Books in the SPIE/IEEE Series on Imaging Science & Engineering series

Nonlinear Filters for Image Processing Editors: Edward R. Dougherty, Texas A&M University Jaakko T. Astola, Tampere University of Technology Part of the SPIE/IEEE Series on Imaging Science & Engineering This text covers key mathematical principles and algorithms for nonlinear filters used in image processing. Readers will gain an in-depth understanding of the underlying mathematical and filter design methodologies needed to construct and utilize nonlinear filters in a variety of applications. The 11 chapters, written by experts in the field, explore topics of contemporary interest as well as fundamentals drawn from nonlinear filtering's historical roots in mathematical morphology and digital signal processing. Linear filtering has dominated image processing, partly because the mathematical analysis is much easier than for nonlinear operators. However, nonlinear filters often yield superior results. This book explains in depth various filter options and the types of applications for which they are best suited. The presentation is rigorous, yet accessible to engineers with a solid background in mathematics. Contents: Logical image operators (E. R. Dougherty, J. Barrera). Computational gray-scale operators (E. R. Dougherty, J. Barrera). Translation-invariant set operators (E. R. Dougherty). Granulometric filters (E.R. Dougherty, Y. Chen). Easy recipes for morphological filters (H. J. A. M. Heijmans). Introduction to connected operators (H. J. A. M. Heijmans). Representation and optimization of stack filters (J. T. Astola, P. Kuosmanen). Invariant signals of median and stack filters (J. T. Astola, P. Kuosmanen). Binary polynomial transforms and logical correlation (K. O. Egiazarian, J. T. Astola, S. S. Agaian). Applications of binary polynomial transforms (K. O. Egiazarian, J. T. Astola, S. S. Agaian, R. Öktem). Random sets in view of image filtering applications (I. S. Molchanov).

Random Processes for Image and Signal Processing Edward R. Dougherty Second in the SPIE/IEEE Series on Imaging Science & Engineering Science and engineering deal with temporal, spatial, and higher-dimensional processes that vary randomly from observation to observation. Deterministic analysis does not provide a framework for understanding the ensemble of observations, nor does it provide a mechanism for predicting future events. Random processes provide the tools to bridge these gaps. Readers of this book will gain an intuitive appreciation of random functions, in addition to understanding theory and processes necessary for sophisticated applications. The initial chapter covers basic theory of probability, with special attention to multivariate distributions and functions of several random variables. Subsequent topics include the basic properties of random functions, canonical representation, transform coding, optimal filter design (linear and nonlinear), neural networks, discrete- and continuous-time Markov chains, and the theory of random closed sets. This book can be used as a one-semester course for students with a strong background in probability and statistics or as a full-year course for students who lack such preparation. The large number of imaging applications also makes it useful for graduate courses on image processing. Contents: Probability theory. Random processes. Canonical representation. Optimal filtering. Random models. Bibliography. Index.