Topology Of Digital Images

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Topology of Digital Images

James F. Peters
Topology of Digital Images Book PDF

Author : James F. Peters
Publisher : Springer Science & Business Media
Page : 414 pages
File Size : 41,5 Mb
Release : 2014-01-28
Category : Technology & Engineering
ISBN : 9783642538452

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Topology of Digital Images by James F. Peters Pdf

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.

Computational Geometry, Topology and Physics of Digital Images with Applications

James F. Peters
Computational Geometry Topology and Physics of Digital Images with Applications Book PDF

Author : James F. Peters
Publisher : Springer Nature
Page : 440 pages
File Size : 53,6 Mb
Release : 2019-10-03
Category : Technology & Engineering
ISBN : 9783030221928

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

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.

Topological Algorithms for Digital Image Processing

T.Y. Kong,A. Rosenfeld
Topological Algorithms for Digital Image Processing Book PDF

Author : T.Y. Kong,A. Rosenfeld
Publisher : Elsevier
Page : 291 pages
File Size : 46,6 Mb
Release : 1996-07-17
Category : Computers
ISBN : 0080552048

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Topological Algorithms for Digital Image Processing by T.Y. Kong,A. Rosenfeld Pdf

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.

Image Processing with Cellular Topology

Vladimir Kovalevsky
Image Processing with Cellular Topology Book PDF

Author : Vladimir Kovalevsky
Publisher : Springer Nature
Page : 191 pages
File Size : 48,9 Mb
Release : 2022-03-26
Category : Computers
ISBN : 9789811657726

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Image Processing with Cellular Topology by Vladimir Kovalevsky Pdf

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.

Computational Proximity

James F. Peters
Computational Proximity Book PDF

Author : James F. Peters
Publisher : Springer
Page : 0 pages
File Size : 51,9 Mb
Release : 2016-04-29
Category : Technology & Engineering
ISBN : 3319302604

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Computational Proximity by James F. Peters Pdf

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.

Topology with Applications

Somashekhar A. Naimpally,James F. Peters
Topology with Applications Book PDF

Author : Somashekhar A. Naimpally,James F. Peters
Publisher : World Scientific
Page : 294 pages
File Size : 43,6 Mb
Release : 2013
Category : Mathematics
ISBN : 9789814407663

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Topology with Applications by Somashekhar A. Naimpally,James F. Peters Pdf

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.

Binary Digital Image Processing

Stéphane Marchand-Maillet,Yazid M. Sharaiha
Binary Digital Image Processing Book PDF

Author : Stéphane Marchand-Maillet,Yazid M. Sharaiha
Publisher : Elsevier
Page : 368 pages
File Size : 51,7 Mb
Release : 1999-12-01
Category : Technology & Engineering
ISBN : 0080527825

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Binary Digital Image Processing by Stéphane Marchand-Maillet,Yazid M. Sharaiha Pdf

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

Reinhard Klette,Azriel Rosenfeld
Digital Geometry Book PDF

Author : Reinhard Klette,Azriel Rosenfeld
Publisher : Morgan Kaufmann
Page : 676 pages
File Size : 49,9 Mb
Release : 2004-08-06
Category : Computers
ISBN : 9781558608610

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Digital Geometry by Reinhard Klette,Azriel Rosenfeld Pdf

The first book on digital geometry by the leaders in the field.

Computational Topology in Image Context

Rebeca Marfil,Mariletty Calderón,Fernando Díaz del Río,Pedro Real,Antonio Bandera
Computational Topology in Image Context Book PDF

Author : Rebeca Marfil,Mariletty Calderón,Fernando Díaz del Río,Pedro Real,Antonio Bandera
Publisher : Springer
Page : 191 pages
File Size : 53,5 Mb
Release : 2019-01-10
Category : Computers
ISBN : 9783030108281

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Computational Topology in Image Context by Rebeca Marfil,Mariletty Calderón,Fernando Díaz del Río,Pedro Real,Antonio Bandera Pdf

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.

Computational Topology in Image Context

Alexandra Bac,Jean-Luc Mari
Computational Topology in Image Context Book PDF

Author : Alexandra Bac,Jean-Luc Mari
Publisher : Springer
Page : 303 pages
File Size : 55,6 Mb
Release : 2016-06-01
Category : Computers
ISBN : 9783319394411

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Computational Topology in Image Context by Alexandra Bac,Jean-Luc Mari Pdf

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

Isabelle Debled-Rennesson,Eric Domenjoud,Bertrand Kerautret,Philippe Even
Discrete Geometry for Computer Imagery Book PDF

Author : Isabelle Debled-Rennesson,Eric Domenjoud,Bertrand Kerautret,Philippe Even
Publisher : Springer
Page : 538 pages
File Size : 51,5 Mb
Release : 2011-03-29
Category : Computers
ISBN : 9783642198670

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Discrete Geometry for Computer Imagery by Isabelle Debled-Rennesson,Eric Domenjoud,Bertrand Kerautret,Philippe Even Pdf

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.

Digital and Image Geometry

Gilles Bertrand,Atsushi Imiya,Reinhard Klette
Digital and Image Geometry Book PDF

Author : Gilles Bertrand,Atsushi Imiya,Reinhard Klette
Publisher : Springer Science & Business Media
Page : 455 pages
File Size : 41,8 Mb
Release : 2002-01-16
Category : Computers
ISBN : 9783540430797

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Digital and Image Geometry by Gilles Bertrand,Atsushi Imiya,Reinhard Klette Pdf

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.

Discrete Geometry for Computer Imagery

Attila Kuba
Discrete Geometry for Computer Imagery Book PDF

Author : Attila Kuba
Publisher : Springer Science & Business Media
Page : 701 pages
File Size : 54,9 Mb
Release : 2006-10-10
Category : Computers
ISBN : 9783540476511

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Discrete Geometry for Computer Imagery by Attila Kuba Pdf

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.

Computational Topology in Image Context

Massimo Ferri,Patrizio Frosini,Claudia Landi,Andrea Cerri,Barbara Di Fabio
Computational Topology in Image Context Book PDF

Author : Massimo Ferri,Patrizio Frosini,Claudia Landi,Andrea Cerri,Barbara Di Fabio
Publisher : Springer
Page : 166 pages
File Size : 44,5 Mb
Release : 2012-06-13
Category : Computers
ISBN : 9783642302381

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Computational Topology in Image Context by Massimo Ferri,Patrizio Frosini,Claudia Landi,Andrea Cerri,Barbara Di Fabio Pdf

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.

Combinatorial Image Analysis

Valentin E. Brimkov,Reneta P. Barneva
Combinatorial Image Analysis Book PDF

Author : Valentin E. Brimkov,Reneta P. Barneva
Publisher : Springer
Page : 357 pages
File Size : 42,6 Mb
Release : 2017-05-15
Category : Computers
ISBN : 9783319591087

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Combinatorial Image Analysis by Valentin E. Brimkov,Reneta P. Barneva Pdf

This book constitutes the proceedings of the 18th International Workshop on Combinatorial Image Analysis, IWCIA 2017, held in Plovdiv, Bulgaria, in June 2017. The 27 revised full papers presented were carefully reviewed and selected from 47 submissions. The workshop is organized in topical sections of theoretical foundations and theory of applications, namely: discrete geometry and topology; tilings and patterns; grammars, models and other technical tools for image analysis; image segmentation, classification; reconstruction; compression; texture analysis; bioimaging.