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 : 414 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 414 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 : 0080552048
Total Pages : 301 pages
Book Rating : 4.0/5 (85 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 301 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 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.

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.

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.

Mathematics of Digital Images

Author : S. G. Hoggar
Publisher : Cambridge University Press
ISBN 13 : 9781139451352
Total Pages : 896 pages
Book Rating : 4.4/5 (513 download)

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Book Synopsis Mathematics of Digital Images by : S. G. Hoggar

Download or read book Mathematics of Digital Images written by S. G. Hoggar and published by Cambridge University Press. This book was released on 2006-09-14 with total page 896 pages. Available in PDF, EPUB and Kindle. Book excerpt: Compression, restoration and recognition are three of the key components of digital imaging. The mathematics needed to understand and carry out all these components are explained here in a style that is at once rigorous and practical with many worked examples, exercises with solutions, pseudocode, and sample calculations on images. The introduction lists fast tracks to special topics such as Principal Component Analysis, and ways into and through the book, which abounds with illustrations. The first part describes plane geometry and pattern-generating symmetries, along with some on 3D rotation and reflection matrices. Subsequent chapters cover vectors, matrices and probability. These are applied to simulation, Bayesian methods, Shannon's information theory, compression, filtering and tomography. The book will be suited for advanced courses or for self-study. It will appeal to all those working in biomedical imaging and diagnosis, computer graphics, machine vision, remote sensing, image processing and information theory and its applications.

Digital Topology with Applications to Image-processing

Author : T. Yung Kong
Publisher :
ISBN 13 :
Total Pages : 324 pages
Book Rating : 4.:/5 (519 download)

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Book Synopsis Digital Topology with Applications to Image-processing by : T. Yung Kong

Download or read book Digital Topology with Applications to Image-processing written by T. Yung Kong and published by . This book was released on 1985 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Digital Topology with Applications to Image-processing

Author : T. Yung Kong
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (519 download)

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Book Synopsis Digital Topology with Applications to Image-processing by : T. Yung Kong

Download or read book Digital Topology with Applications to Image-processing written by T. Yung Kong and published by . This book was released on 1985 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Digital Geometry

Author : Reinhard Klette
Publisher : Elsevier
ISBN 13 : 0080477267
Total Pages : 675 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 675 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 : 0080527825
Total Pages : 279 pages
Book Rating : 4.0/5 (85 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 279 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

Continuous Representations of Digital Images

Author : Chung-Nim Lee
Publisher :
ISBN 13 :
Total Pages : 32 pages
Book Rating : 4.:/5 (149 download)

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Book Synopsis Continuous Representations of Digital Images by : Chung-Nim Lee

Download or read book Continuous Representations of Digital Images written by Chung-Nim Lee and published by . This book was released on 1985 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: A 2D digital image S is represented conventionally by the union of grid squares containing pixels of S which we denote by F(S). This gives the correct topology for S with 8-adjacency, and with a little imagination, 4-adjacency can also be properly handled. However, one encounters difficulty in extending basic 2D results to 3D digital images. The last few years have seen the need for better methods which give a closer link with well developed continuous topology, especially with the advent of digital surface theory. We define a new continuous model F(S) by refining F(S). We show that this gives a better bridge between the two subjects, digital and continuous topologies. We also show how this space F(S) is related to two other continuous models. Although we concentrate only on 2D images in this paper, the concepts and general ideas extend to 3D images. A 3D version of this paper is in preparation.

Digital and Image Geometry

Author : Gilles Bertrand
Publisher : Springer
ISBN 13 : 3540455760
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. This book was released on 2003-07-31 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.

A Computational Introduction to Digital Image Processing

Author : Alasdair McAndrew
Publisher : CRC Press
ISBN 13 : 148224733X
Total Pages : 555 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis A Computational Introduction to Digital Image Processing by : Alasdair McAndrew

Download or read book A Computational Introduction to Digital Image Processing written by Alasdair McAndrew and published by CRC Press. This book was released on 2015-10-28 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: Highly Regarded, Accessible Approach to Image Processing Using Open-Source and Commercial SoftwareA Computational Introduction to Digital Image Processing, Second Edition explores the nature and use of digital images and shows how they can be obtained, stored, and displayed. Taking a strictly elementary perspective, the book only covers topics that

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 Topology and Applications to Multidimensional Image Processing

Author : Alasdair McAndrew
Publisher :
ISBN 13 :
Total Pages : 376 pages
Book Rating : 4.:/5 (225 download)

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Book Synopsis Digital Topology and Applications to Multidimensional Image Processing by : Alasdair McAndrew

Download or read book Digital Topology and Applications to Multidimensional Image Processing written by Alasdair McAndrew and published by . This book was released on 1996 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Computational Topology for Biomedical Image and Data Analysis

Author : Rodrigo Rojas Moraleda
Publisher : CRC Press
ISBN 13 : 0429810997
Total Pages : 116 pages
Book Rating : 4.4/5 (298 download)

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Book Synopsis Computational Topology for Biomedical Image and Data Analysis by : Rodrigo Rojas Moraleda

Download or read book Computational Topology for Biomedical Image and Data Analysis written by Rodrigo Rojas Moraleda and published by CRC Press. This book was released on 2019-07-12 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an accessible yet rigorous introduction to topology and homology focused on the simplicial space. It presents a compact pipeline from the foundations of topology to biomedical applications. It will be of interest to medical physicists, computer scientists, and engineers, as well as undergraduate and graduate students interested in this topic. Features: Presents a practical guide to algebraic topology as well as persistence homology Contains application examples in the field of biomedicine, including the analysis of histological images and point cloud data

Digital and Discrete Geometry

Author : Li M. Chen
Publisher : Springer
ISBN 13 : 3319120999
Total Pages : 325 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Digital and Discrete Geometry by : Li M. Chen

Download or read book Digital and Discrete Geometry written by Li M. Chen and published by Springer. This book was released on 2014-12-12 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.