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Informationen zum Autor Laurent Najman is Professor in the Informatics Department of ESIEE, Paris and a member of the Institut Gaspard Monge, Paris-Est Marne-la-Vallée University in France. His current research interest is discrete mathematical morphology. Hugues Talbot is Associate Professor at ESIEE, Paris, France. His research interests include mathematical morphology, image segmentation, thin feature analysis, texture analysis, discrete and continuous optimization and associated algorithms. Klappentext Mathematical Morphology allows for the analysis and processing of geometrical structures using techniques based on the fields of set theory, lattice theory, topology, and random functions. It is the basis of morphological image processing, and finds applications in fields including digital image processing (DSP), as well as areas for graphs, surface meshes, solids, and other spatial structures. This book presents an up-to-date treatment of mathematical morphology, based on the three pillars that made it an important field of theoretical work and practical application: a solid theoretical foundation, a large body of applications and an efficient implementation.The book is divided into five parts and includes 20 chapters. The five parts are structured as follows:* Part I sets out the fundamental aspects of the discipline, starting with a general introduction, followed by two more theory-focused chapters, one addressing its mathematical structure and including an updated formalism, which is the result of several decades of work.* Part II extends this formalism to some non-deterministic aspects of the theory, in particular detailing links with other disciplines such as stereology, geostatistics and fuzzy logic.* Part III addresses the theory of morphological filtering and segmentation, featuring modern connected approaches, from both theoretical and practical aspects.* Part IV features practical aspects of mathematical morphology, in particular how to deal with color and multivariate data, links to discrete geometry and topology, and some algorithmic aspects - without which applications would be impossible.* Part V showcases all the previously noted fields of work through a sample of interesting, representative and varied applications. Zusammenfassung Mathematical morphology was historically the first non-linear theory in the field of image processing. It rests on three pillars that make its success: a solid theory, a wide scope, and an effective implementation. Inhaltsverzeichnis Preface xv PART I. FOUNDATIONS 1 Chapter 1. Introduction to Mathematical Morphology 3 Laurent NAJMAN, Hugues TALBOT 1.1. First steps with mathematical morphology: dilations and erosions 4 1.2. Morphological filtering 12 1.3. Residues 22 1.4. Distance transform, skeletons and granulometric curves 24 1.5. Hierarchies and the watershed transform 30 1.6. Some concluding thoughts 33 Chapter 2. Algebraic Foundations of Morphology 35 Christian RONSE, Jean SERRA 2.1. Introduction 35 2.2. Complete lattices 36 2.3. Examples of lattices 42 2.4. Closings and openings 51 2.5. Adjunctions 56 2.6. Connections and connective segmentation 64 2.7. Morphological filtering and hierarchies 75 Chapter 3.Watersheds in Discrete Spaces 81 Gilles BERTRAND, Michel COUPRIE, Jean COUSTY, Laurent NAJMAN 3.1. Watersheds on the vertices of a graph 82 3.2. Watershed cuts: watershed on the edges of a graph 90 3.3. Watersheds in complexes 101 PART II. EVALUATING AND DECIDING 109 Chapter 4. An Introduction to Measurement Theory for Image Analysis 111 Hugues TALBOT, Jean SERRA, Laurent NAJMAN 4.1. Introduction 111 4.2. General requirements 112 4.3. Convex ring and Minkowski functionals 113 4.4. Stereology and Minkowski fun...
