Chapter 8
Low Dimensionality Representations and Matching

This chapter investigates the possibility of alternative ways to represent iconic data so that a large variety of images can be faithfully described using vectors of reduced dimensionality. Besides significant storage savings, these approaches provide significant benefits to template detection and recognition algorithm, improving their efficiency and effectiveness. Three main approaches are considered: principal components analysis (PCA), independent components analysis (ICA), and linear discriminant analysis (LDA). Probabilistic and kernel variants of PCA are described and criteria for choosing the optimal representation dimensionality are discussed. The basics of ICA are provided and Bayesian and classification tuned versions of LDA presented. An application of PCA to the synthesis of facial images and mug-shot database browsing is discussed.

keywords: principal components analysis, independent components analysis, linear discriminant analysis, kernel PCA, dimensionality reduction, image retrieval.