Ebook: Mathematical Morphology and its Applications to Image and Signal Processing

Mathematical morphology (MM) is a powerful methodology for the quantitative analysis of geometrical structures. It consists of a broad and coherent collection of theoretical concepts, nonlinear signal operators, and algorithms aiming at extracting, from images or other geometrical objects, information related to their shape and size. Its mathematical origins stem from set theory, lattice algebra, and integral and stochastic geometry.
MM was initiated in the late 1960s by G. Matheron and J. Serra at the Fontainebleau School of Mines in France. Originally it was applied to analyzing images from geological or biological specimens. However, its rich theoretical framework, algorithmic efficiency, easy implementability on special hardware, and suitability for many shape- oriented problems have propelled its widespread diffusion and adoption by many academic and industry groups in many countries as one among the dominant image analysis methodologies.
The purpose of Mathematical Morphology and its Applications to Imageand Signal Processing is to provide the image analysis community with a sampling from the current developments in the theoretical (deterministic and stochastic) and computational aspects of MM and its applications to image and signal processing. The book consists of the papers presented at the ISMM'96 grouped into the following themes:

• Theory
• Connectivity
• Filtering
• Nonlinear System Related to Morphology
• Algorithms/Architectures
• Granulometries, Texture
• Segmentation
• Image Sequence Analysis
• Learning
• Document Analysis
• Applications

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Mathematical morphology (MM) is a powerful methodology for the quantitative analysis of geometrical structures. It consists of a broad and coherent collection of theoretical concepts, nonlinear signal operators, and algorithms aiming at extracting, from images or other geometrical objects, information related to their shape and size. Its mathematical origins stem from set theory, lattice algebra, and integral and stochastic geometry.
MM was initiated in the late 1960s by G. Matheron and J. Serra at the Fontainebleau School of Mines in France. Originally it was applied to analyzing images from geological or biological specimens. However, its rich theoretical framework, algorithmic efficiency, easy implementability on special hardware, and suitability for many shape- oriented problems have propelled its widespread diffusion and adoption by many academic and industry groups in many countries as one among the dominant image analysis methodologies.
The purpose of Mathematical Morphology and its Applications to Imageand Signal Processing is to provide the image analysis community with a sampling from the current developments in the theoretical (deterministic and stochastic) and computational aspects of MM and its applications to image and signal processing. The book consists of the papers presented at the ISMM'96 grouped into the following themes:

• Theory
• Connectivity
• Filtering
• Nonlinear System Related to Morphology
• Algorithms/Architectures
• Granulometries, Texture
• Segmentation
• Image Sequence Analysis
• Learning
• Document Analysis
• Applications

---

Mathematical morphology (MM) is a powerful methodology for the quantitative analysis of geometrical structures. It consists of a broad and coherent collection of theoretical concepts, nonlinear signal operators, and algorithms aiming at extracting, from images or other geometrical objects, information related to their shape and size. Its mathematical origins stem from set theory, lattice algebra, and integral and stochastic geometry.
MM was initiated in the late 1960s by G. Matheron and J. Serra at the Fontainebleau School of Mines in France. Originally it was applied to analyzing images from geological or biological specimens. However, its rich theoretical framework, algorithmic efficiency, easy implementability on special hardware, and suitability for many shape- oriented problems have propelled its widespread diffusion and adoption by many academic and industry groups in many countries as one among the dominant image analysis methodologies.
The purpose of Mathematical Morphology and its Applications to Imageand Signal Processing is to provide the image analysis community with a sampling from the current developments in the theoretical (deterministic and stochastic) and computational aspects of MM and its applications to image and signal processing. The book consists of the papers presented at the ISMM'96 grouped into the following themes:

• Theory
• Connectivity
• Filtering
• Nonlinear System Related to Morphology
• Algorithms/Architectures
• Granulometries, Texture
• Segmentation
• Image Sequence Analysis
• Learning
• Document Analysis
• Applications

Content:
Front Matter....Pages i-xi
Introduction....Pages 1-5
Metric Convexity in the Context of Mathematical Morphology....Pages 7-14
Support Function and Minkowski Addition of Non-Convex Sets....Pages 15-22
Lattice Operators Underlying Dynamic Systems....Pages 23-30
Comparison of Multiscale Morphology Approaches: PDE Implemented Via Curve Evolution Versus Chamfer Distance Transform....Pages 31-40
An Attribute-Based Approach to Mathematical Morphology....Pages 41-48
Spatially-Variant Mathematical Morphology....Pages 49-56
The Generalized Tailor Problem....Pages 57-64
Discrete Random Functions: Modeling and Analysis Using Mathematical Morphology....Pages 65-72
Morphological Sampling of Random Closed Sets....Pages 73-80
Connectivity on Complete Lattices....Pages 81-96
Practical Extensions of Connected Operators....Pages 97-110
Region Adjacency Graphs and Connected Morphological Operators....Pages 111-118
Space Connectivity and Translation-Invariance....Pages 119-126
Morphological Filters for Dummies....Pages 127-137
Alternating Sequential Filters by Adaptive-Neighborhood Structuring Functions....Pages 139-146
Quadratic Structuring Functions in Mathematical Morphology....Pages 147-154
MRL-Filters and Their Adaptive Optimal Design for Image Processing....Pages 155-162
Weighted Composite Order-Statistics Filters....Pages 163-170
Links between Mathematical Morphology, Rough Sets, Fuzzy Logic and Higher Order Neural Networks....Pages 171-177
Grey-Scale Soft Morphological Filter Optimization by Genetic Algorithms....Pages 179-186
The Viterbi Optimal Runlength-Constrained Approximation Nonlinear Filter....Pages 187-193
Recursive Morphology Using Line Structuring Elements....Pages 195-202
A Morphological Algorithm for Linear Segment Detection....Pages 203-218
Toward the Optimal Decomposition of Arbitrarily Shaped Structuring Elements by Means of a Genetic Approach....Pages 219-226
A Data Dependent Architecture Based on Seeded Region Growing Strategy for Advanced Morphological Operators....Pages 227-234
Implementing Morphological Image Operators Via Trained Neural Networks....Pages 235-243
Optimal and Adaptive Design of Reconstructive Granulometric Filters....Pages 245-252
Periodic Lines and their Application to Granulometries....Pages 253-261
Local Grayscale Granulometries Based on Opening Trees....Pages 263-272
Integrating Size Information into Intensity Histogram....Pages 273-280
Probabilistic Model of Rough Surfaces Obtained by Electro-Erosion....Pages 281-288
A Textural Analysis by Mathematical Morphology....Pages 289-296
Computation of Watersheds Based on Parallel Graph Algorithms....Pages 297-304
Segmentation Algorithm by Multicriteria Region Merging....Pages 305-312
Temporal Stability in Sequence Segmentation Using the Watershed Algorithm....Pages 313-320
The Dynamics of Minima and Contours....Pages 321-328
A Morphological Interpolation Method for Mosaic Images....Pages 329-336
Multivalued Morphology and its Application in Moving Object Segmentation and Tracking....Pages 337-344
Mathematical Morphology for Image Sequences Using the Knowledge of Dynamics....Pages 345-352
Motion Picture Restoration Using Morphological Tools....Pages 353-360
Segmentation-Based Morphological Interpolation of Partition Sequences....Pages 361-368
Set Operations on Closed Intervals and their Applications to the Automatic Programming of MMach’s....Pages 369-376
Automatic Programming of MMach’s for OCR....Pages 377-384
Morphological Preprocessing and Binarization for OCR Systems....Pages 385-392
Adaptive Directional Morphology with Application to Document Analysis....Pages 393-400
Segmentation of 3D Pulmonary Trees Using Mathematical Morphology....Pages 401-408
Automatic 3-Dimensional Segmentation of MR Brain Tissue Using Filters by Reconstruction....Pages 409-416
Robust Extraction of Axon Fibers from Large-Scale Electron Micrograph Mosaics....Pages 417-424
Strong Edge Features for Image Coding....Pages 425-432
Water Depth Determination Using Mathematical Morphology....Pages 433-441
Geometrical and Topological Characterization of Cork Cells by Digital Image Analysis....Pages 443-450
Back Matter....Pages 451-458
....Pages 459-466