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.
Author: Valentin E. Brimkov
Publisher: Springer Science & Business Media
Category: Technology & Engineering
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: Jayanta MukhopadhyayPublish On: 2016-04-19
In different ways, digital geometry may be defined depending upon the
neighborhood definition of a point in the space. Digital images from different
imaging technologies such as CT Scan, MRI, PET, etc. are also available in 3-D
Author: Jayanta Mukhopadhyay
Publisher: CRC Press
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 Geometry for Computer Imagery , DGCI , Szeged , 2006-10-25—27 .
Member of the Program Committee . GeoNet VI , Porto - Novo , 2007-06-10—17 .
Scientifically responsible for the theme Discrete and Combinatorial Geometry ...
This book provides comprehensive coverage of the modern methods for geometric problems in the computing sciences.
Author: Li M. Chen
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.
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.
Author: Gilles Bertrand
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.
Digital geometry deals with geometric properties of subsets of digital images or, equivalently, with geometric properties of finite sets of lattice points.
Author: Reinhard Klette
Digital geometry deals with geometric properties of subsets of digital images or, equivalently, with geometric properties of finite sets of lattice points. Digital geometry can anticipate progress in imaging technology allowing higher and higher spatial resolution. It seems that the input data in both fields will "converge" to data embedded in digital arrays of very high spatial resolution.
Abstract : Purpose: Poland's syndrome patients often seek medical interventions to improve their aesthetic appearances. Design and manufacturing technologies make it possible to produce custom-made implants for such medical conditions.
Abstract : Purpose: Poland's syndrome patients often seek medical interventions to improve their aesthetic appearances. Design and manufacturing technologies make it possible to produce custom-made implants for such medical conditions. The purpose of this study was to compare the 3D digital geometries that were designed using Magics and Geomagic ® Freeform ® for two anonymous case studies of Poland's syndrome patients. Design/methodology/approach: Computed tomography data were acquired and processed in Mimics ® to isolate the pectoralis muscles in STL file format. STL files were imported into Magics and Geomagic ® Freeform ® to design 3D digital geometries. Thereafter, comparative analyses were performed of the respective 3D digital geometries. Findings: The angle between the vertical and oblique planes for both sides of the thorax was 6.5° for the female and 14° for the male. The surface areas and volumes of the geometries for the female were smaller than the male. Deviation analyses between the healthy side and reconstructed side of a thorax showed that 73 per cent of the test points for Magics and 78 per cent for Geomagic ® Freeform ® fell in the nominated tolerance region of >−5 and
Cell complexes are relevant for modelling discrete sets and their inter -
relationships within the context of digital image analysis : see for example
contributions on recent conferences in digital geometry and topology such as ( 1 ,
4 Classification of Digital Curves Curves are considered in the classical geometry
as objects with zero width and zero area . In digital geometry we consider the
number of pixels ( being elementary areas ) in a subset S as the measure of the ...
This book presents the analysis of textured images using fractal geometry, and discusses its application to imaging science and computer vision when modeling natural objects.
Author: Martin J. Turner
Publisher: Academic Press
This book presents the analysis of textured images using fractal geometry, and discusses its application to imaging science and computer vision when modeling natural objects. The authors explore the methods which can be used to simulate, analyze, and interpret coherent images, and demonstrate a new approach which segments each image into regions of similarity that can be characterized by a random fractal with a given fractal dimension. Fractal Geometry in Digital Imaging is based on a research project, but has been written with a broad coverage and user friendly math to make the book accessible to a wider audience. It includes real world experiences and applications using the techniques described. * Discusses the analysis of textured images using fractal geometry * Explores the methods used to simulate, analyze, and interpret coherent images * Contains coverage of real world experiences and applications * Written in a user friendly style
This book constitutes the thoroughly refereed proceedings of the 20th IAPR International Conference on Discrete Geometry for Computer Imagery, DGCI 2017, held in Vienna, Austria, in September 2017.
Author: Walter G. Kropatsch
This book constitutes the thoroughly refereed proceedings of the 20th IAPR International Conference on Discrete Geometry for Computer Imagery, DGCI 2017, held in Vienna, Austria, in September 2017. The 28 revised full papers presented together with 3 invited talks were carefully selected from 36 submissions. The papers are organized in topical sections on geometric transforms; discrete tomography; discrete modeling and visualization; morphological analysis; discrete shape representation, recognition and analysis; discrete and combinatorial topology; discrete models and tools; models for discrete geometry.
Author: ACM Special Interest Group for Automata and Computability TheoryPublish On: 1992
DIGITAL GEOMETRY Azriel Rosenfeld Center for Automation Research
University of Maryland College Park, Maryland 20742-3411 ABSTRACT Digital geometry deals with the study of geometric properties of subsets of digital images
- i.e., ...
Author: ACM Special Interest Group for Automata and Computability Theory
Preface Conformal geometry is in the intersection of many fields in pure
mathematics , such as Riemann surface theory ... Recently , with the rapid
development of three dimensional digital scanning technology , computer aided geometric ...
Author: Xianfeng David Gu
Publisher: International Pressof Boston Incorporated
Computational conformal geometry is an emerging inter-disciplinary field, with applications to algebraic topology, differential geometry and Riemann surface theories applied to geometric modeling, computer graphics, computer vision, medical imaging, visualization, scientific computation, and many other engineering fields.This new volume presents thorough introductions to the theoretical foundations—as well as to the practical algorithms—of computational conformal geometry. These have direct applications to engineering and digital geometric processing, including surface parameterization, surface matching, brain mapping, 3-D face recognition and identification, facial expression and animation, dynamic face tracking, mesh-spline conversion, and more.
"La narraci6n literaria es la evocaci6n de las nostalgias. " ("Literary narration is the evocation of nostalgia. ") G. G. Marquez, interview in Puerta del Sol, VII, 4, 1996.
Author: Gabor T. Herman
Publisher: Springer Science & Business Media
"La narraci6n literaria es la evocaci6n de las nostalgias. " ("Literary narration is the evocation of nostalgia. ") G. G. Marquez, interview in Puerta del Sol, VII, 4, 1996. A Personal Prehistory In 1972 I started cooperating with members of the Biodynamics Research Unit at the Mayo Clinic in Rochester, Minnesota, which was under the direction of Earl H. Wood. At that time, their ambitious (and eventually realized) dream was to build the Dynamic Spatial Reconstructor (DSR), a device capable of collecting data regarding the attenuation of X-rays through the human body fast enough for stop-action imaging the full extent of the beating heart inside the thorax. Such a device can be applied to study the dynamic processes of cardiopulmonary physiology, in a manner similar to the application of an ordinary cr (computerized tomography) scanner to observing stationary anatomy. The standard method of displaying the information produced by a cr scanner consists of showing two-dimensional images, corresponding to maps of the X-ray attenuation coefficient in slices through the body. (Since different tissue types attenuate X-rays differently, such maps provide a good visualization of what is in the body in those slices; bone - which attenuates X-rays a lot - appears white, air appears black, tumors typically appear less dark than the surrounding healthy tissue, etc. ) However, it seemed to me that this display mode would not be appropriate for the DSR.
Geometry of the Optic Cup by Stereophotogrammetry In the past years ,
experimental methods have been devised to measure ... In this thesis , we
examine computer - aided digital stereophotogrammetry as a more systematic
and quantitative ...
This book discusses the computational geometry, topology and physics of digital images and video frame sequences.
Author: James F. Peters
Publisher: Springer Nature
Category: Technology & Engineering
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.
This volume contains fourteen papers presented at the AMS Special Session on Geometry Related to Computer Vision, held in Hoboken, New Jersey in October 1989.
Author: Robert A. Melter
Publisher: American Mathematical Soc.
Since its genesis more than thirty-five years ago, the field of computer vision has been known by various names, including pattern recognitions, image analysis, and image understanding. The central problem of computer vision is obtaining descriptive information by computer analysis of images of a scene. Together with the related fields of image processing and computer graphics, it has become an established discipline at the interface between computer science and electrical engineering. This volume contains fourteen papers presented at the AMS Special Session on Geometry Related to Computer Vision, held in Hoboken, New Jersey in October 1989. This book makes the results presented at the Special Session, which previously had been available only in the computer science literature, more widely available within the mathematical sciences community. Geometry plays a major role in computer vision, since scene descriptions always involve geometrical properties of, and relations among, the objects or surfaces in the scene. The papers in this book provide a good sampling of geometric problems connected with computer vision. They deal with digital lines and curves, polygons, shape decompositions, digital connectedness and surfaces, digital metrics, and generalizations to higher-dimensional and graph-structured ``spaces.'' Aimed at computer scientists specializing in image processing, computer vision, and pattern recognition--as well as mathematicians interested in applications to computer science--this book will provide readers with a view of how geometry is currently being applied to problems in computer vision.
We denote the 8 - neighbors of Yo as follows ; on a Abstract Several existing
thinning algorithms are assessed from the digital geometry viewpoint . Through
this investigation two significant properties are elucidated . Firstly , it is shown that