In numerous applications involving high dimensional data, certain subspace techniques such as principal components analysis (PCA) may be utilized in feature extraction. Often, PCA can reduce the dimensionality while retaining most of the significant information of the original data. This can be beneficial not only for representation of the data more compactly (compression), but also for transforming the data into a more useful form for applications involving feature extraction and classification. Relatively recent developments with PCA extend conventional principal components analysis to newer variants of PCA which appear particularly useful in computer vision and image applications: (1) two dimensional PCA ("2D PCA"), and (2) bidirectional or bilateral two dimensional PCA ("B2DPCA", "Bi2DPCA", or "(2D)² PCA"). The latter category includes an iterative version which is an example of coupled subspace analysis or "CSA"; the non-iterative version is known as projective Bi2DPCA. In this thesis, these PCA variants are considered as special cases of the more general CSA. Theoretical advantages of 2D PCA and bidirectional PCA over conventional PCA should arise from the fact that significant information about the spatial relationship between image pixels may be discarded in conventional PCA as the image is represented by a large column vector, whereas 2D PCA and bidirectional PCA techniques can preserve more of this information by representing the image as a matrix rather than a long vector. The problems of small sample size, and curse of dimensionality are also alleviated to some extent, particularly in the cases of B2DPCA and iterated CSA. Some of these PCA variants have been proposed in various image recognition applications recently, including biometric identification using iris texture, face images, and palm prints, and categorization of wood species based on wood grain texture to name a few examples. So, while much focus has been placed on feature extraction methods such as use of Gabor wavelets or similar techniques for some applications such as iris recognition, some subspace techniques, including some of these PCA variants, have shown promise in conjunction with image preprocessing techniques for removal of uneven background illumination and contrast enhancement. In this thesis, the image application of biometric iris recognition is chosen as the means of evaluating potential advantages of these newer PCA variants, including CSA, in the context of feature extraction and classification. The rich texture information of these images, and the utilization of effective image registration techniques, yields images which are well suited for this purpose. As the primary focus of this thesis, these PCA variants are evalulated using closed set identification test mode, and are compared using Euclidean distance single nearest neighbor classifier; images are preprocessed using top-hat filtering and contrast limiting adaptive histogram equalization (CLAHE). Use of multiple test (probe) images is considered, and the impact on performance is considered also for training image sets with 2, 3, and 4 sample images per class. Concurrently, the application of iris image recognition is addressed in detail. Other applications for which these PCA variants and preprocessing techniques may be beneficial are discussed in the concluding section.
