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\title{Comparison of Different Algorithm for Face Recognition}
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             \author[1]{Hemant  Makwana}

             \affil[1]{  RGPV}

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\date{\small \em Received: 11 December 2012 Accepted: 5 January 2013 Published: 15 January 2013}

\maketitle


\begin{abstract}
        


This paper is about the different algorithms which are used for face recognition. There are so many algorithms which are available for face recognition .There are two approaches by which the face can be recognize i.e. face Geometry based and face appearance based. The appearance based technique is also sub divided into two technique i.e. local feature and global feature based. The technique of local feature based are Discrete Cosine Transform (DCT).In this paper we study the two global features (holistic) appearance based algorithm i.e. Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA) in which every face image is converted into 1D, we are using 1D for all the calculation and then compare these two algorithm with the help of FAR (False Acceptance Rate),FRR (False Rejection Rate),Time, Memory and checks which algorithm gives the better result.

\end{abstract}


\keywords{euclidean distance, false acceptance rate, false rejection rate, linear discriminant analysis, principle component analysis, scatter matrix.}

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\let\tabcellsep& 	 	 		 
\section[{Introduction}]{Introduction}\par
here are so many faces which the any normal human being seen in his daily life, but out of which they remember few of them. The faces which they remember are based on some feature based means they not exactly know the correct face but they know the feature of the particular face of the person. There are some special feature by which a exact person are recognize, like his color of eyes, shape of the ear which are remain same his all life. There are some features which are changes as the age is increase like shape of nose, shape of the lips etc. face Recognition is very complex process that find the exact match or minimum threshold value face to find out because the face image which are coming for recognition may contain noise or may be the light in the face or the color in the face image is not proper. the face which are coming for recognition purpose contain many useful information but using all these information is very much time consuming and consume lots of cost, so we reduce the some data like in this manner by which the useful information are not discarded. For this we are using PCA which is the reduction technique which reduces the parameter of the images.PCA uses Eigenfaces and Euclidean distance for matching the correct face from the database. We also use the LDA algorithm for face recognition, which is quite better then PCA algorithm. We seen later how lda is better then pca? The Face Recognition are used in many places like Air ports, Military bases, Government offices, also use for daily attendance purpose in the multinational companies. Face Recognition has two phases first phase is the training of the faces which the faces are saved in the database and second face is the verification phase in which they have to find the exact match of the face which are present in the database.\par
?: Assistant Professor in Oriental Institute of Science \& Technology, Jabalpur, India. e-mail: ruprahtaran@gmail.com II. 
\section[{Overview of the System}]{Overview of the System}\par
The proposed face recognition system consists of two module which are the enrollment and verification phases as depicted in Fig. \hyperref[fig_0]{1}.It consists of several sub modules which are Sensor, Feature, Extraction, Score Generation and the threshold. The Enrollment Module contains the Sensor and Feature Extraction while verification module contains score generation and threshold. The purpose of the pre-processing module is to reduce or eliminate some of the variations in face due to illumination. It normalized and enhanced the face image to improve the recognition performance of the system. In preprocessing technique the color image is first converted into gray scale or in black \& white image. After that according to the algorithm the steps are apply into the image to store in the database and calculate the threshold value of those images, threshold value is also saved in the database. The first and second steps are completed in the enrollment module. By using the normalization process, system robustness against scaling, posture, facial expression and illumination is increased.  {\ref [5][6]} b) Verification Module A user's face is once again acquired and system uses this to either identify who the user is, or verify the claimed identity of the user. The input to the face verification module is the face image, which is derived from two sources from the camera or from the database. While identification involves comparing the acquired biometric information against templates corresponding to all users in the database, verification involves comparison with only those templates corresponding to claimed identity. The image are again go for the respective algorithm and generated the score this score is compare with the threshold value which are saved in the database, the third and the forth step are completed in this module and respective output are shown in front of the user screen. decorrelation and dimensionality reduction to facilitate decision making. In mathematical terms, the principal components of the distribution of faces or the eigenvectors of the covariance matrix of the set of face images, is sought by treating an image as a vector in a very high dimensional face space \hyperref[b6]{[7]} [8] \hyperref[b8]{[9]}.We apply PCA on this database and get the unique feature vectors using the following method .Suppose there are P patterns and each pattern has t training images of m x n configuration. 
\section[{III. Algorithm for Face Recognition}]{III. Algorithm for Face Recognition}\par
? The database is rearranged in the form of a matrix where each column represents an image. ? With the help of Eigen values and Eigen vectors covariance matrix is computed. ? Feature vector for each image is then computed.\par
This feature vector represents the signature of the image. Signature matrix for whole database is then computed. ? Euclidian distance of the image is computed with all the signatures in the database. ? Image is identified as the one which gives least distance with the signature of the image to recognize. 
\section[{Advantage of this Algorithm}]{Advantage of this Algorithm}\par
? It completely decorrelates any data in the transform domain.\par
? it packs the most energy (variance) in the fewest number of transform coefficient. ? It minimizes the MSE (mean square error) between the reconstructed and original data for any specified data compression. ? It minimizes the total entropy of the data. 
\section[{Disadvantage of this Algorithm}]{Disadvantage of this Algorithm}\par
? There is not fast algorithm for its implementation.\par
? The PCA is not a fixed transform but has to be generated for each type of data statistics ? There is considerable computational effort are needed for generation of Eigen values and Eigen values of the covariance matrix.\par
b) Linear Discriminant Analysis (LDA)\par
LDA seeks directions that are efficient for discrimination between the data.LDA maximizes the between-class scatter and minimizes the within-class scatters. This criterion tries to maximize the ratio of the determinant of the between-class scatter matrix of the projected samples to the determinant of the within-class scatter matrix of the projected samples. Fisher discriminants group images of the same class and separates images of different classes. Images are projected from N2-dimensional space to C dimensional space (where C is the number of classes of images). To    
\section[{IV. Comparison Between the Algorithms}]{IV. Comparison Between the Algorithms}\par
We will compare these two algorithms with respect of FAR (False Acceptance Rate), FRR (False Rejection Rate), memory and time.\par
False Rejection Rate: The probability that system will fail to identify an enrollee. This is also called type I error rate.     ? Project faces onto a lower dimensional sub-space.\par
? No distinction between inter-and intra-class variability ? Reduce the dimension of the data from N2 to M ? Verify if the image is a face at all. ? Problems with illumination, head pose, etc.\par
? Optimal for representation but not for discrimination. 
\section[{Linear Discriminant Analysis (LDA)}]{Linear Discriminant Analysis (LDA)}\par
? Find a sub-space which maximizes the ratio of inter class and intra-class variability. ? Same intra-class variability for all classes.\par
? Work also with various illuminations, etc ? Reduce dimension of the data from N2 to P-1 ? Can only classify a face which is "known" to the database.\par
V. 
\section[{Conclusion}]{Conclusion}\par
The paper has presented a comparison of different type of face recognition algorithm like PCA, LDA algorithm. The overall performance for verification of image by using theses two algorithm we concluded that the LDA gives the better performance as comparison with the PCA algorithm. The main difference between these algorithm when we perform Analysis and experimental results indicates that the PCA works well when the lightening variation is small. LDA works gives better accuracy in facial expression. We also notice that PCA are time consuming as compare with the LDA algorithm. Also we test with the help of FAR\&FRR term than we concluded that LDA shows better result than PCA. \begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-2.png}
\caption{\label{fig_0}Figure 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-3.png}
\caption{\label{fig_1}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-4.png}
\caption{\label{fig_2}F}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2}\includegraphics[]{image-5.png}
\caption{\label{fig_3}Figure 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3}\includegraphics[]{image-6.png}
\caption{\label{fig_4}Figure 3 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-7.png}
\caption{\label{fig_5}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{4}\includegraphics[]{image-8.png}
\caption{\label{fig_6}Figure 4 :}\end{figure}
     			\footnote{© 2013 Global Journals Inc. (US)} 			\footnote{Comparison of Different Algorithm for Face Recognition} 		 		\backmatter  			  				\begin{bibitemlist}{1}
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