Ebook: Mathematical Morphology and Its Applications to Image Processing

Mathematical morphology (MM) is a theory for the analysis of spatial structures. It is called morphology since it aims at analysing the shape and form of objects, and it is mathematical in the sense that the analysis is based on set theory, topology, lattice algebra, random functions, etc.
MM is not only a theory, but also a powerful image analysis technique. The purpose of the present book is to provide the image analysis community with a snapshot of current theoretical and applied developments of MM. The book consists of forty-five contributions classified by subject. It demonstrates a wide range of topics suited to the morphological approach.

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Mathematical morphology (MM) is a theory for the analysis of spatial structures. It is called morphology since it aims at analysing the shape and form of objects, and it is mathematical in the sense that the analysis is based on set theory, topology, lattice algebra, random functions, etc.
MM is not only a theory, but also a powerful image analysis technique. The purpose of the present book is to provide the image analysis community with a snapshot of current theoretical and applied developments of MM. The book consists of forty-five contributions classified by subject. It demonstrates a wide range of topics suited to the morphological approach.

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Mathematical morphology (MM) is a theory for the analysis of spatial structures. It is called morphology since it aims at analysing the shape and form of objects, and it is mathematical in the sense that the analysis is based on set theory, topology, lattice algebra, random functions, etc.
MM is not only a theory, but also a powerful image analysis technique. The purpose of the present book is to provide the image analysis community with a snapshot of current theoretical and applied developments of MM. The book consists of forty-five contributions classified by subject. It demonstrates a wide range of topics suited to the morphological approach.

Content:
Front Matter....Pages i-ix
Introduction....Pages 1-4
Set Operator Decomposition and Conditionally Translation Invariant Elementary Operators....Pages 5-12
Mutational Equations of Morphological Dilation Tubes....Pages 13-20
Thresholdings, Umbrae, Residuals, and Surpluses of L-Images....Pages 21-28
Adaptive Parameterized Openings....Pages 29-36
Synthesis of Adaptive Weighted Order Statistic Filters with Gradient Algorithms....Pages 37-44
A Spatially Variant, Locally Adaptive, Background Normalization Operator....Pages 45-52
Using Genetic Algorithms in the Design of Morphological Filters....Pages 53-59
Minimal Generator Basis of a Finite Structural Opening....Pages 61-68
Watershed, Hierarchical Segmentation and Waterfall Algorithm....Pages 69-76
Minimum Spanning Forests for Morphological Segmentation....Pages 77-84
The Flat Zone Approach and Color Images....Pages 85-92
Joint Region and Motion Estimation with Morphological Tools....Pages 93-100
Morphological Segmentation of Image Sequences....Pages 101-108
Critical Morphological Sampling and Its Applications to Image Coding....Pages 109-116
A Sampling Approach Based on Equicontinuity....Pages 117-124
Application of Morphological Filters for Contour Image Sequence Coding....Pages 125-132
The Geodesic Morphological Skeleton and Fast Transformation Algorithms....Pages 133-140
Multi-Parameter Skeleton Decomposition....Pages 141-148
Morphological Systems Theory: Slope Transforms, Max—Min Differential Equations, Envelope Filters, and Sampling....Pages 149-160
Two Dual Representations of Morphology Based on the Parallel Normal Transport Property....Pages 161-170
Dominance and Incidence Structures with Applications to Stochastic Geometry and Mathematical Morphology....Pages 171-178
The Multiscale Morphology Decomposition Theorem....Pages 179-184
Statistical Pattern Spectrum for Binary Pattern Recognition....Pages 185-192
Generalized Geodesic Distances Applied to Interpolation and Shape Description....Pages 193-200
Performance Analysis of a Morphological Voronoi Tessellation Algorithm....Pages 201-208
Optimization in Voronoi Diagrams....Pages 209-216
A Stochastic Tessellation of Digital Space....Pages 217-224
Liquid Phase Sintered Materials Modelling by Random Closed Sets....Pages 225-232
Monte Carlo Estimation of Morphological Granulometric Discrete Size Distributions....Pages 233-240
On the Implementation of Morphological Operations....Pages 241-248
An Evaluation of Priority Queues for Mathematical Morphology....Pages 249-256
One Pixel Thick Skeletons....Pages 257-264
Fast Grayscale Granulometry Algorithms....Pages 265-272
An Efficient Implementation Technique of Adaptive Morphological Operations....Pages 273-280
Implementation of a Distributed Watershed Algorithm....Pages 281-288
Visualization of Minkowski Operations by Computer Graphics Techniques....Pages 289-296
Morphogenesis Simulations with Lattice Gas....Pages 297-304
Single Object Geometry — The Stereology of Registered Serial Sections....Pages 305-307
Texture Classification Using Neural Networks and Local Granulometries....Pages 309-316
Fusion of MR and CT Images of the Human Brain Using Multiresolution Morphology....Pages 317-324
Morphological Scheme for Morphometric Analysis of Epidermal Biopsy Images....Pages 325-331
Automatic Quantification of Spine Parameters from X-ray Images by Means of Morphological Tools....Pages 333-340
Image Processing: A Key to Success in Industrial Applications....Pages 341-352
Radar Image Analysis Using Morphological Filters....Pages 353-360
Application of Morphological Operators to Supervised Multidimensional Data Classification....Pages 361-368
Back Matter....Pages 369-385

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Mathematical morphology (MM) is a theory for the analysis of spatial structures. It is called morphology since it aims at analysing the shape and form of objects, and it is mathematical in the sense that the analysis is based on set theory, topology, lattice algebra, random functions, etc.
MM is not only a theory, but also a powerful image analysis technique. The purpose of the present book is to provide the image analysis community with a snapshot of current theoretical and applied developments of MM. The book consists of forty-five contributions classified by subject. It demonstrates a wide range of topics suited to the morphological approach.

Content:
Front Matter....Pages i-ix
Introduction....Pages 1-4
Set Operator Decomposition and Conditionally Translation Invariant Elementary Operators....Pages 5-12
Mutational Equations of Morphological Dilation Tubes....Pages 13-20
Thresholdings, Umbrae, Residuals, and Surpluses of L-Images....Pages 21-28
Adaptive Parameterized Openings....Pages 29-36
Synthesis of Adaptive Weighted Order Statistic Filters with Gradient Algorithms....Pages 37-44
A Spatially Variant, Locally Adaptive, Background Normalization Operator....Pages 45-52
Using Genetic Algorithms in the Design of Morphological Filters....Pages 53-59
Minimal Generator Basis of a Finite Structural Opening....Pages 61-68
Watershed, Hierarchical Segmentation and Waterfall Algorithm....Pages 69-76
Minimum Spanning Forests for Morphological Segmentation....Pages 77-84
The Flat Zone Approach and Color Images....Pages 85-92
Joint Region and Motion Estimation with Morphological Tools....Pages 93-100
Morphological Segmentation of Image Sequences....Pages 101-108
Critical Morphological Sampling and Its Applications to Image Coding....Pages 109-116
A Sampling Approach Based on Equicontinuity....Pages 117-124
Application of Morphological Filters for Contour Image Sequence Coding....Pages 125-132
The Geodesic Morphological Skeleton and Fast Transformation Algorithms....Pages 133-140
Multi-Parameter Skeleton Decomposition....Pages 141-148
Morphological Systems Theory: Slope Transforms, Max—Min Differential Equations, Envelope Filters, and Sampling....Pages 149-160
Two Dual Representations of Morphology Based on the Parallel Normal Transport Property....Pages 161-170
Dominance and Incidence Structures with Applications to Stochastic Geometry and Mathematical Morphology....Pages 171-178
The Multiscale Morphology Decomposition Theorem....Pages 179-184
Statistical Pattern Spectrum for Binary Pattern Recognition....Pages 185-192
Generalized Geodesic Distances Applied to Interpolation and Shape Description....Pages 193-200
Performance Analysis of a Morphological Voronoi Tessellation Algorithm....Pages 201-208
Optimization in Voronoi Diagrams....Pages 209-216
A Stochastic Tessellation of Digital Space....Pages 217-224
Liquid Phase Sintered Materials Modelling by Random Closed Sets....Pages 225-232
Monte Carlo Estimation of Morphological Granulometric Discrete Size Distributions....Pages 233-240
On the Implementation of Morphological Operations....Pages 241-248
An Evaluation of Priority Queues for Mathematical Morphology....Pages 249-256
One Pixel Thick Skeletons....Pages 257-264
Fast Grayscale Granulometry Algorithms....Pages 265-272
An Efficient Implementation Technique of Adaptive Morphological Operations....Pages 273-280
Implementation of a Distributed Watershed Algorithm....Pages 281-288
Visualization of Minkowski Operations by Computer Graphics Techniques....Pages 289-296
Morphogenesis Simulations with Lattice Gas....Pages 297-304
Single Object Geometry — The Stereology of Registered Serial Sections....Pages 305-307
Texture Classification Using Neural Networks and Local Granulometries....Pages 309-316
Fusion of MR and CT Images of the Human Brain Using Multiresolution Morphology....Pages 317-324
Morphological Scheme for Morphometric Analysis of Epidermal Biopsy Images....Pages 325-331
Automatic Quantification of Spine Parameters from X-ray Images by Means of Morphological Tools....Pages 333-340
Image Processing: A Key to Success in Industrial Applications....Pages 341-352
Radar Image Analysis Using Morphological Filters....Pages 353-360
Application of Morphological Operators to Supervised Multidimensional Data Classification....Pages 361-368
Back Matter....Pages 369-385
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