Morphological Image Operators

1st Edition, Volume 216 - September 1, 2020
Imprint: Academic Press
Editors: Martin Hÿtch, Peter W. Hawkes
Language: English
Hardback ISBN:
9 7 8 - 0 - 1 2 - 8 2 1 0 0 3 - 1
eBook ISBN:
9 7 8 - 0 - 1 2 - 8 2 1 0 0 4 - 8

Advances in Imaging and Electron Physics, Volume 216, merges two long-running serials, Advances in Electronics and Electron Physics and Advances in Optical and Electron Microscopy… Read more

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Advances in Imaging and Electron Physics, Volume 216, merges two long-running serials, Advances in Electronics and Electron Physics and Advances in Optical and Electron Microscopy. The series features extended articles on the physics of electron devices (especially semiconductor devices), particle optics at high and low energies, microlithography, image science, digital image processing, electromagnetic wave propagation, electron microscopy and the computing methods used in all these domains.

Cover image
Title page
Table of Contents
Copyright
Contributor
Preface
Editorial Preface
Chapter One: First principles
Abstract
1.1. A typical example
1.2. Morphological convolution
1.3. A bird's eye view
1.4. Historical remarks
References
Chapter Two: Complete lattices
Abstract
2.1. Basic concepts
2.2. Boolean lattices
2.3. Regular closed sets
2.4. Boolean functions
2.5. Bibliographical notes
References
Chapter Three: Operators on complete lattices
Abstract
3.1. Lattice operators
3.2. Adjunctions
3.3. Openings and closings
3.4. Conditional operators
3.5. Activity ordering
3.6. The centre on non-Boolean lattices
3.7. Bibliographical notes
References
Chapter Four: Operators which are translation invariant
Abstract
4.1. Set model for binary images
4.2. Hit-or-miss operator
4.3. Dilation and erosion
4.4. Opening and closing
4.5. Boolean functions
4.6. Grey-scale morphology
4.7. Bibliographical notes
References
Chapter Five: Adjunctions, dilations, and erosions
Abstract
5.1. General properties of adjunctions
5.2. T-invariance: the abelian case
5.3. Self-dual and Boolean lattices
5.4. Representation theorems
5.5. Translation invariant morphology
5.6. Polar morphology
5.7. Grey-scale functions
5.8. T-invariance: the nonabelian case
5.9. Translation–rotation morphology
5.10. Bibliographical notes
References
Chapter Six: Openings and closings
Abstract
6.1. Algebraic theory of T-openings
6.2. Self-dual and Boolean lattices
6.3. Adjunctional openings and closings
6.4. T-openings: the nonabelian case
6.5. Annular openings
6.6. Openings from inf-overfilters
6.7. Granulometries
6.8. Dominance and incidence structures
6.9. Bibliographical notes
References
Chapter Seven: Hit-or-miss topology and semi-continuity
Abstract
7.1. Topology: basic concepts
7.2. Metric spaces
7.3. Hausdorff metric
7.4. Hit-or-miss topology
7.5. Myope topology
7.6. Semi-continuity
7.7. Basis representations
7.8. Bibliographical notes
References
Chapter Eight: Discretization
Abstract
8.1. Statement of the problem
8.2. Morphological sampling
8.3. Discretization of images
8.4. Discretization of operators
8.5. Covering discretization
8.6. Bibliographical notes
References
Chapter Nine: Convexity, distance, and connectivity
Abstract
9.1. Convexity
9.2. Geodesic distance and M-convexity
9.3. Metric dilations
9.4. Distance transform
9.5. Geodesic and conditional operators
9.6. Granulometries
9.7. Connectivity
9.8. Skeleton
9.9. Discrete metric spaces
9.10. Bibliographical notes
References
Chapter Ten: Lattice representations of functions
Abstract
10.1. Introduction
10.2. Admissible complete lattices
10.3. Power-type lattices
10.4. Function representations
10.5. Semi-continuous functions
10.6. Extension of lattice operators
10.7. Lattices with negation
10.8. Operators: from sets to functions
10.9. Bibliographical notes
References
Chapter Eleven: Morphology for grey-scale images
Abstract
11.1. Functions and threshold sets
11.2. Semi-flat function operators
11.3. Flat function operators
11.4. Flat operators and Boolean functions
11.5. H-operators
11.6. Umbra transform
11.7. Grey-value set Z‾
11.8. Finite grey-value sets
11.9. Finite grey-value sets and truncation
11.10. Geodesic and conditional operators
11.11. Granulometries
11.12. Bibliographical notes
References
Chapter Twelve: Morphological filters
Abstract
12.1. Filters, overfilters, etc.
12.2. Lattice of filters
12.3. Lattice of strong filters
12.4. Invariance domain
12.5. The middle filter
12.6. Alternating sequential filters
12.7. Bibliographical notes
References
Chapter Thirteen: Filtering and iteration
Abstract
13.1. Order convergence
13.2. Order continuity
13.3. Relation with the hit-or-miss topology
13.4. Translation invariant set operators
13.5. Finite window operators
13.6. Iteration and idempotence
13.7. Iteration of the centre operator
13.8. From centre operator to middle filter
13.9. Self-dual operators and filters
13.10. Bibliographical notes
References
References
References
Notation Index
Subject Index

Martin Hÿtch

Dr Martin Hÿtch, serial editor for the book series “Advances in Imaging and Electron Physics (AIEP)”, is a senior scientist at the French National Centre for Research (CNRS) in Toulouse. He moved to France after receiving his PhD from the University of Cambridge in 1991 on “Quantitative high-resolution transmission electron microscopy (HRTEM)”, joining the CNRS in Paris as permanent staff member in 1995. His research focuses on the development of quantitative electron microscopy techniques for materials science applications. He is notably the inventor of Geometric Phase Analysis (GPA) and Dark-Field Electron Holography (DFEH), two techniques for the measurement of strain at the nanoscale. Since moving to the CEMES-CNRS in Toulouse in 2004, he has been working on aberration-corrected HRTEM and electron holography for the study of electronic devices, nanocrystals and ferroelectrics. He was laureate of the prestigious European Microscopy Award for Physical Sciences of the European Microscopy Society in 2008. To date he has published 130 papers in international journals, filed 6 patents and has given over 70 invited talks at international conferences and workshops.

Affiliations and expertise

Senior Scientist, French National Centre for Research (CNRS), Toulouse, France

Peter W. Hawkes

Peter Hawkes obtained his M.A. and Ph.D (and later, Sc.D.) from the University of Cambridge, where he subsequently held Fellowships of Peterhouse and of Churchill College. From 1959 – 1975, he worked in the electron microscope section of the Cavendish Laboratory in Cambridge, after which he joined the CNRS Laboratory of Electron Optics in Toulouse, of which he was Director in 1987. He was Founder-President of the European Microscopy Society and is a Fellow of the Microscopy and Optical Societies of America. He is a member of the editorial boards of several microscopy journals and serial editor of Advances in Electron Optics.

Affiliations and expertise

Founder-President of the European Microscopy Society and Fellow, Microscopy and Optical Societies of America; member of the editorial boards of several microscopy journals and Serial Editor, Advances in Electron Optics, France

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