Handbook of Face Recognition
Containing a comprehensive account of face recognition research and technology, this handbook provides coverage of the concepts, methods, and algorithms for automated face detection and recognition.
TABLE OF CONTENTS Handbook of Face Recognition
Chapter 7: Face Recognition in Subspaces
Gregory Shakhnarovich [1] and Baback Moghaddam [2]
Images of faces, represented as high-dimensional pixel arrays, often belong to a manifold of intrinsically low dimension. Face recognition, and computer vision research in general, has witnessed a growing interest in techniques that capitalize on this observation and apply algebraic and statistical tools for extraction and analysis of the underlying manifold. In this chapter we describe in roughly chronologic order techniques that identify, parameterize, and analyze linear and nonlinear subspaces, from the original Eigenfaces technique to the recently introduced Bayesian method for probabilistic similarity analysis. We also discuss comparative experimental evaluation of some of these techniques as well as practical issues related to the application of subspace methods for varying pose, illumination, and expression.
1 Face Space and its Dimensionality
Computer analysis of face images deals with a visual signal (light reflected off the surface of a face) that is registered by a digital sensor as an array of pixel values. The pixels may encode color or only intensity. In this chapter we assume the latter case (i.e., gray-level imagery). After proper normalization and resizing to a fixed m-by- n size, the pixel array can be represented as a point (i.e., vector) in an mn-dimensional image space by simply writing its pixel values in a fixed (typically raster) order. A critical issue in the analysis of such multidimensional data is the dimensionality, the number of coordinates necessary to specify a data point. Below we discuss the factors...
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