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CHAPTER ONE
INTRODUCTION
1.0 Background of the study
Facial aging, a new facet that has lately been added to the problem of face recognition, poses interesting theoretical and practical challenges to the scholar's research field. This common interest among research working in diverse field is motivated by remarkable ability to recognize an individual and the fact that human activity is a fundamental concern both in everyday life and cyberspace. Face recognition is an importance research problems spanning numerous fields and disciplines such as image processing, pattern recognition, neural networks, computer visions and computer graphics, psychology, statistics, neuroscientist, engineering, computer scientist, etc.

According Chellappa, Zhao & Philips (2009), posited that largely attribute face recognition numerous practical application which is based on reasons: the first reason is the wide range of commercial and law enforcement application such as bankcard identification, access control, Mug shots searching, security monitoring, and surveillance system, is a fundamental human behaviour that is essential for effective communications and interactions among people. The second reason is the available of feasible technologies after over four decades of research. Although a trivial task for the human brain, face recognition has proved to be extremely difficult to imitate through computer vision system, since although commonalities exist between human faces, thus the human face vary considerably in terms of age, skin, colour and gender (Nagi & Ahmed,2008). Furthermore, the determination to infer the intelligence or character from facial appearance is suspect, the human ability to recognize faces is remarkable (Turk & Pentland, 1991). According to Rahman (2013), the state of having many parts of a face features originate from continuous changes in the facial features that take place over time. Regard of these changes, we are sometime unable to recognize a person very easily over a period of time.

The study explores the Bayesian framework approach for automatically recognizing facial action in sequence of image or detecting human face in an input imagery and recognizing the facial look with respect time. Unlike other sources of variation (lighting, pose, and expression) which can be controlled during face image acquisition, face aging is an inevitable natural process during the lifespan of an individual. Face recognition system is a computer application for automatically identifying or verifying a person from a digital image or a video frame from a video source. One of the ways to do this is by comparing selected facial features from the image and a facial database. Human face recognition is the tenacity to recognize individual by their facial characteristics. The conventional methods for facial characteristics features of facial organs includes eyes, nose, ears and mouth (sometime open with the teeth showing or closed) (Bartlett et al, 1999). In biometric, Face recognition uses computer software to determine the identity of the individual. According to Woodward et al, (2003), Face recognition falls into the category of biometrics which is "the automatic recognition of a person using distinguishing traits"

Over the past few decades, face recognition happens to be one of the increasing prevalent trends in image analysis and processing. Scientist (neuroscientist) and researchers are making exertions to model the face space as principal manifold fixed in a high dimensional subspace or vector which can be used for classification purposes. PCA, LDA and Bayesian are three subspace methods extensively studied in recent times. Previously, face recognition algorithms used simple geometric models, but the recognition process has now developed into science of advanced mathematical representation and matching process. There are also major advancements and initiative in the past few years have motivated face recognition technology into the spot light. Face recognition is an integral part of biometrics and it has a number of strengths to be recommended over its peer in certain circumstances, (Chellappa et al, 1995). Face recognition can be used as for both verification (in this case, the system needs to confirm or reject the claimed identity of the input face) and identification (the input to the system is unknown face, and the system reports back to determined identity from a database of known individual), thus has many applications such as security systems, credit card verification and criminal identification.

In general, face recognition techniques can be separated into two groups grounded on the face representation they employ: that is appearance-based (photometric-based) and featured-based (geometric-based). The appearance-based which uses complete texture features and is applied to either whole-face or specific regions in a face image and; feature-based, which uses geometric facial features (mouth, eyes, brows, cheeks etc.) and geometric relationships between them.

Geometry feature based methods uses the facial feature measures such as distance between eyes, ratio of distance between eyes and nose etc., but it is significantly different from the feature-based techniques that it constructs the topological graph using the facial features of each subject. Thus face recognition based on geometric feature of a face is probably the most intuitive approach to face recognition.

Currently, all face recognition techniques work in either of the two ways. One is local face recognition system which uses facial features (nose, mouth, eyes) of a face. That is to consider the fiducial points in the face to associate the face with a person. The local-feature method computes the descriptor from parts of the face and gathers information into one descriptor. Some local-feature methods are, Local Feature Analysis (LFA), Garbor Features, Elastic Bunch Graph Matching (EBGM) and Local Binary Pattern Feature Agrawal et al., (2014).

The second approach or global face recognition system uses the whole face to identify a person. The principle of whole face method is to construct a subspace using Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), Independent Component Analysis (ICA), Random Projection (RP), or Non-negative Matrix Factorization (NMF). These are all dimensionality reduction algorithms that seek to reduce the large dimensional face image data to small dimension for matching.

This study centers on statistical application of the face recognition performance which focused on Bayesian age difference classifier that classifies face images of individuals based on age differences and performs face verification/ identification across age progression. Further, study explores the similarity of faces across age progression. Since age separated face images invariably differ in illumination and pose, study proposes pre-processing methods for minimizing such variations (mean centering and whitening). Again, the research explores and compares techniques for automatically recognizing facial actions in sequence of images or detecting an "unknown" human face in input imagery and recognizing the faces under various environmental constraints. This thesis make used of more inherent statistical methods (Multivariate methods) to assess the performance of face recognition algorithms under variable environmental constraints with respect to age.

1.1 Statement of Problem
The problem of face recognition of human face continue to attract researcher from various diverse discipline based on face recognition numerous application. The major challenges in designing a face recognition system include variation in lighting, facial expression, head pose and age. The face recognition application have collateral information such as race, age, gender, facial expression, or speech may be used in narrowing the search (enhancing recognition). Lings et al (2002), claimed that challenging task in face recognition is due to human face varying with respect to time in many aspects that includes facial texture (wrinkles), shape (body weight), facial hair, presence of glasses etc. A number of approaches have been proposed to achieve lighting, facial expression and/or head pose invariant to face recognition. Otto, Han and Jain (2002) have revealed that other sources of variation (lighting, pose and facial expression) which can be controlled during face image acquisition, face aging is an unavoidable natural occurrence during the lifespan of the individual.
Human faces experience considerable amount of variations with aging. Face aging is generally slow and irreversible process. There are some general changes when people are aging differently and aging show different aging recognition. From child birth to adulthood the changes occur in the face size. The face size changes from the child to adulthood image. The face size changes that is the shape of eyes, nose, mouth, eyebrows and lips changes from child to adulthood.
While face images have conventionally been used in identification documents such as school's ID, national ID, passports, driver's licenses, voter ID, NHIL cards, etc., in recent years, face images are being increasingly used as additional means of authentication in applications such as credit/debit cards and in places of high security. Since faces image experience gradual variations due to aging, sporadically updating face databases with more recent images of subjects might be necessary for the success of face recognition systems. Since sporadically updating such large databases would be a dreary task, a better alternative would be to develop face recognition systems that verify the identity of individuals from a pair of age separated face images. Understanding the role of age progression in affecting the similarity between two face images of an individual is important in such responsibilities.

Also, face recognition systems have been proven to be sensitive to factors such as illumination and gesture, their sensitivity to facial aging effects is yet to be studied. The study analyse the task of face recognition across ages and determine how age gap impact face recognition system using statistical application. The aim of the study is to determine whether or not ageing is statistically significance in human face recognition system. The statistical analysis performed was based the Bayesian classifier approach to face recognition tackles the problem of a given pair of difference ages separated face image of an individual.



1.2 Motivation of the study
Although facial recognition has been rampant due it's diverse applications in law enforcement agency and others. The real world applications are rich and attractive. Different peoples have different aging process which is determined not only by person's genes but also from the other factors like living style, sociality, and nature. The face recognition uses in the identification and verification has improved but the used of Bayes classifier with high dimensional covariates estimators with the main focus on age disparity in image processing has not being a studied.

Traditionally, student's attendance in University of Ghana examination center is taken manually by using attendance sheet which consist of the photograph of the facial looks of the student given by University authority to verify that students eligibility of taking that particular examination. With this manual system, there are some cases that student in their final year or less facial looks varies significantly due to age variation. This sometimes makes invigilators invigilating the student's finds difficult in identifying the student by matching the facial looks with their current image before they are ask to sign the attendance sheet.

Because of this problem, a system may be needed in order to identify the attendance of the students more accurately without the manual trace by invigilators. A face recognition device will be employ using a Bayes classifier with high dimensional covariates estimators. This system will help verify the attendance of students in an examination halls by invigilators to avoid impersonation of student's taken their examination.

1.3 Objectives
The main objective of this investigation is to identify an individual from ageing images that are stored in a database and to define bio-metric templates containing discriminatory features that are least affected by with-in-person types of variations in order to enable accurate identity verification (Zhao et al, 2003). The specific objectives are:
To employ Bayesian classifier decision making in the image recognition.
To use preprocessing techniques such as noise reduction in order to enhance the image of the individual.
To investigate the ageing on difference facial component and categories using a component based face representation and matching algorithm.
To predict the performance of a face recognition system based on image analysis.
To integrate the Bayes classifier and face tracking system to build a real time facial ageing recognition system.

1.4 Research Question
How does age progression affect the similarity between a pair of face images of an individual?
What is the confidence associated with establishing the identity between a pair of age separated face images?
How does facial aging effects impact recognition performance?
What constitutes an age-invariant signature for faces?

1.5 Methodology
The research focused on running some template-based recognition algorithms on a created face frontal database and subsequently evaluated the recognition performance based a Bayesian age difference classifiers approach.

Face image data were passed to face recognition modules as input for the system. The input image samples of a local Ghanaian Facial Frontal View (GFFV).


1.6 Significance of the Study
Face recognition is relevant for its multiple uses in the areas of Law of Enforcement, Biometric, security, and other commercial uses.
The study spells out face recognition as a non-invasive method with a sense of primary identification.
The face verification system authenticates a person's claimed identity.
Serve as literature review for further research.
Again, this study will serve as a catalyst to breed interest and further research into the other aspects of biometrics in Ghana. This stems from the fact that face recognition is a multifaceted phenomenon and no one research is capable of addressing it in full. This makes this study justifiable and worthwhile.








Areas
Application of Face Recognition
Information Security
Accessing Security, Data Privacy, User authentication, Intranet security, Application security, file encryption, securing trading terminal, medical records, Internet access, TV-Parental control, Personal device logon, desktop logon
Access Management
Secure access Authentication
Biometric
Personal Identification (National ID, Passport, Driver's licenses,) Welfare fraud, Entitlement programs Immigration, voter registration, multimedia communication(synthetics face),
Law Enforcement
Advanced Video surveillance, Forensic Reconstruction of Face remains, CCTV Control, Portal control, Post event analysis, Ship lifting, Suspect trading and Investigation
Entertainment Leisure
Virtual reality, Photo camera, Training program, Human-robot interaction, Human-computer-interaction and home video games
1.7 Some Applications of Facial Recognition
Table 1.0: Some application of recognition
1.8 Scope and Delimitation
The study rely on a personal identification (verification) system based on analysis of frontal or profile image of the face which served as a benchmark.
The ageing process is uncontrollable, thus every person age different and often ageing is with respect to time.
1.9 Limitation
Individuals can be found or demand frontal view pose orientation.
There are many problems with illumination conditions.
Face recognition tests revealed that the lighting variant is one the bottleneck in face recognition.
In cases where lightening condition are different from the gallery, identity decision is wrong in many cases.
1.10 Data Analysis
The analytic tool that will be used for the image training and recognition is the MATLAB-Octave which will be implemented in MATLAB R2009a version.

1.11 Organisation
The study is organized into five chapters. Chapter one gives an introduction and general background of the study. This constitutes the statement of the problem, objectives of the study, significance of the study, scope and delimitation of the study, chapter organization including general overview on face recognition using Bayesian. The chapter two covers review of articles and related issues on face recognition using Bayes classifiers with high dimensional covariate estimators. Chapter three will provide detail of the research methodology employ in this study. This methodology entailed the statistical Bayesian classifier in face recognition. In chapter four the study presents the analysis of the data results and discussion. Chapter five gives the finding, conclusion and recommendations.





CHAPTER TWO
LITERATURE REVIEW
2.1 Introduction
This chapter presents the discussion of existing theoretical, conceptual and empirical literature on face recognition based on Bayesian classifiers. It aims to portray an understanding of the main concepts in the present study as they exist in literature and the gaps that pertain in literature insofar as the Bayesian classifier on face recognition with high dimensional covariate. It also presents relevant theories which explain the concepts as well as a review of extant studies done both in Ghana and other jurisdiction. This studies will includes Principal Component Analysis approach, Linear Discriminant Analysis approach Independent Component Analysis approach and other relevant areas.

2.2 Human Face Recognition
For a human face recognition system the important feature is its parallel processing capacity. Since the face recognition and the retention or memory of faces are crucial skill for our survival or evolution would not have given us these startling abilities. Studies revealed that the natural preference for face like images and even a few weeks after birth, a new-born baby is attracted to face-like stimuli.

Much research has been done on the human face recognition system, and perceptual, developmental, neuro-psychological, neuro-physiological, and functional neuro-imaging studies have indicated that face recognition in primates is a specialized capacity in the ventral portions of occipito-temporal and frontal cortices and in the medial temporal lobes (Rodman et al., 1993). In fact, there is a condition called prosopagnosia, which is caused by brain injury, strokes or genetic factors. Suffers are unable to recognize faces while object recognition and other visual skills are largely unimpaired (Gauthier et al., 1999). Similarly there are patients with visual object agnosia, who are impaired at recognizing objects but who have normal face recognition abilities (Moscovitch et al., 1997). These findings seem to corroborate the theory that there are specialized areas in the brain that perform face recognition.
Although the areas of our brain, which perform face recognition, are known, the methodology of our distinctive face recognition system is not wholly understood. The most popular hypothesis among neuro-psychologists is that all of human have an average face prototype, assembled from all the faces humans have seen throughout are lifetime. Humans then categorise each face come across according to that particular face's variation from our average face prototype (Haxby et al., 1996 and de Haan et al., 1998). Work using caricatures of faces has collaborated this theory. When the Euclidean distance of an individual's face from the average face prototype is increased creating a caricature or exaggerated face, it was found that test subjects displayed increased recognition of that individual (Deffenbacher, 1998 and Brennan, 1982).


Also, when building artificial face recognition systems, scientists try to understand the architecture of human face recognition system. Focusing on the methodology of human face recognition system may be useful to understand the basic system. However, the human face recognition system utilizes more than that of the machine recognition system which is just 2-D data. The human face recognition system uses some data obtained from some or all of the senses; visual, auditory, tactile, etc. All these data is used either individually or collectively for storage and remembering of faces. In many cases, the surroundings also play a vital role in human face recognition system. It is difficult for a machine recognition system to handle so much data and their combinations. However, it is also tough for a human to remember many faces due to storage limitations. For a human face recognition system the important feature is its parallel processing capacity.

The issue "which features humans use for face recognition" has been studied and it has been argued that both global and local features are used for face recognition. The results indicated that it is harder for humans to recognize faces which they consider as neither "attractive" nor "unattractive". Both holistic and feature information are important for the human face recognition system.
Studies suggest the possibility of global descriptions serving as a front end for better feature based perception. Chellappa et al (1995). If there are dominant features present such as big ears, a small nose, etc. holistic descriptions may not be used. Also, recent studies show that an inverted face (i.e. all the intensity values are subtracted from 255 to obtain the inverse image in the grey scale) is much harder to recognize than a normal face.

Hair, eyes, mouth, face outline have been determined to be more important than nose for perceiving and remembering faces. It has also been found that the upper part of the face is more useful than the lower part of the face for recognition. Also, aesthetic attributes (e.g. beauty, attractiveness, pleasantness, etc.) play an important role in face recognition; the more attractive the faces are easily remembered. For humans, photographic negatives of faces are difficult to recognize. But, there is not much study on why it is difficult to recognize negative images of human faces.

Bruce (1999) conducted a study on the direction of illumination and showed the importance of top lighting. He demonstrated that it is easier for humans to recognize faces illuminated from top to bottom than the faces illuminated from bottom to top.

The statistical technique, which is used in this thesis for automated face recognition will be of special interest because it closely resembles our own innate face recognition system.
This model promises recognition accuracy far in excess of a basic template matching technique, which involves comparing raw pixel intensity values.


2.3 Recent Approach to Face Recognition
Face recognition has been an active and interested research area over last 60 years for most researchers. Since Bledsoe (1960) pioneer the first face recognition test. Others scholars emanating from various discipline such as Computer Science, Psychologists, Neuroscientists, Engineers and Statisticians have predominant research in the field. This research spans several disciplines such as image processing, pattern recognition, computer vision, and neural networks. Psychologists and neuroscientists mainly deal with the human perception part of the topic, whereas engineers studying on machine recognition of human faces deal with the computational aspects of face recognition. Face recognition has applications mainly in the fields of biometrics, access control, law enforcement, and security and surveillance systems.


2.4 Face Recognition
Over the last few decades many techniques have been proposed for face recognition. Many of the techniques proposed during the early stages of computer vision cannot be considered successful, but almost all of the recent approaches to the face recognition problem have been creditable. According to the research by Brunelli and Poggio (1993) all approaches to human face recognition can be divided into two strategies:
Geometrical features
Template matching.

2.4.1 Face recognition using geometrical features
This technique involves computation of a set of geometrical features such as nose width and length, mouth position and chin shape, etc. from the picture of the face we want to recognize. This set of features is then matched with the features of known individuals. A suitable metric such as Euclidean distance (finding the closest vector) can be used to find the closest match. Most pioneering work in face recognition was done using geometric features (Kanade, 1973), although Craw et al. (1987) did relatively recent work in this area.
(Figure)

The advantage of using geometrical features as a basis for face recognition is that recognition is possible even at very low resolutions and with noisy images (images with many disorderly pixel intensities). Although the face cannot be viewed in detail its overall geometrical configuration can be extracted for face recognition. The technique's main disadvantage is that automated extraction of the facial geometrical features is very hard. Automated geometrical feature extraction based recognition is also very sensitive to the scaling and rotation of a face in the image plane (Brunelli and Poggio, 1993). This is apparent when we examine Kanade's (1973) results where he reported a recognition rate of between 45-75 % with a database of only 20 people. However if these features are extracted manually as in Goldstein et al. (1971), and Kaya and Kobayashi (1972) satisfactory results may be obtained.

2.4.2 Face recognition using template matching
This is similar the template matching technique used in face detection, except here we are not trying to classify an image as a 'face' or 'non-face' but are trying to recognize a face.
(Figure)

The basis of the template matching strategy is to extract whole facial regions (matrix of pixels) and compare these with the stored images of known individuals. Once again Euclidean distance can be used to find the closest match. A simple version of template matching is that a test image represented as a two-dimensional array of intensity values is compared using a suitable metric, such as the Euclidean distance, with a single template representing the whole face. There are several other more sophisticated versions of template matching on face recognition. One can use more than one face template from different viewpoints to represent an individual's face. The simple technique of comparing grey-scale intensity values for face recognition was used by Baron (1981).

However there are far more sophisticated methods of template matching for face recognition. These involve extensive pre-processing and transformation of the extracted grey-level intensity values. For example, Turk and Pentland (1991a) used Principal Component Analysis, sometimes known as the eigenfaces approach, to pre-process the gray-levels and Wiskott et al. (1997) used Elastic Graphs encoded using Gabor filters to pre-process the extracted regions.
An investigation of geometrical features versus template matching for face recognition by
Brunelli and Poggio (1993) suggested that the optimal strategy for face recognition is holistic and corresponds to template matching. In the simplest form of template matching, the image (as 2-D intensity values) is compared with a single template representing the whole face using a distance metric. Their study concluded that although a feature based strategy may offer higher recognition speed and smaller memory requirements, template based techniques offer superior recognition accuracy.

Huang (1998) explained that template matching is conceptually related to all-inclusive approach which attempts to identify faces using global representations. These types of methods approach the face image as a whole and try to extract features from the whole face region and then classify the image by applying a face classifier. One of the methods used to extract features in a complete system, is based on statistical approaches.

2.5 STATISTICAL APPROACH
The statistical approach to face recognition using Bayes classifier with high dimensional covariates includes template matching based on the system where training and test images are matched by measuring the correlation. In addition, statistical methods include the projection based methods such as Principal Component Analysis (PCA) approach, Linear Discriminant Analysis (LDA) approach, Independent Component Analysis (ICA) approach and Elastic Bunch Graph Matching (EBGM).

STATISTICAL TECHNIQUES FOR FACE RECOGNITION
Throughout the past few decades there have been many face recognition system techniques proposed and implemented. Some of the common methods described by the researchers of the respective fields are:

2.5.1 Face Recognition by PCA
The Eigenfaces method is one of the mostly used algorithm for face recognition system due to its simplicity and easy implementation. Karhunen-Loeve is based on the eigenfaces technique in which the Principal Component Analysis (PCA) is used. The aim purposed of this method is successfully used to perform dimensionality reduction; therefore the Principal Component Analysis is described as low dimensional subspace of an image in the short period of time. This make the principal component analysis more efficient in processing time and storage. Principal Component Analysis is used by face recognition and detection as a statistical criterion for measuring the notion of 'best representation of the difference between the training faces'. Mathematically, Eigenfaces are the principal components divide the face into feature vectors. The feature vector information can be obtained from covariance matrix. These Eigenvectors are used to quantify the variation between multiple faces. The faces are characterized by the linear combination of highest Eigenvalues. Each face can be considered as a linear combination of the eigenfaces. The face can be approximated by using the eigenvectors having the largest eigenvalues. The best N eigenfaces define an N dimensional space, which is called as the "face space". Thus construct a face space and project the image into eigen face.

In Karl Pearson (1901), PCA is a standard statistical technique that can be used to reduce the dimensionality of a data set, and is useful when obtained data have some redundancy. This result in reduction of variables into smaller number of variables called Principal Components which will account for most of the variance in the observed variable.

Sirovich and Kirby (1987) were the first to utilize Principal Components Analysis (PCA) to economically represent face images. They demonstrated that any particular face can be efficiently represented along the standard face picture (Eigen picture) coordinate space, and that any face can be approximately reconstructed by using just a small collection of Eigen pictures and the corresponding projections along each Eigen picture.



Turk and Pentland (1991) discovered that while using the eigenfaces technique, the residual error could be used to detect faces in images, a discovery that enabled real-time automated face recognition systems. Although the approach was somewhat constrained by environmental factors, it nonetheless created significant interest in furthering development of automated face recognition technologies.



Starner et al (1994) posited that, an important feature of PCA is that one can reconstruct any original image from the training set by combining the eigenfaces. They stipulated that, by means of PCA one can transform each original image of the training set into a corresponding eigen face. The original face image can be reconstructed from eigenfaces if all the eigenfaces (features) are added in the right proportion. Each eigenfaces represents only certain features of the face, which may or may not be present in the original image.
Samal and Iyengar (1995) proposed a PCA face detection scheme based on face silhouettes. Instead of eigenfaces, they generated eigen silhouettes and combined this with standard image processing techniques (edge detection thinning, thresholding) and the generalized Hough transform. They reported a detection rate of 92% on a dataset of 129 images (63 face images and 66 general images)where in the case of the face images, the face occupy most of the image.

Belhumeur et al. (1997) argued that although PCA appears to work well when a single image of each individual is available, but when multiple images per person are present, by choosing the projection which maximizes total scatter, PCA retains unwanted variations due to lighting and facial expression.


Kanade (1973), employed simple image processing methods to extract a vector of 16 facial parameters - which were ratios of distances, areas and angles (to compensate for the varying size of the pictures) - and used a simple Euclidean distance measure for matching to achieve a peak performance of 75% on a database of 20 different people using 2 images per person (one for reference and one for testing).


Cox et al. (1996) reported a recognition performance of 95% on a database of 685 images (a single image for each individual) using a 30-dimensional feature vector derived from 35 facial features. However, the facial features were manually extracted, so it is reasonable to assume that the recognition performance would have been much lower if an automated, and hence less precise, feature extraction method had been adopted.

Moghaddam and Pentland (1995) used the Eigenfaces Method for image coding of human faces for potential applications such as video telephony, database image compression and face recognition.



Lee et al. (1999) proposed a method using PCA which detects the head of an individual in a complex background and then recognize the person by comparing the characteristics of the face to those of known individuals.



Crowley and Schwerdt (1999), in a study suggested that, PCA is used for coding and compression for video streams of talking heads. They suggest that a typical video sequence of a talking head can often be coded in less than 16 dimensions.



Moghaddam et al. (1999), (1998), and (2000), suggested the Bayesian PCA method. By this system, the eigenfaces method based on simple subspace-restricted norms is extended to use a probabilistic measure of similarity. Also, another difference from the standard Eigenfaces approach is that this method uses the image differences in the training and test stages. The difference of each image belonging to the same individual with each other is fed into the system as intrapersonal difference, and the difference of one image with an image from different class is fed into the system as extra personal difference. Finally, when a test image comes, it is subtracted from each image in the database and each difference is fed into the system. For the biggest similarity (i.e. smallest difference) with one of the training images, the test image is decided to be in that class. The mathematical theory is mainly studied in Moghaddam and Pentland (1997).

Moghaddam (2002) introduced his study on several techniques; Principal Component Analysis (PCA), Independent Component Analysis (ICA), and nonlinear Kernel PCA (KPCA). He examined and tested these systems using the FERET database. He argued that the experimental results demonstrate the simplicity, computational economy and performance superiority of the Bayesian PCA method over other methods.



Chung et al. (1999) suggested the use of PCA and Gabor Filters together. Their method consists of two parts: In the first part, Gabor Filters are used to extract facial features from the original image on predefined fiducial points. In the second part, PCA is used to classify the facial features optimally. They suggested the use of combining these two methods in order to overcome the shortcomings of PCA. They argued that, when raw images are used as a matrix of PCA, the eigenspace cannot reflect the correlation of facial feature well, as original face images have deformation due to in-plane, in-depth rotation and illumination and contrast variation. Also they argued that, they have overcome these problems using Gabor Filters in extracting facial features.

Asiedu et al (2015), focuses on statistical evaluation of the recognition performance of PCA/SVD and Whitened PCA/SVD under variable environmental constraints (variable facial expressions). They explores and compares techniques for automatically recognizing facial actions in sequence of images or detecting an "unknown" human face in input imagery and recognizing the faces under various environmental constraints. Their study uses more intrinsic statistical methods (Multivariate methods) to assess the performance of face recognition algorithms under variable environmental constraints. They argue that evident from the statistical methods that, the algorithms considered are significantly different in recognizing all poses except the angry pose.

Baah (2013), employ the use of eigenfaces approach, thus an application of principal component analysis to facial images, provides a practical solution that is well fitted for the problem of face recognition. He argue that based on the result, PCA is very fast, relatively simple, and works well in a constrained environment.

The accuracy of eigenfaces depends on many things. As it takes the pixel value as comparison for the projection, the accuracy would decrease with varying light intensity. Preprocessing of image is required to achieve satisfactory result. An advantage of this algorithm is that the eigenfaces were invented exactly for those purpose what makes the system very efficient (Jaiswal, Bhadanira & Jadam, 2013).

One of the drawback in Principal Component Analysis (PCA) is that it is sensitive for lightening conditions and the position of the head. Disadvantages-Finding the eigenvectors and eigenvalues are time consuming on PPC. The size and location of each face image must remain similar PCA (eigenfaces) approach maps features to principle subspaces that contain most energy (Jaiswal, Bhadanira & Jadam, 2013).

2.5.2 Face recognition by Multilinear Principal Component Analysis
One extension of PCA is that of applying PCA to tensors or multilinear arrays which results in a method known as multilinear principal components analysis (MPCA) (Lu, Plataniotis & Venetsanopoulos, 2008). Since a face image is most naturally a multilinear array, meaning that there are two dimensions describing the location of each pixel in a face image, the idea is to determine a multilinear projection for the image, instead of forming a one- dimensional (1D) vector from the face image and finding a linear projection for the vector. It is thought that the multilinear projection will better capture the correlation between neighborhood pixels that is otherwise lost in forming a 1D vector from the image (Harguess &Aggarwal, 2009).
2.5.2.1 Kernel Methods
The face manifold is subspace need not to be linear. Kernel methods are generalization of linear method. Direct non-linear manifold schemes are explores to learn this non-linear manifold (Wiskott, et al, 1995).
However, PCA only uses the second order statistical information in data. As a result, it fails to perform well in nonlinear cases. Kernel PCA (KPCA) is able to capture the nonlinear correlations among data points, and in some cases has been more successful than conventional PCA. Yanmei Wang and Tang (2004), propose a method of feature extraction for facial recognition based on KPCA, and the nearest neighbor classifier making use of Euclidean distance is adopted.

Experimental results show a high recognition rate of using KPCA. Kernel principal component analysis (Huang & Shao, 2004, Yan et al, 2007) is a method of non-linear feature extraction. With the Cover's theorem, as in equation (***), nonlinearly separable patterns in an input space will become linearly separable with high probability if the input space is transformed nonlinearly into a high-dimensional feature space. Thus, therefore, map an input variable into a high-dimensional feature space, and then perform PCA

Performing PCA in the high-dimensional feature space can obtain high-order statistics of the input variables, that is, also the initial motivation of the KPCA. However, it is difficult to directly compute both the covariance matrix and its corresponding eigenvectors and eigenvalues in the high-dimensional feature space. It is computationally intensive to compute the dot products of vectors with a high-dimension. Fortunately, kernel tricks can be employed to avoid this difficulty, which computes the dot products in the original low-dimensional input space by means of a kernel function


2.5.3 Face Recognition by Fisher face
Fisher faces is one the most successfully widely used method for face recognition. It is based on appearance method. In 1930 R.A Fisher developed linear/fisher discriminant analysis for face recognition (Fisher.1936). It aims to find the most discriminative features maximizing the ratio of determinant of between-class variations to within-class variations. A number of LDA-based methods have been proposed in face recognition. However, due to their parametric nature which assumes that the samples satisfy normal distribution, all these methods suffer from serious performance degeneration for cases of non-normal distribution.
In Sirovich & Kirby (1987), a nonparametric technique is proposed to overcome this problem for the case of two classes, in which a nonparametric between-class scatter is defined. However, it does not give a definition for multi- class problems. To apply it to face recognition, which is a typical multi-class recognition problem, a novel algorithm called nonparametric discriminant analysis (NDA) (Chen & Tan, 2005) which extends the definition of the nonparametric between-class scatter matrix to the multi-class problem.
For high dimensional problems, there are often not enough training samples to guarantee the within class scatter matrix non-singularity. Inspired by the idea of the unified subspace (Zhang et al, 2010), propose a novel method called principal nonparametric subspace analysis (PNSA) to extract nonparametric discriminating features within the principal subspace of within class scatter matrix, This will help to stabilize the transformation and thus improve the recognition performance.

Shufu Xie proposed that, block-based Fisher's linear discriminant (BFLD) (Gao et al, 2009) to reduce the dimensionality of the proposed descriptor and at the same time enhance its discriminative power. Finally, by using BFLD, fuse local patterns of Gabor magnitude and phase for face recognition. The fusion of magnitude and phase further enhance the recognition accuracy when they are encoded by local patterns and combined with BFLD.

The classical LDA cannot be directly applied due to the singularity problem of scatter matrix. Several extensions of LDA, including pseudo-inverse LDA, Direct LDA, and LDA/QR were proposed in recent years to deal with this problem. Rong-Hua Li, Eddie, C.L. Chan and George Baciu (2010) proposed a well-known feature extraction algorithm for human face images which deals with the classical singularity problem of scatter matrices.

Linear Discriminant Analysis via QR decomposition (LDA/QR) and Direct Linear Discriminant Analysis (DLDA) are two types of LDA algorithms to solve this singularity problem. And also they verified the equivalence relationship among these two LDAs. The DLDA and LDA/QR algorithms achieve the same classification accuracy on both ORL and Yale face dataset, which verify the theoretical analysis.

Fisher faces is the direct use of (Fisher) linear discriminant analysis (LDA) to face recognition (Belhumeur, Hespanha, and Kriegman, 1996). LDA searches for the projection axes on which the data points of different classes are far from each other while requiring data points of the same class to be close to each other. Unlike PCA which encodes information in an orthogonal linear space, LDA encodes discriminating information in a linearly separable space using bases that are not necessarily orthogonal. It is generally believed that algorithms based on LDA are superior to those based on PCA. However, other work such as (Martinez & Kak, 2001) showed that, when the training data set is small, PCA can outperform LDA, and also that PCA is less sensitive to different training data sets. All used LDA to find set of basis images which maximizes the ratio of between-class scatter to within-class scatter.
Fisher face is similar to Eigen face but with enhancement of better classification of different classes image. With Fisher Linear Discriminant, one can classify the training set to deal with different people and different facial expression. We have better accuracy in facial expression than Eigen face approach. Besides, Fisher face removes the first three principal components which are responsible for light intensity changes; it is more invariant to light intensity (Sushma Jaiswal, Dr. (Smt.) Sarita Singh Bhadauria, Dr. Rakesh Singh Jadon, 2011).
The disadvantage of LDA is that within the class the scatter matrix is always single, since the number of pixels in images is larger than the number of images so it can increase detection of error rate if there is a variation in pose and lighting condition within same images. So to overcome this problem many algorithms has been proposed. Because the fisher faces technique uses the advantage of within-class information so it minimizes the variation within class, so the problem with variations in the same images such as lighting variations can be overcome (Jyoti & Sapkal, 2012).
Furthermore, another disadvantages of Fisher face are that LDA is more complex than Eigen face to finding the projection of face space. Calculation of ratio of between-class scatter to within-class scatter requires a lot of processing time. Besides, due to the need of better classification, the dimension of projection in face space is not as compact as Eigen face, results in larger storage of the face and more processing time in recognition (Sushma Jaiswal, Dr. (Smt.) Sarita Singh Bhadauria, Dr. Rakesh Singh Jadon, 2011)

2.5.4 Face Recognition by Neural Network
The main objective of the neural network in the face recognition is the feasibility of training a system to capture the complex class of face patterns. To get the best performance by the neural network, it has to be extensively tuned number of layers, number of nodes, learning rates, etc. The neural networks are nonlinear in the network so it is widely used technique for face recognition. So, the feature extraction step may be more efficient than the Principal Component Analysis.

To model our way of recognizing faces is imitated somewhat by employing neural network. This is accomplished with the aim of developing recognition systems that incorporates artificial intelligence for the sake of coming up with a system that is intelligent. The use of neural networks for face recognition has been shown by (Fan & Verma, 2005) and (Shaoning, Kim & Sung, 2005). According to KeLu, Xiaofei & Zhao (2006), suggested that the semi-supervised learning method must be used to support vector machines for face recognition. There have been many efforts in which in addition to the common techniques neural networks were implemented. For example in (Jamil, Iqbal, S. & Iqbal, N, 2005) a system was proposed that uses a combination of eigenfaces and neural network. In (P.Latha, Dr.L.Ganesan & Dr.S.Annadurai, 2009), first stated that the dimensionality of face image is reduced by the Principal component analysis (PCA) and later the recognition is done by the Back propagation Neural Network (BPNN). The disadvantage of the neural network approach is that when the number of classes increases (Kirby &Sirovich, 1990; Yang, Kriegman and NarendraAhuja, 2002)

2.5.5 Elastic Bunch Graph Matching
All human faces share a similar topological in structure; faces are represented as graphs, with node fiducially points (eyes, nose, etc.) and edge labelled with 2-D distance vectors. Each node contain 40 sets of complex Gabor wavelet coefficients at different scale and orientations (phase, amplitude), called the "jets". Recognition is based on labeled graph, a labelled graph is a set of nodes connected by edge labeled as jets, and edges are labeled as distance (Zhao et al 2006).

2.5.5 Trace Transform
The Trace transform, a generalization of the random transform, is a new tool for image processing which be used for recognizing objects under transformation e.g. rotation, translation and scaling; to produce a trace transform one computes a function tracing lines of an image. Different trace transform be produced from an image using different trace functional (Hu L and Wei Z, 2009).

Face Recognition across Age progression
Hu Kwan et al (1994) stated that age classification from face image that is young /old using face anthropometry.
Alice O'Toole (1997) also predicted that age perception using 3D head caricature; exaggeration of wrinkles increased perceived age.
Tidderman et al (2001) suggested that prototyping and transforming facial texture; age perception.
Lanitis et al (2002) build ageing functions using PCA coefficient of shape and texture of faces. They further evaluated the performance for different classifiers for age estimation, including Artificial Neural Network (ANN), nearest neighbor classifier. The Active Appearance Model (AAM) method is used for the representation for the face images (used for coding face images). The quadratic function is actually a regression function. This function is used to relate the face representations to age labels and is also called as quadratic function classifier

Bayesian Approach
According to Narayanan and Chellapa (2006) studies revealed that the Bayesian age-difference classifier can be used to verify adult face images across age progression. The study further stated that the lesser the variations due to facial hair, facial expressions and glasses on age separated face image, the better the success of the age-difference classifier.
Two-dimensional face recognition suffered from pose changes, while three-dimensional approaches are with high computational complexity. Besides the improvement in recognition rate, this system reduces the misclassification that could occur in traditional single-view systems. ShinYee Tsai and Angela Chih-Wei Tang (2008) proposed a system that fuses the individual recognition results of two images of the same identity with different viewing angles based on Bayesian theory. Bayesian approach uses the similarity of each person and is trained by determining the reliability of each identity of the two channels. Different form traditional PCA based approaches, SVM classifiers (Denis et al 2003) are used instead of minimum distance classifier to enhance the robustness. Experimental results show that this two-view face recognition system has achieved a higher recognition rate compared with traditional 2D single-view face recognition systems.











CHAPTER THREE
METHODOLOGY
This chapter discusses the main tools and statistical techniques that will be used to analyse the empirical databases of a face recognition system in the next chapter.
3.1 Introduction
This chapter presents the research methodology employed by the study to arrive at the various findings and conclusions. The chapter focuses on the data, research design and statistical framework. The aim of the proposed methodology is to provide the means of comparison of face recognition methods, not the combination of face detection and recognition. Thus the databases used is conductive for the extraction of the face from image. In addition, most theories in face recognition methodology has proved that the human face is geometrically normalized to standard size and projected pixels focus on the eye position.
The study is applied to passport photo identification task that involve 124 Ghanaians university students image pairs, where each pair is the same person taken at different years.

Data Acquisition
The objects image of data collection will be Frontal facial images from a labelled faces in the wild. A real time face image database is created for the purpose of benchmarking the face recognition system. Face images from a standard database which is a secondary source data will be extracted from University of Ghana Basic and Computing (UGBC directorate) and used for this study. Specifically 150 facial image (mainly Statistics and Actuarial Science Students for 2013 academic year) will be collected from UGBC directorate with preference to universally accepted facial expression/looks. This facial image will form a standard databases available for research purposes which could be used to test the performance of face recognition system.

The collected image will be resized into a uniform dimension and captured into a face database. For the purposes of this project, the study will use two face data set. Both data sets provide ground truth information on the race and gender of subjects, and contain significant age gaps between multiple face images of a given subject. For each subject, the study will sampled two images with the desired age gap (4 year age difference). The first image of the subjects in each subset are used for training (past image) and then subjects current image will be used for evaluation.

Research Design
The pre-processing stages, through the feature extraction stage to the recognition stage. The database shown in the design contains the train image set which are trained per the recognition module and their corresponding information stored in memory for recognition purpose.
The unknown face shown in the design is also called the test image. This is introduced to be recognized in the database per the recognition module. The test image also is exposed to the entire recognition processes shown below and its important information kept in memory for comparison and identi cation.




RECOGNITION PROCEDURE
The study focused on employing Bayesian classifier recognition algorithms on a created face ageing database. The research evaluated the recognition performance of the algorithms and subsequently compared their results on the created face ageing database.
Face image data were passed to face recognition modules as input for the system. The face images passed were transformed into operationally compatible format (resizing images into uniform dimension).

The facial recognition process normally has four interrelated phases or steps. The first step is preprocessing, the second is feature extraction, and the final cumulative step is face recognition. These steps depend on each other and often use similar techniques.

PREPROCESSING
Face images analysis are pre-processed and enhanced to improve the recognition performance of the system. This is to help reduce the noise level and make the estimation process simpler and better conditioned. Based on requirement some of the following pre-processing techniques are used in the proposed face recognition system. Different types of pre-processing/enhancement techniques related to the face recognition process are explained as fallows with the help of flow chart and corresponding face images.

Face images of different candidates with different facial expressions are taken with a Canon Powershot S3 IS 6.0 megapixel digital camera in the size of 1200 × 1600 pixels (2.0 megapixels). All face images taken resemble the following general features:
Uniform illumination condition
Light color background
Face is upright and frontal position
Tolerance for tilting and rotation up to 10 degree
The face image are present in the face ageing databases, considering Ghanaian Frontal View (GFV) in this database that stored and; are captured using a digital Canon camera with pixel (64* 64). The image present in the GFV databases are greyscale or color. The greyscale undergoes preprocessing using the face image, due to noise the GFV face image is converted into grey scale image. There exist two rotations are present in the grey scale image that is in and out-of-scale. To improve the accuracy of the facial component a non-reflective similarity transformation is applied to normalize each face image based in the fiducial point on the face.

Figure an image will be captured using a camera and fed as probe image to the recognition system. The images then are pre-processed to enhance its quality. The features are then extracted using suitable schemes. These features are then classified using appropriate classifying algorithm.

Preprocessing Techniques
The basic pre-processing methods used in the experiment. The input color image is converted into gray image. Using suitable cropping (face detection) schemes, the image is cropped and then resized to meet the requirement. The image is then normalized to have uniform intensity/gray level. Image is then filtered using low pass filter.

Face Cropping
Face cropping is also an important task to achieve high recognition rate. Cropping can be done using various face detection techniques. Face detection involves detecting a face from an image using complete image (image based approach) or by detecting one or more features from the image (Feature based approach) such as nose, eyes, lips etc. Face detection can also be done based on active shape models such as locating head boundary.
The study used image based approach which includes a window scanning technique with fixed and dynamic mask size and feature based approach which includes color segmentation. Mask size is determined empirically for better recognition rate. In feature based approach, image is transferred from RGB color space to YCbCr color space provided Cb and Cr values satisfies following conditions: 77 Cb 127 and 133 Cr 173. Using dilation, erosion and morphological operations face is detected.

Image Resizing
The resulted image from various face detection schemes has been resized using nearest neighbor interpolation method with specified output size.

Image Normalisation

Image de-noising and Filtering
Images are often by default have Gaussian noise due to illumination variations. To de-noise it we work on pixel based filtering techniques. In this study, Low Pass Filter (LPF) was applied to eliminate high frequency information and retain only with low frequency information.

Feature Extraction
Statistical approach for face recognition algorithm
Images of faces, represented as high-dimensional pixel arrays, often belong to a manifold of lower dimension. In statistical approach, each image is represented in terms of d features. So, it's viewed as a point (vector) in a d-dimensional space. The dimensionality -number of coordinates needed to specify a data point- of this data is too high. Therefore, the goal is to choose and apply the right statistical tool for extraction and analysis of the under laying manifold. These tools must de ne the embedded face space in the image space and extract the basic functions from the face space. This would permit patterns belonging to di erent classes to occupy disjoint and compacted regions in the feature space. Consequently, the study is required to de ne a line, curve, plane or hyperplane that separates faces belonging to di erent classes. Many of these statistical tools are not used alone. They are modi ed or extended by researchers in order to get better results. Some of them are embedded into bigger systems, or they are just a part of a recognition algorithm. Many of them can be found along classi cation methods like a DCT embedded in a Bayesian Network or a Gabor Wavelet used with a Fuzzy Multilayer Perceptron.

Appearance Approach
Appearance based face recognition techniques (Donner et al, 2006) have received significant attention from a wide range of research areas such as biometrics, pattern recognition, computer vision and machine mining (Huang & Shao, 2004). Although humans can recognize faces easily, building automated face recognition systems remains a great challenge in computer-based automated recognition research. To have a clear and high-level categorization, instead follow a guideline suggested by the psychological study of how humans use holistic and local features. Specifically, the proposed papers have the following categorization: Holistic approaches and Hybrid approaches

Holistic approaches
Among appearance-based holistic approaches, Eigenfaces and Fisher faces have proved (Solar, & Navarreto, 2005, Turk & Pentland, 1991) to be effective in experiments with large databases. In holistic approaches, several authors have taken either whole faces as features or Gabor wavelet filtered whole faces

PCA
PCA mainly are focus on data reduction and interpretation which explains the variance-covariance structure of a set of variables though a fewer linear combination of these variables. PCA is a statistical approach to recognition including object recognize for aligned. This process convert high dimensional image into each two dimensional image into a dimensional vector. Each face image is represented as a weight sum (feature vector) of the principle component which are stored in one dimensional array. Each component represent only a certain feature of the face. PCA is an orthogonal transformation (generates a set of orthonormal basis vectors) of the coordinate system in which the pixels are described and maximizes the scatter of all the projected samples. The main idea of the PCA is to find the vectors which best account for the distribution of face image within the entire image space and construct a face space and project the image into face space. The PCA aims to extract a subspace where the variance is maximized.
To perform a principal component analysis on the data set:
The normalized training image in the N-dimensional space is stored in a vector of size N. Let the normalized training face image set, Get an original image data; let p1 ,p2 ,p3 ,………….pm are represented as M×1 vectors.
Each of the normalized training face images is mean centered. This is done by subtracting the mean face image from each of the normalized training images. The mean image is represented as a column vector where each scalar is the mean of all corresponding pixels of the training images,
Compute the mean vector p = 1m (1).
Subtract the mean. Thus after normalizing the images to unity norm and subtracting the grand mean a new image set is derived, where. Each represents a normalized image with dimensionality M, ,
The column vectors are combined into a data matrix which is multiplied by its transpose to create a covariance matrix. Calculate the covariance matrix of the normalized image set as: (2)
This covariance matrix is symmetric and matrix is the size of the matrix.
Compute the eigenvalues and eigenvector of the covariance matrix is intractable for face image.
Let and .
Forming a feature vector: eigenvectors are order by eigenvalues from the highest or lowest, thus given the component in order of significance. The eigenvector with highest is the principal component of the data set since the eigenvectors spanned the most variance in the matrix. The feature vector formed by choosing the largest eigenvalue. The eigenvector with the highest eigenvalues correspond to the direction in which the data have maximum variances.
Deriving the new data set, the study will chose the principal component (eigenvectors) to keep in our data and formed a feature vector, the study will simply take the transpose of the vector and multiply it on the left of the original data set transpose.
Final data=Row feature*Row data adjusted

LDA
LDA is supervised dimensional technique based on a linear projection from the high dimensional space to a low dimensional space by maximizing the between class scatter and minimizing the within-class scatter. It is mainly used as feature extraction step before classification and provide dimensionality reduction of feature vectors without a loss of information.

LDA classifies faces of unknown individuals based on a set of training images of known individuals. The technique finds the underlying vectors in the facial feature space (vectors) that would maximize the variance between individuals (or classes) and minimize the variance within a number of samples of the same person (ie within a class).

In LDA for all the samples of all classes, define two measure:
Within-class scatter matrix
(6), where is the number of classes, is the ith sample class j, is the mean of class j, is the number of samples between class scatter matrix.
(7), where represents the mean all classes.
The LDA principles tries to maximize the ratio determinant of the between-class scatter matrix of the projected samples.