Correlation is a robust and general technique for pattern recognition and is used in many applications, such as automatic target recognition, biometric recognition and optical character recognition The design, analysis and use of correlation pattern recognition algorithms requires background information, including linear systems theory, random variables and processes, matrix/vector methods, detection and estimation theory, digital signal processing and optical processing This 2005 book provides a needed review of this diverse background material and develops the signal processing theory, the pattern recognition metrics, and the practical application know-how from basic premises It shows both digital and optical implementations It also contains technology presented by the team that developed it and includes case studies of significant interest, such as face and fingerprint recognition Suitable for graduate students taking courses in pattern recognition theory, whilst reaching technical levels of interest to the professional practitioner

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Correlation Pattern Recognition

This article describes a complete theory of spatial coherence for undulator radiation sources. Current estimations of coherence properties often assume that undulator sources are quasi-homogeneous, like thermal sources, and rely on the application of the van Cittert–Zernike theorem for calculating the degree of transverse coherence. Such assumption is not adequate when treating third generation light sources, because the vertical (geometrical) emittance of the electron beam is comparable or even much smaller than the radiation wavelength in a very wide spectral interval that spans over four orders of magnitude (from 0.1 up to 10 3 A ). Sometimes, the so-called Gaussian–Schell model, that is widely used in statistical optics in the description of partially coherent sources, is applied as an alternative to the quasi-homogeneous model. However, as we will demonstrate, this model fails to properly describe coherent properties of X-ray beams from non-homogeneous undulator sources. As a result, a more rigorous analysis is required. We propose a technique, based on statistical optics and Fourier optics, to explicitly calculate the cross-spectral density of an undulator source in the most general case, at any position after the undulator. Our theory, that makes consistent use of dimensionless analysis, allows relatively easy treatment and physical understanding of many asymptotes of the parameter space, together with their region of applicability. Particular emphasis is given to the asymptotic situation when the horizontal emittance is much larger than the radiation wavelength, and the vertical emittance is arbitrary. This case is practically relevant for third generation synchrotron radiation sources.

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Transverse coherence properties of X-ray beams in third-generation synchrotron radiation sources

In response to comments by Borovoi [J. Opt. Soc. Am. A19, 2517 (2002)] on my earlier work [J. Opt. Soc. Am. A18, 1929 (2001)], the kinetic approach to extinction is compared with the traditional radiative transfer formalism and advantages of the former are illustrated with concrete examples. It is pointed out that the basic differential equation dI(l)=-cσI(l)dl already implies perfect randomness (absence of correlations) on small scales. One of the consequences is that the extinction of radiation in a negatively correlated random medium cannot be treated within the traditional framework. This limits the usefulness of the Jensen inequality. Also, simple counterexamples to theorems given in the first reference above and in Dokl. Akad. Nauk SSSR, 276, 1374 (1984) are presented.

On the extinction of radiation by a homogeneous but spatially correlated random medium: reply to comment

Laser beam quality, entropy and the limits of beam shaping

We consider Brownian motion in the space of fields and show that such a random field interacting with threshold type detectors produces clicks at random moments of time. The corresponding probabili ...

Edward L. O'Neil

Papers

Introduction to Statistical Optics