Gabor wavelets and kernel direct discriminant analysis for face recognition

Kernel discriminant analysis (KDA) and the kernel principal component analysis (KPCA), which are the extension of the linear discriminant analysis (LDA) and the principal component analysis (PCA), respectively, from linear domain to nonlinear domain via the kernel trick, are two very popular nonlinear feature extraction methods. In this paper, we present a new feature extraction algorithm by combing KDA and KPCA, and then apply it to the face recognition task. The experimental results on Yale face dataset show that the proposed method can significantly improve the performance both KDA and KPCA.

This paper presents a novel Gabor-based kernel Principal Component Analysis (PCA) method by integrating the Gabor wavelet representation of face images and the kernel PCA method for face recognition. Gabor wavelets first derive desirable facial features characterized by spatial frequency, spatial locality, and orientation selectivity to cope with the variations due to illumination and facial expression changes. The kernel PCA method is then extended to include fractional power polynomial models for enhanced face recognition performance. A fractional power polynomial, however, does not necessarily define a kernel function, as it might not define a positive semidefinite Gram matrix. Note that the sigmoid kernels, one of the three classes of widely used kernel functions (polynomial kernels, Gaussian kernels, and sigmoid kernels), do not actually define a positive semidefinite Gram matrix either. Nevertheless, the sigmoid kernels have been successfully used in practice, such as in building support vector machines. In order to derive real kernel PCA features, we apply only those kernel PCA eigenvectors that are associated with positive eigenvalues. The feasibility of the Gabor-based kernel PCA method with fractional power polynomial models has been successfully tested on both frontal and pose-angled face recognition, using two data sets from the FERET database and the CMU PIE database, respectively. The FERET data set contains 600 frontal face images of 200 subjects, while the PIE data set consists of 680 images across five poses (left and right profiles, left and right half profiles, and frontal view) with two different facial expressions (neutral and smiling) of 68 subjects. The effectiveness of the Gabor-based kernel PCA method with fractional power polynomial models is shown in terms of both absolute performance indices and comparative performance against the PCA method, the kernel PCA method with polynomial kernels, the kernel PCA method with fractional power polynomial models, the Gabor wavelet-based PCA method, and the Gabor wavelet-based kernel PCA method with polynomial kernels.

Support Vector Machines and Kernel methods have become very popular as methods for learning from examples. In this paper, in order to solve the non-linear and the time of recognition problem, recent advanced techniques are presented. For example, Kernel Principal Components and Proximal Support Vector Machines, Kernel Principal Components Analysis can describe multiple correlations between pixels in the image recognition, and can handle the high order statistics of the original data, at the same time the nonlinear features of the image can be preferably extracted. Proximal Support Vector Machines is an improvement for these characters of Support Vector Machines, combines the proximal algorithm with Support Vector Machines, has a better ability of nonlinear mapping and a stronger generalization capability, and the pace of Proximal Support Vector Machines is very enhanced. In this paper, the computer simulation was progressed based on ORL face database, the effectiveness of the Proximal Support Vector Machines algorithm and Kernel Principal Components Analysis algorithm were shown by experimental results.

This paper introduces a novel 2D Gabor-Fisher Classifier for face recognition. The 2D-GFC method applies the 2D Fisher Linear Discriminant Analysis (2D-LDA) to the gaborfaces which is derived from the Gabor wavelets representation of face images. In our method, Gabor wavelets first derive desirable facial features characterized by spatial frequency, spatial locality, and orientation selectivity to cope with the variations due to illumination and facial expression changes. 2D-LDA is then used to enhance the face recognition performance by maximizing the Fisher's linear projection criterion. To evaluate the performance of 2D-GFC, experiments were conducted on FERET database with several other methods.

This paper presents a novel face recognition method by integrating the Gabor wavelet representation of face images and the enhanced powerful discriminator, complete Kernel Fisher Discriminant (CKFD) with fractional power polynomial (FPP) models. The novelty of this paper comes from (1) Gabor wavelet, is employed to extract desirable facial features characterized by spatial frequency, spatial locality and orientation selectivity to cope with the variations in illumination and facial expressions, which improves the recognition performance; (2) a recently proposed powerful discriminator, namely CKFD, which enhances its discriminating ability using two kinds of discriminant information (i.e., regular and irregular information), is employed to classify the Gabor features; (3) the FPP models, are employed to CKFD analysis to enhance the discriminating ability. Comparing with existing principal component analysis, linear discriminant analysis, kernel principal component analysis, KFD and CKFD methods, the proposed method gives the superior results with the ORL, Yale and UMIST face databases.

This paper presents a novel algorithm - robust kernel principal component analysis (robust KPCA), on the basis of the research of kernel principal component analysis (KPCA) and robust principal component analysis (RPCA). First, this algorithm sets the radius of the images of the training samples in the feature space using kernel tricks, then determines whether the samples are outliers or not, and finally analyzes the training samples which have eliminated the outliers using KPCA algorithm. The improved KPCA algorithm not only retains the non-linearity property of KPCA algorithm but also gets better robustness. Because the effects of outliers are eliminated, robust KPCA algorithm gets higher accuracy than KPCA algorithm for data analysis. The simulation experiments show that the robust KPCA algorithm developed is better than the KPCA algorithm.

In the biometrics community, face and speaker recognition are mature fields in which several systems have been proposed over the past twenty years. While existing systems perform well under controlled recording conditions, mismatch caused by the use of different sensors or a lack of cooperation from the subject still significantly affects performance, especially in challenging scenarios such as in forensics. Furthermore, existing methods suffer from scalability issues, which prevents them from taking advantage of increasingly large amounts of training data. This is otherwise a promising approach to improve accuracy in such challenging scenarios. In this thesis we address these problems of mismatch and complexity by developing scalable probabilistic models that we apply to face, speaker and bimodal recognition. Our contributions are four-fold. First, we propose a unified framework for session variability modeling techniques based on Gaussian mixture models (GMM), that encompasses inter-session variability (ISV) modeling, joint factor analysis (JFA) and total variability (TV) modeling. Second, we propose a novel exact and scalable formulation of probabilistic linear discriminant analysis (PLDA), which is a probabilistic and generative framework that models between-class and within-class variations. This formulation solves a major scalability issue, by improving both the time complexity of the training procedure from cubic to linear with respect to the number of samples per class, and the complexity of the scoring procedure. Furthermore, the implementations of all the proposed techniques are integrated into a novel collaborative open source software library called Bob 1 that enforces fair evaluations and encourages reproducible research. Fourth and finally, large-scale experiments are conducted with all of the above machine learning algorithms on several databases such as FRGC for face recognition, NIST SRE12 for speaker recognition and MOBIO for bimodal recognition, showing competitive performances.

Face detection is the first step in the face recognition system. The Neural network as well as Gabor wavelet based face detection is proposed in this paper. The proposed system applies neural network algorithm to make the slanting face upright and Gabor wavelet is used to extract the invariable features from the selected window. The principal component analysis is applied to identify the person from the data base. The Proposed system gives very high detection efficiency with low number of false alarms. We have shown the results on different test sets with different degrees of variability of the face patterns. In this paper, we present a new approach for determining the orientation of face in the selected window and then use this information to rotate the face upright

In this paper, a robust face recognition algorithm is proposed, which is based on the elastic graph matching (EGM) and discriminative feature analysis algorithm. We introduce a cost function for the EGM taking account of variations in face pose and facial expressions, and propose its optimization procedure. Our proposed cost function uses a set of Gabor-wavelet-based features, called robust jet, which are robust against the variations. The robust jet is defined in terms of discrete Fourier transform coefficients of Gabor coefficients. To cope with the difference between face poses of test face and reference faces, 2 x 2 warping matrix is incorporated in the proposed cost function. For the discriminative feature analysis, linear projection discriminant analysis and kernel-based projection discriminant analysis are introduced. These methods are motivated to solve the small-size problem of training samples. The basic idea of PDA is that a class is represented by a subspace spanned by some training samples of the class instead of using sample mean vector, that the distance from a pattern to a class is defined by using the error vector between the pattern and its projection to the subspace representing the class, and that an optimum feature selection rule is developed using the distance concept in a similar way as in the conventional linear discriminant analysis. In order to evaluate the performance of our face recognition algorithm, we carried out some experiments using the well-known FERET face database, and compared the performance with recently developed approaches. We observed that our algorithm outperformed the compared approaches.

Recently, the nonlinear projection trick (NPT) was introduced enabling direct computation of coordinates of samples in a reproducing kernel Hilbert space. With NPT, any machine learning algorithm can be extended to a kernel version without relying on the so called kernel trick. However, NPT is inherently difficult to be implemented incrementally because an ever increasing kernel matrix should be treated as additional training samples are introduced. In this paper, an incremental version of the NPT (INPT) is proposed based on the observation that the centerization step in NPT is unnecessary. Because the proposed INPT does not change the coordinates of the old data, the coordinates obtained by INPT can directly be used in any incremental methods to implement a kernel version of the incremental methods. The effectiveness of the INPT is shown by applying it to implement incremental versions of kernel methods such as, kernel singular value decomposition, kernel principal component analysis, and kernel discriminant analysis which are utilized for problems of kernel matrix reconstruction, letter classification, and face image retrieval, respectively.

A novel feature extraction method that utilizes nonlinear mapping from the original data space to the feature space is presented in this dissertation. Feature extraction methods aim to find compact representations of data that are easy to classify. Measurements with similar values are grouped to same category, while those with differing values are deemed to be of separate categories. For most practical systems, the meaningful features of a pattern class lie in a low dimensional nonlinear constraint region (manifold) within the high dimensional data space. A learning algorithm to model this nonlinear region and to project patterns to this feature space is developed. Least squares estimation approach that utilizes interdependency between points in training patterns is used to form the nonlinear region. The proposed feature extraction strategy is employed to improve face recognition accuracy under varying illumination conditions and facial expressions. Though the face features show variations under these conditions, the features of one individual tend to cluster together and can be considered as a neighborhood. Low dimensional representations of face patterns in the feature space may lie in a nonlinear constraint region, which when modeled leads to efficient pattern classification. A feature space encompassing multiple pattern classes can be trained by modeling a separate constraint region for each pattern class and obtaining a mean constraint region by averaging all the individual regions. Unlike most other nonlinear techniques, the proposed method provides an easy intuitive way to place new points onto a nonlinear region in the feature space. The proposed feature extraction and classification method results in improved accuracy when compared to the classical linear representations. Face recognition accuracy is further improved by introducing the concepts of modularity, discriminant analysis and phase congruency into the proposed method. In the modular approach, feature components are extracted from different sub-modules of the images and concatenated to make a single vector to represent a face region. By doing this we are able to extract features that are more representative of the local features of the face. When projected onto an arbitrary line, samples from well formed clusters could produce a confused mixture of samples from all the classes leading to poor recognition. Discriminant analysis aims to find an optimal line orientation for which the data classes are well separated. Experiments performed on various databases to evaluate the performance of the proposed face recognition technique have shown improvement in recognition accuracy, especially under varying illumination conditions and facial expressions. This shows that the integration of multiple subspaces, each representing a part of a higher order nonlinear function, could represent a pattern with variability. Research work is progressing to investigate the effectiveness of subspace projection methodology for building manifolds with other nonlinear functions and to identify the optimum nonlinear function from an object classification perspective.

In kernel methods, choosing a suitable kernel is in dispensable for favorable results. No well-founded methods, however, have been established in general for unsupervised learning. We focus on kernel Princ ipal Component Analysis (kernel PCA), which is a nonlinear extension of principal component analysis and ha s been used electively for extracting nonlinear featu res and reducing dimensionality. As a kernel method , kernel PCA also suffers from the problem of kernel choice. Although cross-validation is a popular meth od for choosing hyperparameters, it is not applicable straightforwardly to choose a kernel in kernel PCA because of the incomparable norms given by differen t kernels. It is important, thus, to develop a well founded method for choosing a kernel in kernel PCA. This study proposes a method for choosing hyperparameters in kernel PCA (kernel and the number of components) based on cross-validation for the comparable reconstruction errors of pre-images in t he original space. The experimental results on synthesized and real-world datasets demonstrate tha t the proposed method successfully selects an appropriate kernel and the number of components in kernel PCA in terms of visualization and classification errors on the principal components. The results imply that the proposed method enables automatic design of hyperparameters in kernel PCA.

There is a trend in recent machine learning community to construct a nonlinear version of a linear algorithm using the 'kernel method', e.g. Support Vector Machines (SVMs), kernel principal component analysis, kernel fisher discriminant analysis and the recent kernel clustering algorithms. In unsupervised clustering algorithms using kernel method, typically, a nonlinear mapping is used first to map the data into a potentially much higher feature space, where clustering is then performed. A drawback of these kernel clustering algorithms is thatthe clustering prototypes lie in high dimensional feature space and hence lack clear and intuitive descriptions unless using additional projection approximation from the feature to the data space as done in the existing literatures. In this paper, a novel clustering algorithm using the 'kernel method' based on the classical fuzzy clustering algorithm (FCM) is proposed and called as kernel fuzzy c-means algorithm (KFCM). KFCM adopts a new kernel-induced metric in the data space to replace the original Euclidean norm metric in FCM and the clustered prototypes still lie in the data space so that the clustering results can be reformulated and interpreted in the original space. Our analysis shows that KFCM is robust to noise and outliers and also tolerates unequal sized clusters. And finally this property is utilized to cluster incomplete data. Experiments on two artificial and one real datasets show that KFCM hasbetter clustering performance and more robust than several modifications of FCM for incomplete data clustering.

Machine learning and pattern recognition recently become a hot topic in computing world. This is due to the fast-growing of resources as well as techniques that make it easier to solve machine learning and pattern recognition problems. Problems that require machine learning solutions may be very simple for humans but actually can be very complex for machines to solve them. Face recognition is amongst those problems. Almost all human can easily recognize others without require specific knowledge to do it, different from machines which require its. This paper discussed face recognition task using machine learning strategies which involved Kernel Principal Component Analysis (KPCA) and Support Vector Machine (SVM) to identify person. KPCA extracted features from 2D image input and produced the important features of an image input. The extracted face features are recognized by SVM by classifying human face according to their stored identity in a database. SVM, which was basically a binary classifier worked by using one-against-one strategy to compare the face feature vector of a single test image to the stored face image in a face image database. Experiment results on grayscale images with size 92x112 pixels gave 96.25% of accuracy rate. Hence, KPCA and SVM for face recognition is a robust machine learning method.

A novel feature selection strategy for improved face recognition in images with variations due to illumination conditions, facial expressions, and partial occlusions is presented in this dissertation. A hybrid face recognition system that uses feature maps of phase congruency and modular kernel spaces is developed. Phase congruency provides a measure that is independent of the overall magnitude of a signal, making it invariant to variations in image illumination and contrast. A novel modular kernel spaces approach is developed and implemented on the phase congruency feature maps. Smaller sub-regions from a predefined neighborhood within the phase congruency images of the training samples are merged to obtain a large set of features. These features are then projected into higher dimensional spaces using kernel methods. The unique modularization procedure developed in this research takes into consideration that the facial variations in a real world scenario are confined to local regions. The additional pixel dependencies that are considered based on their importance help in providing additional information for classification. This procedure also helps in robust localization of the variations, further improving classification accuracy. The effectiveness of the new feature selection strategy has been demonstrated by employing it in two specific applications via face authentication in low resolution cameras and face recognition using multiple sensors (visible and infrared). The face authentication system uses low quality images captured by a web camera. The optical sensor of the web camera is very sensitive to environmental illumination variations. It is observed that the feature selection policy overcomes the facial and environmental variations. A methodology based on multiple training images and clustering is also incorporated to overcome the additional challenges of computational efficiency and the subject's non involvement. A multi-sensor image fusion based face recognition methodology that uses the proposed feature selection technique is presented in this dissertation. Research studies have indicated that complementary information from different sensors helps in improving the recognition accuracy compared to individual modalities. A decision level fusion methodology is also developed which provides better performance compared to individual as well as data level fusion modalities. The new decision level fusion technique is also robust to registration discrepancies, which is a very important factor in operational scenarios. Research work is progressing to use the new face recognition technique in multi-view images by employing independent systems for separate views and integrating the results with an appropriate voting procedure.