Mathematical Nonlinear Image Processing

1. Front Matter

   Pages i-iii

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2. Introduction

   • Edward R. Dougherty, Jaakko Astola

   Pages 1-1

3. Statistical Properties, Fixed Points, and Decomposition with WMMR Filters

   • Harold Longbotham, David Eberly

   Pages 3-20

4. Asymptotic Behavior of Morphological Filters

   • Lasse Koskinen, Jaakko Astola

   Pages 21-39

5. NonLinear Filtering Structure for Image Smoothing in Mixed-Noise Environments

   • Robert L. Stevenson, Susan M. Schweizer

   Pages 41-58

6. Root-Signal Sets of Morphological Filters and their Use in Variable-Length BTC Image Coding

   • Qiaofei Wang, Moncef Gabbouj, Yrjö Neuvo

   Pages 59-75

7. Unification of Nonlinear Filtering in the Context of Binary Logical Calculus, Part I: Binary Filters

   • Edward R. Dougherty, Robert M. Haralick

   Pages 77-87

8. Unification of Nonlinear Filtering in the Context of Binary Logical Calculus, Part II: Gray-Scale Filters

   • Edward R. Dougherty

   Pages 89-96

9. Morphological Analysis of Discrete Random Shapes

   • John Goutsias

   Pages 97-119

10. Inverse Problems for Granulometries by Erosion

    • Juliette Mattioli, Michel Schmitt

    Pages 121-136

11. Design of a Multitask Neurovision Processor

    • George K. Knopf, Madan M. Gupta

    Pages 137-154

12. Wilson—Cowan Neural-Network Model in Image Processing

    • Kari Mantere, Jussi Parkkinen, Timo Jaaskelainen, Madan M. Gupta

    Pages 155-163

13. Clustering Properties of Hierarchical Self-Organizing Maps

    • Jouko Lampinen, Erkki Oja

    Pages 165-176

Mathematical Nonlinear Image Processing deals with a fast growing research area. The development of the subject springs from two factors: (1) the great expansion of nonlinear methods applied to problems in imaging and vision, and (2) the degree to which nonlinear approaches are both using and fostering new developments in diverse areas of mathematics. Mathematical Nonlinear Image Processing will be of interest to people working in the areas of applied mathematics as well as researchers in computer vision. Mathematical Nonlinear Image Processing is an edited volume of original research. It has also been published as a special issue of the Journal of Mathematical Imaging and Vision. (Volume 2, Issue 2/3).

• Erosion
• Signal
• calculus
• computer vision
• image processing
• imaging
• model

• Rochester Institute of Technology, Rochester, USA

  Edward R. Dougherty

• University of Tampere, Tampere, Finland

  Jaakko Astola

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