Mathematical Morphology and Its Applications to Image Processing (Computational Imaging and Vision (2))

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. 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 Scale is a concept the antiquity of which can hardly be traced. Certainly the familiar phenomena that accompany sc ale changes in optical patterns are mentioned in the earliest written records. The most obvious topological changes such as the creation or annihilation of details have been a topic to philosophers, artists and later scientists. This appears to of fascination be the case for all cultures from which extensive written records exist. For th instance, chinese 17 c artist manuals remark that'distant faces have no eyes'. The merging of details is also obvious to many authors, e. g., Lucretius mentions the fact that distant islands look like a single one. The one topo­ logical event that is (to the best of my knowledge) mentioned only late (by th John Ruskin in his'Elements of drawing'of the mid 19 c) is the splitting of a blob on blurring. The change of images on a gradual increase of resolu­ tion has been a recurring theme in the arts (e. g., the poetic description of the distant armada in Calderon's The Constant Prince) and this'mystery'(as Ruskin calls it) is constantly exploited by painters. Mathematical morphology (MM) is a theory for the analysis of spatial structures. It aims at analyzing the shape and form of objects, and is based on set theory, topology, lattice algebra, random functions, and so on. This text presents current theoretical and applied developments of MM. This book is a primer on geometry-driven, nonlinear diffusion as a new paradigm for vision. It gives a thorough overview of current linear and nonlinear scale-space theory, presenting many viewpoints such as the variational approach, curve evolution and nonlinear diffusion equations For th instance, chinese 17 c artist manuals remark that "distant faces have no eyes" . , the poetic description of the distant armada in Calderon's The Constant Prince) and this "mystery" (as Ruskin calls it) is constantly exploited by painters. Edited By Bart M. Ter Haar Romeny. Includes Bibliographical References (p. 411-428) And Index.