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Author : Reinhard Klette,Azriel Rosenfeld
Publisher : Morgan Kaufmann
Page : 676 pages
File Size : 41,9 Mb
Release : 2004-08-06
Category : Computers
ISBN : 9781558608610
The first book on digital geometry by the leaders in the field.
Author : Reinhard Klette,Azriel Rosenfeld
Publisher : Elsevier
Page : 672 pages
File Size : 42,7 Mb
Release : 2004-09-04
Category : Computers
ISBN : 9780080477268
Digital geometry is about deriving geometric information from digital pictures. The field emerged from its mathematical roots some forty-years ago through work in computer-based imaging, and it is used today in many fields, such as digital image processing and analysis (with applications in medical imaging, pattern recognition, and robotics) and of course computer graphics. Digital Geometry is the first book to detail the concepts, algorithms, and practices of the discipline. This comphrehensive text and reference provides an introduction to the mathematical foundations of digital geometry, some of which date back to ancient times, and also discusses the key processes involved, such as geometric algorithms as well as operations on pictures. *A comprehensive text and reference written by pioneers in digital geometry, image processing and analysis, and computer vision *Provides a collection of state-of-the-art algorithms for a wide variety of geometrical picture analysis tasks, including extracting data from digital images and making geometric measurements on the data *Includes exercises, examples, and references to related or more advanced work
Author : Jayanta Mukhopadhyay,Partha Pratim Das,Samiran Chattopadhyay,Partha Bhowmick,Biswa Nath Chatterji
Publisher : CRC Press
Page : 316 pages
File Size : 47,9 Mb
Release : 2016-04-19
Category : Computers
ISBN : 9781466505681
Exploring theories and applications developed during the last 30 years, Digital Geometry in Image Processing presents a mathematical treatment of the properties of digital metric spaces and their relevance in analyzing shapes in two and three dimensions. Unlike similar books, this one connects the two areas of image processing and digital geometry,
Author : Valentin E. Brimkov,Reneta P. Barneva
Publisher : Springer Science & Business Media
Page : 430 pages
File Size : 40,9 Mb
Release : 2012-05-20
Category : Technology & Engineering
ISBN : 9789400741744
Digital geometry emerged as an independent discipline in the second half of the last century. It deals with geometric properties of digital objects and is developed with the unambiguous goal to provide rigorous theoretical foundations for devising new advanced approaches and algorithms for various problems of visual computing. Different aspects of digital geometry have been addressed in the literature. This book is the first one that explicitly focuses on the presentation of the most important digital geometry algorithms. Each chapter provides a brief survey on a major research area related to the general volume theme, description and analysis of related fundamental algorithms, as well as new original contributions by the authors. Every chapter contains a section in which interesting open problems are addressed.
Author : Li M. Chen
Publisher : Springer
Page : 322 pages
File Size : 54,8 Mb
Release : 2014-12-12
Category : Computers
ISBN : 9783319120997
This book provides comprehensive coverage of the modern methods for geometric problems in the computing sciences. It also covers concurrent topics in data sciences including geometric processing, manifold learning, Google search, cloud data, and R-tree for wireless networks and BigData. The author investigates digital geometry and its related constructive methods in discrete geometry, offering detailed methods and algorithms. The book is divided into five sections: basic geometry; digital curves, surfaces and manifolds; discretely represented objects; geometric computation and processing; and advanced topics. Chapters especially focus on the applications of these methods to other types of geometry, algebraic topology, image processing, computer vision and computer graphics. Digital and Discrete Geometry: Theory and Algorithms targets researchers and professionals working in digital image processing analysis, medical imaging (such as CT and MRI) and informatics, computer graphics, computer vision, biometrics, and information theory. Advanced-level students in electrical engineering, mathematics, and computer science will also find this book useful as a secondary text book or reference. Praise for this book: This book does present a large collection of important concepts, of mathematical, geometrical, or algorithmical nature, that are frequently used in computer graphics and image processing. These concepts range from graphs through manifolds to homology. Of particular value are the sections dealing with discrete versions of classic continuous notions. The reader finds compact definitions and concise explanations that often appeal to intuition, avoiding finer, but then necessarily more complicated, arguments... As a first introduction, or as a reference for professionals working in computer graphics or image processing, this book should be of considerable value." - Prof. Dr. Rolf Klein, University of Bonn.
Author : Jayanta Mukhopadhyay,Partha Pratim Das,Samiran Chattopadhyay,Partha Bhowmick,Biswa Nath Chatterji
Publisher : CRC Press
Page : 320 pages
File Size : 48,9 Mb
Release : 2013-04-05
Category : Computers
ISBN : 9781466505674
Exploring theories and applications developed during the last 30 years, Digital Geometry in Image Processing presents a mathematical treatment of the properties of digital metric spaces and their relevance in analyzing shapes in two and three dimensions. Unlike similar books, this one connects the two areas of image processing and digital geometry, highlighting important results of digital geometry that are currently used in image analysis and processing. The book discusses different digital geometries in multi-dimensional integral coordinate spaces. It also describes interesting properties of the geometries, including metric and topological properties, shapes of circles and spheres, proximity to Euclidean norms, and number theoretic representations of geometric objects such as straight lines and circles. The authors—all active researchers in image processing and digital geometry—demonstrate how these concepts and properties are useful in various techniques for image processing and analysis. In particular, the book covers applications in object representation and shape analysis. With many figures (some in color) and end-of-chapter exercises, this book provides an in-depth, unified account of digital metrics, the characterization of digital curves and straight lines, and their uses in shape analysis. It gives you insight on the latest two- and three-dimensional image processing applications.
Author : Christer Oscar Kiselman
Publisher : World Scientific
Page : 488 pages
File Size : 54,7 Mb
Release : 2022-01-06
Category : Mathematics
ISBN : 9789811248313
The author presents three distinct but related branches of science in this book: digital geometry, mathematical morphology, and discrete optimization. They are united by a common mindset as well as by the many applications where they are useful. In addition to being useful, each of these relatively new branches of science is also intellectually challenging.The book contains a systematic study of inverses of mappings between ordered sets, and so offers a uniquely helpful organization in the approach to several phenomena related to duality.To prepare the ground for discrete convexity, there are chapters on convexity in real vector spaces in anticipation of the many challenging problems coming up in digital geometry. To prepare for the study of new topologies introduced to serve in discrete spaces, there is also a chapter on classical topology.The book is intended for general readers with a modest background in mathematics and for advanced undergraduate students as well as beginning graduate students.
Author : Gilles Bertrand,Atsushi Imiya,Reinhard Klette
Publisher : Springer Science & Business Media
Page : 455 pages
File Size : 53,6 Mb
Release : 2002-01-16
Category : Computers
ISBN : 9783540430797
Images or discrete objects, to be analyzed based on digital image data, need to be represented, analyzed, transformed, recovered etc. These problems have stimulated many interesting developments in theoretical foundations of image processing. This coherent anthology presents 27 state-of-the-art surveys and research papers on digital image geometry and topology. It is based on a winter school held at Dagstuhl Castle, Germany in December 2000 and offers topical sections on topology, representation, geometry, multigrid convergence, and shape similarity and simplification.
Author : James F. Peters
Publisher : Springer Nature
Page : 440 pages
File Size : 52,9 Mb
Release : 2019-10-03
Category : Technology & Engineering
ISBN : 9783030221928
This book discusses the computational geometry, topology and physics of digital images and video frame sequences. This trio of computational approaches encompasses the study of shape complexes, optical vortex nerves and proximities embedded in triangulated video frames and single images, while computational geometry focuses on the geometric structures that infuse triangulated visual scenes. The book first addresses the topology of cellular complexes to provide a basis for an introductory study of the computational topology of visual scenes, exploring the fabric, shapes and structures typically found in visual scenes. The book then examines the inherent geometry and topology of visual scenes, and the fine structure of light and light caustics of visual scenes, which bring into play catastrophe theory and the appearance of light caustic folds and cusps. Following on from this, the book introduces optical vortex nerves in triangulated digital images. In this context, computational physics is synonymous with the study of the fine structure of light choreographed in video frames. This choreography appears as a sequence of snapshots of light reflected and refracted from surface shapes, providing a solid foundation for detecting, analyzing and classifying visual scene shapes.
Author : Martin J. Turner,Jonathan M. Blackledge,Patrick R. Andrews
Publisher : Academic Press
Page : 352 pages
File Size : 52,8 Mb
Release : 1998-06-23
Category : Computers
ISBN : 0127039708
This book is concerned with the theory and application of fractal geometry in digital imaging. Throughout the book, a series of new approaches to defining fractals are illustrated, such as the analysis of the fractal power spectrum and the use of fractional differentials. Several new algorithms and applications are also discussed and applied to real life images. Fractal Geometry in Digital imaging will appeal to postgraduates, researchers and practitioners in image processing, mathematics and computing, information technology and engineering.
Author : Mario Botsch,Leif Kobbelt,Mark Pauly,Pierre Alliez,Bruno Levy
Publisher : CRC Press
Page : 244 pages
File Size : 44,9 Mb
Release : 2010-10-07
Category : Computers
ISBN : 9781568814261
Geometry processing, or mesh processing, is a fast-growing area of research that uses concepts from applied mathematics, computer science, and engineering to design efficient algorithms for the acquisition, reconstruction, analysis, manipulation, simulation, and transmission of complex 3D models. Applications of geometry processing algorithms already cover a wide range of areas from multimedia, entertainment, and classical computer-aided design, to biomedical computing, reverse engineering, and scientific computing. Over the last several years, triangle meshes have become increasingly popular, as irregular triangle meshes have developed into a valuable alternative to traditional spline surfaces. This book discusses the whole geometry processing pipeline based on triangle meshes. The pipeline starts with data input, for example, a model acquired by 3D scanning techniques. This data can then go through processes of error removal, mesh creation, smoothing, conversion, morphing, and more. The authors detail techniques for those processes using triangle meshes. A supplemental website contains downloads and additional information.
Author : Wolfgang Förstner,Bernhard P. Wrobel
Publisher : Springer
Page : 816 pages
File Size : 43,9 Mb
Release : 2016-10-04
Category : Computers
ISBN : 9783319115504
This textbook offers a statistical view on the geometry of multiple view analysis, required for camera calibration and orientation and for geometric scene reconstruction based on geometric image features. The authors have backgrounds in geodesy and also long experience with development and research in computer vision, and this is the first book to present a joint approach from the converging fields of photogrammetry and computer vision. Part I of the book provides an introduction to estimation theory, covering aspects such as Bayesian estimation, variance components, and sequential estimation, with a focus on the statistically sound diagnostics of estimation results essential in vision metrology. Part II provides tools for 2D and 3D geometric reasoning using projective geometry. This includes oriented projective geometry and tools for statistically optimal estimation and test of geometric entities and transformations and their relations, tools that are useful also in the context of uncertain reasoning in point clouds. Part III is devoted to modelling the geometry of single and multiple cameras, addressing calibration and orientation, including statistical evaluation and reconstruction of corresponding scene features and surfaces based on geometric image features. The authors provide algorithms for various geometric computation problems in vision metrology, together with mathematical justifications and statistical analysis, thus enabling thorough evaluations. The chapters are self-contained with numerous figures and exercises, and they are supported by an appendix that explains the basic mathematical notation and a detailed index. The book can serve as the basis for undergraduate and graduate courses in photogrammetry, computer vision, and computer graphics. It is also appropriate for researchers, engineers, and software developers in the photogrammetry and GIS industries, particularly those engaged with statistically based geometric computer vision methods.
Author : Elena Barcucci,Andrea Frosini,Simone Rinaldi
Publisher : Springer
Page : 423 pages
File Size : 43,6 Mb
Release : 2014-09-03
Category : Computers
ISBN : 9783319099552
This book constitutes the thoroughly refereed proceedings of the 18th International Conference on Discrete Geometry for Computer Imagery, DGCI 2014, held in Siena, Italy, September 2014. The 34 revised full papers presented were carefully selected from 60 submissions. The papers are organized in topical sections on Models for Discrete Geometry, Discrete and Combinatorial Topology, Geometric Transforms, Discrete Shape Representation, Recognition and Analysis, Discrete Tomography, Morphological Analysis, Discrete Modelling and Visualization, Discrete and Combinatorial Tools for Image Segmentation and Analysis.
Author : Serge Miguet,Annick Montanvert,Stephane Ubeda
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 55,6 Mb
Release : 1996-11-06
Category : Computers
ISBN : 3540620052
This book constitutes the refereed proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery, DGCI'96, held in Lyon, France, in November 1996. Computer imaging essentially depends on discrete models for coding, processing, recognition, representation, etc. The volume presents 24 revised full papers selected from 41 submissions together with 3 invited contributions and a tutorial paper, which bridges the gap between theory and practice. The issues addressed are topology, geometry, shape representation, 3D surfaces and volumes, models for discrete space, image transformation and generation.
Author : Nicolas Normand,Jeanpierre Guédon,Florent Autrusseau
Publisher : Springer
Page : 453 pages
File Size : 54,7 Mb
Release : 2016-04-08
Category : Computers
ISBN : 9783319323602
This book constitutes the refereed proceedings of the 19th IAPR International Conference on Discrete Geometry for Computer Imagery, DGCI 2016, held in Nantes, France, in April 2016. The 32 revised full papers presented together with 2 invited talks were carefully selected from 51 submissions. The papers are organized in topical sections on combinatorial tools; discretization; discrete tomography; discrete and combinatorial topology; shape descriptors; models for discrete geometry; circle drawing; morphological analysis; geometric transforms; and discrete shape representation, recognition and analysis.