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.

Dedication. Foreword. Preface. Acknowledgments. Part I Morphological operators. Binary Decision Diagrams as a New Paradigm for Morphological Machines, Junior Barrera and Ronaldo Fumio Hashimoto Image filtering using morphological amoebas, Romain Lerallut, Étienne Decencière and Fernand Meyer Numerical Residues, Serge Beucher Efficient path openings and closings, Ben Appleton and Hugues Talbot Structuring Elements following the Optical Flow, Nicolas Laveau and Christophe Bernard Recursive Interpolation Technique For Binary Images Based on Morphological Median Sets, Javier Vidal, Jose Crespo and Víctor Maoj. Part II Connected filters and reconstruction. Second-Order Connected Attribute Filters Using Max-Trees Georgios K. Ouzounis and Michael H.F. Wilkinson Transformations with Reconstruction Criteria: Image Segmentation and Filtering Iván R. Terol-Villalobos and Jorge D. Mendiola-Santibañez Attribute-Space Connected Filters Michael H.F. Wilkinson Vector-attribute Filters Erik R. Urbach, Niek J. Boersma and Michael H.F. Wilkinson Ruminations on Tarjan’s Union-Find Algorithm and Connected Operators Thierry Géraud Labelled Reconstruction of Binary Objects: A Vector Propagation Algorithm Michael Buckley and Ryan Lagerstrom Grayscale Level Multiconnectivity Ulisses Braga-Neto Shape-Tree Semilattices Renato Keshet Part III Segmentation. Morphological Segmentations of Colour Images Jean Serra Fast Implementation of Waterfall based on Graphs Beatriz Marcotegui and Serge Beucher Mosaics and Watersheds Laurent Najman, Michel Couprie and Gilles Bertrand A new definition for the dynamics Gilles Bertrand Watershed-driven region-based image retrieval I. Pratikakis, I. Vanhamel, H. Sahli, B. Gatos and S. Perantonis Efficient implementation of the locally constrained watershed transform and seeded region growing Richard Beare Part IV Geometry and topology. Optimal shape andinclusion Jean-Marc Chassery and David Coeurjolly Regular Metric: Definition and Characterization in the Discrete Plane Gerald Jean Francis Banon Euclidean skeletons of 3D data sets in linear time by the integer medial axis transform Wim H. Hesselink, Menno Visser and Jos B.T.M. Roerdink Digitization of Non-regular Shapes Peer Stelldinger Downsampling of binary images using adaptive crossing numbers Etienne Decencière and Michel Bilodeau Grey-weighted, ultrametric and lexicographic distances Fernand Meyer Mathematical modeling of the relationship 'between' based on morphological operators Isabelle Bloch, Olivier Colliot and Roberto M. Cesar Part V Partial differential equations and evolutionary models. Semidiscrete and Discrete Well-Posedness of Shock Filtering Martin Welk and Joachim Weickert A Variational Formulation of PDE’s for Dilations and Levelings Petros Maragos Stochastic Shape Optimisation Costin Alin Caciu, Etienne Decencière and Dominique Jeulin On the local connectivity number of stationary random closed sets Evgueni Spodarev and Volker Schmidt Part VI Texture, colour and multivalued images. Intersize correlation of grain occurrences in textures and its application to texture regeneration Akira Asano, Yasushi Kobayashi and Chie Muraki Texture Segmentation Using Area Morphology Local Granulometries Neil D. Fletcher and Adrian N. Evans Illumination-invariant Morphological Texture Classification Allan Hanbury, Umasankar Kandaswamy and Donald A. Adjeroh Unified morphological color processing framework in a lum/sat/hue representation Jesús Angulo Iterative area seeded region growing for multichannel image simplification Dominik Brunner and Pierre Soille Morphology for Higher-Dimensional Tensor Data via Loewner Ordering B. Burgeth, N. Papenberg, A. Bruhn, M. Welk, C. Feddern, and J. Weickert Part VII Applications in imaging sciences. Using Watershed and Multimodal Data for Vessel