Nonlinear Filters for Image Processing

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).