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.
Logical Image Operators, E.R. Dougherty and J. Barrera; Computational Gray-Scale Operators, E.R. Dougherty and J. Barrera; Translation-Invariant Set Operators, E.R. Dougherty; Granulometric Filters, E.R. Dougherty and 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 and P. Kuosmanen; Invariant Signals of Median and Stack Filters, J.T. Astola and P. Kuosmanen; Binary Polynomial Transforms and Logical Correlation, K.O. Egiazarian et al; Applications of Binary Polynomial Transforms, K.O. Egiazarian et al; Random Sets in View of Image Filtering Applications, I.S. Molchanov.