Nonlinear Filters for Image Processing

"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 use nonlinear filters in a variety of applications.

The 11 chapters explore topics of contemporary interest as well as fundamentals drawn from nonlinear filtering's historical roots in mathematical morphology and digital signal processing. This book examines 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." Preface.

Logical Image Operators (E. Dougherty & J. Barrera).

Computational Gray-Scale Operators (E. Dougherty & J. Barrera).

Translation-Invariant Set Operators (E. Dougherty).

Granulometric Filters (E. Dougherty & Y. Chen)

Easy Recipes for Morphological Filters (H. Heijmans).

Introduction to Connected Operators (H. Heijmans).

Representation and Optimization of Stack Filters (J. Astola & P. Kuosmanen).

Invariant Signals of Median and Stack Filters (J. Astola & P. Kuosmanen).

Binary Polynomial Transforms and Logical Correlation (K. Egiazarian, et al.).

Applications of Binary Polynomial Transforms (K. Egiazarian, et al.).

Random Sets in View of Image Filtering Applications (I. Molchanov).

Index.

EDWARD R. DOUGHERTY, PhD, is Director of the Genomic Signal Processing Laboratory at Texas A&M University, where he holds the Robert M. Kennedy '26 Chair and is Professor in the Department of Electrical and Computer Engineering. He is also co-Director of the Computational Biology Division at the Translational Genomics Research Institute as well as Adjunct Professor in the Department of Bioinformatics and Computational Biology, M. D. Anderson Cancer Center at the University of Texas. Dr. Dougherty has published more than 300 peer-reviewed journal articles and book chapters.

MICHAEL L. BITTNER, PhD, is co-Director and Senior Investigator at the Computational Biology Division at the Translational Genomics Research Institute. Previously, he was associate investigator in the Cancer Genetics Branch of the National Human Genome Research Institute at the National Institutes of Health. Dr. Bittner holds a dozen patents and has published more than 100 articles. 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).