

  The eigenvectors in K are arranged in a descending order of eigenvalues in many applications. In order to compute the dxd eigenvalue from M, 2xd2 matrix has to be solved. In most chances, d=128, hence 16×16 matrix is solved for calculating the eigenvectors and eigenvalues.

  Computer systems requirement for the memory and computation are very high. Matrix theory states that ifN<dxd,thatisN,whichisthenumberoftrainingimage,iss mallerthanM,thecomputationalcomplexity decreases to O(N). Therefore, the implementation of PCA in characterizing the faces has become flexible. The number of training images in most researches is around

  200. But the M rises when the total number of training images in huge, such as2000.

  An images Wavelet decomposition

  In last 10 years, WT has become a useful tool in the analysis of the image. In this paper, WT has been chosen as the option of choice for image decomposition because-

• The resolution of the sub images are decreased when

an image is decomposed by using the WT method. so, the computational complexity also decreases because it operates n an image which has alow resolution. It was observed by Harmon that a

wavelet Daubechies and Haar. We proposed method that uses by coefficients:

h0 = 0.48296291314453 p =0.83651630373781

p =0.22414386804201

p =0.12940952255126

For daubechies mother wavelet and coefficients: h0 =0.5,p =0.5

PROPOSED METHOD

In order to overcome the limitations of the PCA method, this wavelet based PCA method has been developed. also, utilizationof neural networks have been used for classifying faces. A multilayer architecture was adopted,which is fed by the vectors formed by combining wavelet and PCA and decreased inputunits.Usingaparticularfrequencybandofanimageof thefaceforPCAforsolvingthefirstproblem of PCA has beenproposed.

Using a reduced resolution image for dealing with the second limitation of the PCA has been proposed. The proposed system has two stages. one, training step in which extractions of features, reduction of dimensions and adjustment of weight of MLP neural networks is done. Second, recognition step for identifying the unknown images of faces.

In the training stage, feature extraction of reference images and adjusting the neural network parameters is included. In interested domain, the

representational basis of the images is identified in featureextraction.Then,inputimageistranslatedinaccord ancewiththerepresentationalbasis(whichhave been identified in the training stage) in the recognitionstage.

The 3 important steps in the training stage are-

1. For decomposing the reference images, WT is applied. Then, by the decomposition of the wavelet in three levels, sub images of 16×16 pixels which have been obtained, areselected.

2. For obtaining a set of representational basis, by selecting d eigenvectors which correspond to large eigenvalues and sub space projection, PCA is applied on the subimages.

3. The obtained features of the reference images in the precious step are then used for training neural networks with the help of propagation algorithm. The processing carried out in both the training and recognition stage is similar, the only difference being in the recognition stage, the input unknown images are matched with reference images in the recognition stage. WT and PCA are used for transforming the unknown face images intro the representational basis when an unknown face is presented in the recognitionstage.

EXPERIMENTAL RESULT

The database of face image of Yale university and face database of ORL is used for evaluating the the method that has been proposed in this paper.

All the images in the database of Yale university have a 160×121 resolution. But the WT cant be applied as the images dimension are not the power of 2. The images were then cropped to 91×91, and hen resized in 128×128. A third level of WT decomposition was use for changing the resolution of images.

Table 1 and table 2 show the results of the proposed algorithm on the database of Yale university and database of ORL, and have used the hair mother wavelet. The results of the proposed algorithm in the

database of Yale and ORL which have used Daubechies mother wavelet has been shown in table 3 and 4. The performance in recognition on the test image of the Yale and ORL database which have used various components have been shown in table 5 and 6.

TABLE 1. Algorithm applied on Yale database and haarmotherwavelet.

TABLE 2. Algorithm applied on ORL database and haarmotherwavelet.

TABLE 3. Algorithm applied on ORL database and Daubechies motherwavelet.

TABLE 4. Algorithm applied on Yale database and Daubechiesmotherwavelet.

TABLE 5. Recognition performance on testimagesof Yale database using the number ofprincipal

components.

TABLE 6. Recognition performance on test images of ORL database using the number of principal components.

TABLE 7. Recognition performance on test images of Yale database using MLP Neural networks by 25of principal components.

TABLE 8. Recognition performance on test images of ORL database using MLP Neural networks by 40 of principal components.

CONCLUSION

A hybrid approach for face recognition has been presented in this paper, by taking care of three issues. For stagesoffeaturerecognitionandpreprocessing, WTandPCAhavebeenappliedina combinedform.And MLP has been explored for quick decision making when there is a wide variety of facial variations in the classification stage. It can be concluded based on the experiments done on Yale university and ORL databasethatacombinationofWT,PCAandMLPyieldsmost favorableperformance,becauseitexhibits the lowest redundant rate, lowest training time and highest rates ofrecognition.

The proposed method also exhibits the a low load of computation in both the stages- training and

recognition.

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