Topology Of Digital Images

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Topology of Digital Images

Author : James F. Peters
Publisher : Springer Science & Business Media
ISBN 13 : 3642538452
Total Pages : 411 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Topology of Digital Images by : James F. Peters

Download or read book Topology of Digital Images written by James F. Peters and published by Springer Science & Business Media. This book was released on 2014-01-28 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book carries forward recent work on visual patterns and structures in digital images and introduces a near set-based a topology of digital images. Visual patterns arise naturally in digital images viewed as sets of non-abstract points endowed with some form of proximity (nearness) relation. Proximity relations make it possible to construct uniform topologies on the sets of points that constitute a digital image. In keeping with an interest in gaining an understanding of digital images themselves as a rich source of patterns, this book introduces the basics of digital images from a computer vision perspective. In parallel with a computer vision perspective on digital images, this book also introduces the basics of proximity spaces. Not only the traditional view of spatial proximity relations but also the more recent descriptive proximity relations are considered. The beauty of the descriptive proximity approach is that it is possible to discover visual set patterns among sets that are non-overlapping and non-adjacent spatially. By combining the spatial proximity and descriptive proximity approaches, the search for salient visual patterns in digital images is enriched, deepened and broadened. A generous provision of Matlab and Mathematica scripts are used in this book to lay bare the fabric and essential features of digital images for those who are interested in finding visual patterns in images. The combination of computer vision techniques and topological methods lead to a deep understanding of images.

Topological Algorithms for Digital Image Processing

Author : T.Y. Kong
Publisher : Elsevier
ISBN 13 : 9780080552040
Total Pages : 291 pages
Book Rating : 4.5/5 (52 download)

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Book Synopsis Topological Algorithms for Digital Image Processing by : T.Y. Kong

Download or read book Topological Algorithms for Digital Image Processing written by T.Y. Kong and published by Elsevier. This book was released on 1996-07-17 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic topological algorithms are the subject of this new book. It presents their underlying theory and discusses their applications. Due to the wide variety of topics treated in the seven chapters, no attempt has been made to standardize the notation and terminology used by the authors. Each chapter, however, is self-contained and can be read independently of the others. Some of the basic terminology and fundamental concepts of digital topology are reviewed in the appendix which also describes important areas of the field. A bibliography of over 360 references is also provided. The notations and terminologies used in this book will serve to introduce readers to the even wider variety that exists in the voluminous literature dealing with topological algorithms.

Computational Geometry, Topology and Physics of Digital Images with Applications

Author : James F. Peters
Publisher : Springer Nature
ISBN 13 : 303022192X
Total Pages : 440 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Computational Geometry, Topology and Physics of Digital Images with Applications by : James F. Peters

Download or read book Computational Geometry, Topology and Physics of Digital Images with Applications written by James F. Peters and published by Springer Nature. This book was released on 2019-10-03 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Computational Proximity

Author : James F. Peters
Publisher : Springer
ISBN 13 : 9783319302607
Total Pages : 0 pages
Book Rating : 4.3/5 (26 download)

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Book Synopsis Computational Proximity by : James F. Peters

Download or read book Computational Proximity written by James F. Peters and published by Springer. This book was released on 2016-04-29 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces computational proximity (CP) as an algorithmic approach to finding nonempty sets of points that are either close to each other or far apart. Typically in computational proximity, the book starts with some form of proximity space (topological space equipped with a proximity relation) that has an inherent geometry. In CP, two types of near sets are considered, namely, spatially near sets and descriptivelynear sets. It is shown that connectedness, boundedness, mesh nerves, convexity, shapes and shape theory are principal topics in the study of nearness and separation of physical aswell as abstract sets. CP has a hefty visual content. Applications of CP in computer vision, multimedia, brain activity, biology, social networks, and cosmology are included. The book has been derived from the lectures of the author in a graduate course on the topology of digital images taught over the past several years. Many of the students have provided important insights and valuable suggestions. The topics in this monograph introduce many forms of proximities with a computational flavour (especially, what has become known as the strong contact relation), many nuances of topological spaces, and point-free geometry.

Image Processing with Cellular Topology

Author : Vladimir Kovalevsky
Publisher : Springer Nature
ISBN 13 : 9811657726
Total Pages : 191 pages
Book Rating : 4.8/5 (116 download)

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Book Synopsis Image Processing with Cellular Topology by : Vladimir Kovalevsky

Download or read book Image Processing with Cellular Topology written by Vladimir Kovalevsky and published by Springer Nature. This book was released on 2022-03-26 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains why the finite topological space known as abstract cell complex is important for successful image processing and presents image processing methods based on abstract cell complex, especially for tracing and encoding of boundaries of homogeneous regions. Many examples are provided in the book, some teach you how to trace and encode boundaries in binary, indexed and colour images. Other examples explain how to encode a boundary as a sequence of straight-line segments which is important for shape recognition. A new method of edge detection in two- and three-dimensional images is suggested. Also, a discussion problem is included in the book: A derivative is defined as the limit of the relation of the increment of the function to the increment of the argument as the latter tends to zero. Is it not better to estimate derivatives as the relation of the increment of the function to the optimal increment of the argument instead of taking exceedingly small increment which leads to errors? This book addresses all above questions and provide the answers.

Topology with Applications

Author : Somashekhar A. Naimpally
Publisher : World Scientific
ISBN 13 : 9814407666
Total Pages : 294 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Topology with Applications by : Somashekhar A. Naimpally

Download or read book Topology with Applications written by Somashekhar A. Naimpally and published by World Scientific. This book was released on 2013 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: The principal aim of this book is to introduce topology and its many applications viewed within a framework that includes a consideration of compactness, completeness, continuity, filters, function spaces, grills, clusters and bunches, hyperspace topologies, initial and final structures, metric spaces, metrization, nets, proximal continuity, proximity spaces, separation axioms, and uniform spaces.This book provides a complete framework for the study of topology with a variety of applications in science and engineering that include camouflage filters, classification, digital image processing, forgery detection, Hausdorff raster spaces, image analysis, microscopy, paleontology, pattern recognition, population dynamics, stem cell biology, topological psychology, and visual merchandising.It is the first complete presentation on topology with applications considered in the context of proximity spaces, and the nearness and remoteness of sets of objects. A novel feature throughout this book is the use of near and far, discovered by F Riesz over 100 years ago. In addition, it is the first time that this form of topology is presented in the context of a number of new applications.

Digital Geometry

Author : Reinhard Klette
Publisher : Elsevier
ISBN 13 : 0080477267
Total Pages : 672 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Digital Geometry by : Reinhard Klette

Download or read book Digital Geometry written by Reinhard Klette and published by Elsevier. This book was released on 2004-09-04 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Binary Digital Image Processing

Author : Stéphane Marchand-Maillet
Publisher : Elsevier
ISBN 13 : 9780080527826
Total Pages : 368 pages
Book Rating : 4.5/5 (278 download)

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Book Synopsis Binary Digital Image Processing by : Stéphane Marchand-Maillet

Download or read book Binary Digital Image Processing written by Stéphane Marchand-Maillet and published by Elsevier. This book was released on 1999-12-01 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Binary Digital Image Processing is aimed at faculty, postgraduate students and industry specialists. It is both a text reference and a textbook that reviews and analyses the research output in this field of binary image processing. It is aimed at both advanced researchers as well as educating the novice to this area. The theoretical part of this book includes the basic principles required for binary digital image analysis. The practical part which will take an algorithmic approach addresses problems which find applications beyond binary digital line image processing. The book first outlines the theoretical framework underpinning the study of digital image processing with particular reference to those needed for line image processing. The theoretical tools in the first part of the book set the stage for the second and third parts, where low-level binary image processing is addressed and then intermediate level processing of binary line images is studied. The book concludes with some practical applications of this work by reviewing some industrial and software applications (engineering drawing storage and primitive extraction, fingerprint compression). Outlines the theoretical framework underpinning the study of digital image processing with particular reference to binary line image processing Addresses low-level binary image processing, reviewing a number of essential characteristics of binary digital images and providing solution procedures and algorithms Includes detailed reviews of topics in binary digital image processing with up-to-date research references in relation to each of the problems under study Includes some practical applications of this work by reviewing some common applications Covers a range of topics, organised by theoretical field rather than being driven by problem definitions

Digital Geometry

Author : Reinhard Klette
Publisher : Morgan Kaufmann
ISBN 13 : 1558608613
Total Pages : 676 pages
Book Rating : 4.5/5 (586 download)

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Book Synopsis Digital Geometry by : Reinhard Klette

Download or read book Digital Geometry written by Reinhard Klette and published by Morgan Kaufmann. This book was released on 2004-08-06 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book on digital geometry by the leaders in the field.

Computational Topology in Image Context

Author : Rebeca Marfil
Publisher : Springer
ISBN 13 : 3030108287
Total Pages : 191 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Computational Topology in Image Context by : Rebeca Marfil

Download or read book Computational Topology in Image Context written by Rebeca Marfil and published by Springer. This book was released on 2019-01-10 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 7th International Workshop on Computational Topology in Image Context, CTIC 2019, held in Málaga, Spain, in January 2019. The 14 papers presented in this volume were carefully reviewed and selected from 21 submissions. Papers deal with theoretical issues but most of them put the attention on the applicability of concepts and algorithms. These were designed to deal with objects and images, but also with the speech signal. The final application must be for instance in the medical domain or in the robotics one.

Discrete Geometry for Computer Imagery

Author : Isabelle Debled-Rennesson
Publisher : Springer
ISBN 13 : 3642198678
Total Pages : 526 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Discrete Geometry for Computer Imagery by : Isabelle Debled-Rennesson

Download or read book Discrete Geometry for Computer Imagery written by Isabelle Debled-Rennesson and published by Springer. This book was released on 2011-03-29 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 16th IAPR International Conference on Discrete Geometry for Computer Imagery, DGCI 2011, held in Nancy, France, in April 2011. The 20 revised full papers and 20 revised poster papers presented together with 3 invited lectures were carefully reviewed and selected from numerous 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, as well as discrete and combinatorial tools for image segmentation and analysis.

Computational Topology in Image Context

Author : Alexandra Bac
Publisher : Springer
ISBN 13 : 331939441X
Total Pages : 303 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Computational Topology in Image Context by : Alexandra Bac

Download or read book Computational Topology in Image Context written by Alexandra Bac and published by Springer. This book was released on 2016-06-01 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 6th International Workshop on Computational Topology in Image Context, CTIC 2016, held in Marseille, France, in June 2016. The 24 papers presented in this volume were carefully reviewed and selected from 35 submissions. Additionally, this volume contains 2 invited papers. CTIC covers a wide range of topics such as: topological invariants and their computation, homology, cohomology, linking number, fundamental groups; algorithm optimization in discrete geometry, transfer of mathematical tools, parallel computation in multi-dimensional volume context, hierarchical approaches; experimental evaluation of algorithms and heuristics; combinatorial or multi-resolution models; discrete or computational topology; geometric modeling guided by topological constraints; computational topological dynamics; and use of topological information in discrete geometry applications.

Discrete Geometry for Computer Imagery

Author : Attila Kuba
Publisher : Springer Science & Business Media
ISBN 13 : 3540476512
Total Pages : 701 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Discrete Geometry for Computer Imagery by : Attila Kuba

Download or read book Discrete Geometry for Computer Imagery written by Attila Kuba and published by Springer Science & Business Media. This book was released on 2006-10-10 with total page 701 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 13th International Conference on Discrete Geometry for Computer Imagery, DGCI 2006, held in Szeged, Hungary in October 2006. The 28 revised full papers and 27 revised poster papers presented together with two invited papers were carefully reviewed and selected from 99 submissions.

Digital Geometry in Image Processing

Author : Jayanta Mukhopadhyay
Publisher : CRC Press
ISBN 13 : 1466505680
Total Pages : 316 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Digital Geometry in Image Processing by : Jayanta Mukhopadhyay

Download or read book Digital Geometry in Image Processing written by Jayanta Mukhopadhyay and published by CRC Press. This book was released on 2016-04-19 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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,

Digital and Image Geometry

Author : Gilles Bertrand
Publisher : Springer Science & Business Media
ISBN 13 : 3540430792
Total Pages : 455 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Digital and Image Geometry by : Gilles Bertrand

Download or read book Digital and Image Geometry written by Gilles Bertrand and published by Springer Science & Business Media. This book was released on 2002-01-16 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Computational Proximity

Author : James F. Peters
Publisher : Springer
ISBN 13 : 3319302620
Total Pages : 433 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Computational Proximity by : James F. Peters

Download or read book Computational Proximity written by James F. Peters and published by Springer. This book was released on 2016-04-20 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces computational proximity (CP) as an algorithmic approach to finding nonempty sets of points that are either close to each other or far apart. Typically in computational proximity, the book starts with some form of proximity space (topological space equipped with a proximity relation) that has an inherent geometry. In CP, two types of near sets are considered, namely, spatially near sets and descriptivelynear sets. It is shown that connectedness, boundedness, mesh nerves, convexity, shapes and shape theory are principal topics in the study of nearness and separation of physical aswell as abstract sets. CP has a hefty visual content. Applications of CP in computer vision, multimedia, brain activity, biology, social networks, and cosmology are included. The book has been derived from the lectures of the author in a graduate course on the topology of digital images taught over the past several years. Many of the students have provided important insights and valuable suggestions. The topics in this monograph introduce many forms of proximities with a computational flavour (especially, what has become known as the strong contact relation), many nuances of topological spaces, and point-free geometry.

Computational Topology in Image Context

Author : Massimo Ferri
Publisher : Springer
ISBN 13 : 3642302386
Total Pages : 157 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Computational Topology in Image Context by : Massimo Ferri

Download or read book Computational Topology in Image Context written by Massimo Ferri and published by Springer. This book was released on 2012-06-13 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 4th International Workshop on Computational Topology in Image Context, CTIC 2012, held in Bertinoro, Italy, in May 2012. The 16 papers presented in this volume were carefully reviewed and selected for inclusion in this book. They focus on the topology and computation in image context. The workshop is devoted to computational methods using topology for the analysis and comparison of images. The involved research fields comprise computational topology and geometry, discrete topology and geometry, geometrical modeling, algebraic topology for image applications, and any other field involving a geometric-topological approach to image processing.