Pattern recognition using composite features

Pattern recognition aims to classify a pattern into one of the predefined classes. A pattern is represented by a set of variables, which are called primitive variables in this dissertation. For a better classification performance, feature extraction has been widely used to obtain new features from primitive variables. This reduces the number of variables while preserving as much discriminative information as possible. In this dissertation, the main focus is on the feature extraction for pattern recognition. A new method of extracting composite features is derived and then applied to several problems such as eye detection, face recognition, and ordinary pattern classification problems. The method of extracting composite features is first derived from face images. In appearance-based models for face recognition, the intensity of each pixel in a face image is used as a primitive variable. In the proposed method, a composite vector is composed of a number of pixels inside a window on an image. The covariance of composite vectors is obtained from the inner product of composite vectors and can be considered as a generalized form of the covariance of pixels. It contains information on statistical dependency among multiple pixels. The size of the covariance matrix can be controlled by changing the window size or by overlapping the windows. This is a great advantage because manipulation of a large-sized covariance matrix can be avoided and consequently the small sample size problem can be solved. The proposed C-LDA is a linear discriminant analysis (LDA) using the covariance of composite vectors. In C-LDA, features are obtained by linear combinations of the composite vectors. These extracted features are called composite features because each feature is a vector whose dimension is equal to the dimension of the composite vector. This composite feature is further reduced by using a downscaling technique because there are usually strong correlations among the elements of the composite feature. An image can be represented by these reduced composite features, each of which is a small-sized vector. In the case of C-LDA, the small sample size problem rarely occurs and the number of extracted features can be larger than the number of classes because the within-class and between-class scatter matrices have full ranks. The C-LDA is applied to several classification problems. First, composite features are used to detect eyes for face recognition in a facial image. In eye detection, positive samples for eyes are similar and they can be assumed to be normally distributed, while negative samples are not. In this case, it is better to use the objective function in biased discriminant analysis (BDA), rather than the function in LDA. The proposed C-BDA is a biased discriminant analysis using the covariance of composite vectors, which is a variant of C-LDA. In the hybrid cascade detector constructed for eye detection, Haar-like features are used in the earlier stages and composite features obtained from C-BDA are used in the later stages. The experimental results for the FERET database show that the hybrid cascade detector provides eye detection rates of 99.0% and 96.2% for 200 validation images and 1000 test images, respectively. Second, composite features are used for face recognition, where the features are obtained from C-LDA. Comparative experiments are performed using the FERET, CMU, and ORL databases of facial images. The experimental results show that the proposed C-LDA provides the best recognition rate among several methods in all of the tests and provides the robust performance to the variations in facial expression, illumination, and eye coordinates. Third, three types of C-LDA are derived for classification problems of ordinary data sets, which are not image data sets. The proposed C-LDA(E), C-LDA(C), and C-LDA(N) can be considered as generalizations of LDA using the Euclidean distance, LDA using the Chernoff distance, and the nonparametric discriminant analysis, respectively. Experimental results on several data sets indicate that C-LDA provides better classification results than the other methods. Especially on the Sonar data set, C-LDA(E) with the Parzen classifier shows much better performance, compared to previously reported results. In summary, C-LDA is a general method to use the covariance of composite vectors instead of the covariance of primitive variables, and can be applied to several classification problems. C-LDA shows a much better performance than the other methods, especially when adjacent primitive variables are strongly correlated as in image data sets and the Sonar data set.