Mathematical Morphology: 40 Years On

Mathematical Morphology is a speciality in Image Processing and Analysis, which considers images as geometrical objects, to be analyzed through their interactions with other geometrical objects. It relies on several branches of mathematics, such as discrete geometry, topology, lattice theory, partial differential equations, integral geometry and geometrical probability. It has produced fast and efficient algorithms for computer analysis of images, and has found applications in bio-medical imaging, materials science, geoscience, remote sensing, quality control, document processing and data analysis.

This book contains the 43 papers presented at the 7th International Symposium on Mathematical Morphology, held in Paris on April 18-20, 2005. It gives a lively state of the art of current research topics in this field. It also marks a milestone, the 40 years of uninterrupted development of this ever-expanding domain.

Morphological Operators.- Binary Decision Diagrams as a New Paradigm for Morphological Machines.- Image Filtering Using Morphological Amoebas.- Numerical Residues.- Efficient Path Openings and Closings.- Structuring Elements Following the Optical Flow.- Recursive Interpolation Technique for Binary Images Based on Morphological Median Sets.- Connected Filters and Reconstruction.- Second-Order Connected Attribute Filters Using Max-Trees.- Transformations with Reconstruction Criteria: Image Segmentation and Filtering.- Attribute-Space Connected Filters.- Vector-Attribute Filters.- Ruminations on Tarjans Union-Find Algorithm and Connected Operators.- Labelled Reconstruction of Binary Objects: A Vector Propagation Algorithm.- Grayscale Level Multiconnectivity.- Shape-Tree Semilattices.- Segmentation.- Morphological Segmentations of Colour Images.- Fast Implementation of Waterfall Based on Graphs.- Mosaics and Watersheds.- A New Definition for the Dynamics.- Watershed-Driven Region-Based Image Retrieval.- Efficient Implementation of Thelocally Constrained Watershed Transform and Seeded Region Growing.- Geometry and Topology.- Optimal Shape and Inclusion.- Regular Metric: Definition and Characterization in the Discrete Plane.- Euclidean Skeletons of 3D Data Sets in Linear Time by the Integer Medial Axis Transform.- Digitization of Non-Regular Shapes.- Downsampling of Binary Images Using Adaptive Crossing Numbers.- Grey-Weighted, Ultrametric and Lexicographic Distances.- Mathematical Modeling of the Relationship between Based On Morphological Operators.- Partial Differential Equations and Evolutionary Models.- Semidiscrete and Discrete Well-Posedness of Shock Filtering.- A Variational Formulation of PDEs for Dilations and Levelings.- Stochastic Shape Optimisation.-On the Local Connectivity Number of Stationary Random Closed Sets.- Texture, Colour and Multivalued Images.- Intersize Correlation of Grain Occurrences in Textures and Its Application to Texture Regeneration.- Texture Segmentation Using Area Morphology Local Granulometries.- Illumination-Invariant Morphological Texture Classification.- Unified Morphological Color Processing Framework in a Lum/Sat/Hue Representation.- Iterative Area Seeded Region Growing for Multichannel Image Simplification.- Morphology for Higher-Dimensional Tensor Data Via Loewner Ordering.- Applications in Imaging Sciences.- Using Watershed and Multimodal Data for Vessel Segmentation: Application to the Superior Sagittal Sinus.- Using Grey Scale Hit-Or-Miss Transform for Segmenting the Portal Network of the Liver.- Blood Cell Segmentation Using Minimum Area Watershed and Circle Radon Transformations.- Quantifying Mean Shape and Variability of Footprints Using Mean Sets.- Exploiting and Evolving RN Mathematical Morphology Feature Spaces.- Morphological Segmentation Applied to 3D Seismic Data.