Modern Approaches To Discrete Curvature

Author : Laurent Najman,Pascal Romon
Publisher : Springer
Page : 353 pages
File Size : 42,6 Mb
Release : 2017-10-04
Category : Mathematics
ISBN : 9783319580029

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Modern Approaches to Discrete Curvature by Laurent Najman,Pascal Romon Pdf

This book provides a valuable glimpse into discrete curvature, a rich new field of research which blends discrete mathematics, differential geometry, probability and computer graphics. It includes a vast collection of ideas and tools which will offer something new to all interested readers. Discrete geometry has arisen as much as a theoretical development as in response to unforeseen challenges coming from applications. Discrete and continuous geometries have turned out to be intimately connected. Discrete curvature is the key concept connecting them through many bridges in numerous fields: metric spaces, Riemannian and Euclidean geometries, geometric measure theory, topology, partial differential equations, calculus of variations, gradient flows, asymptotic analysis, probability, harmonic analysis, graph theory, etc. In spite of its crucial importance both in theoretical mathematics and in applications, up to now, almost no books have provided a coherent outlook on this emerging field.

Author : David Xianfeng Gu,Emil Saucan
Publisher : CRC Press
Page : 589 pages
File Size : 46,7 Mb
Release : 2023-01-31
Category : Computers
ISBN : 9781000804454

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Classical and Discrete Differential Geometry by David Xianfeng Gu,Emil Saucan Pdf

This book introduces differential geometry and cutting-edge findings from the discipline by incorporating both classical approaches and modern discrete differential geometry across all facets and applications, including graphics and imaging, physics and networks. With curvature as the centerpiece, the authors present the development of differential geometry, from curves to surfaces, thence to higher dimensional manifolds; and from smooth structures to metric spaces, weighted manifolds and complexes, and to images, meshes and networks. The first part of the book is a differential geometric study of curves and surfaces in the Euclidean space, enhanced while the second part deals with higher dimensional manifolds centering on curvature by exploring the various ways of extending it to higher dimensional objects and more general structures and how to return to lower dimensional constructs. The third part focuses on computational algorithms in algebraic topology and conformal geometry, applicable for surface parameterization, shape registration and structured mesh generation. The volume will be a useful reference for students of mathematics and computer science, as well as researchers and engineering professionals who are interested in graphics and imaging, complex networks, differential geometry and curvature.

Author : Li M. Chen
Publisher : Springer
Page : 325 pages
File Size : 50,6 Mb
Release : 2014-12-12
Category : Computers
ISBN : 9783319120997

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Digital and Discrete Geometry by Li M. Chen Pdf

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 : Nicolas Normand,Jeanpierre Guédon,Florent Autrusseau
Publisher : Springer
Page : 453 pages
File Size : 53,7 Mb
Release : 2016-04-08
Category : Computers
ISBN : 9783319323602

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Discrete Geometry for Computer Imagery by Nicolas Normand,Jeanpierre Guédon,Florent Autrusseau Pdf

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.

Author : Xianfeng David Gu,Emil Saucan
Publisher : Unknown
Page : 0 pages
File Size : 50,7 Mb
Release : 2022-12
Category : Geometry, Differential
ISBN : 1032396202

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Classical and Discrete Differential Geometry by Xianfeng David Gu,Emil Saucan Pdf

"This book introduces differential geometry and cutting-edge findings from the discipline by incorporating both classical approaches and modern discrete differential geometry across all facets and applications, including graphics and imaging, physics and networks. With curvature as the centerpiece, the authors present the development of differential geometry, from curves to surfaces, thence to higher dimensional manifolds; and from smooth structures to metric spaces, weighted manifolds and complexes, and to images, meshes and networks. The first part of the book is a differential geometric study of curves and surfaces in the Euclidean space, enhanced while the second part deals with higher dimensional manifolds centering on curvature by exploring the various ways of extending it to higher dimensional objects and more general structures and how to return to lower dimensional constructs. The third part focuses on computational algorithms in algebraic topology and conformal geometry, applicable for surface parameterization, shape registration and structured mesh generation. The volume will be a useful reference for students of mathematics and computer science, as well as researchers and engineering professionals who are interested in graphics and imaging, complex networks, differential geometry and curvature"--

Author : Étienne Baudrier,Benoît Naegel,Adrien Krähenbühl,Mohamed Tajine
Publisher : Springer Nature
Page : 479 pages
File Size : 45,9 Mb
Release : 2022-10-20
Category : Computers
ISBN : 9783031198977

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Discrete Geometry and Mathematical Morphology by Étienne Baudrier,Benoît Naegel,Adrien Krähenbühl,Mohamed Tajine Pdf

This book constitutes the proceedings of the Second IAPR International Conference on Discrete Geometry and Mathematical Morphology, DGMM 2022, which was held during October 24-27, 2022, in Strasbourg, France. The 33 papers included in this volume were carefully reviewed and selected from 45 submissions. They were organized in topical sections as follows: discrete and combinatorial topology; discrete tomography and inverse problems; multivariate and PDE-based mathematical morphology, morphological filtering; hierarchical and Graph-Based Models, Analysis and Segmentation; discrete geometry - models, transforms, and visualization; learning based morphology to Mathematical Morphology; and distance transform. The book also contains 3 invited keynote papers.

Author : Sara Brunetti
Publisher : Springer Nature
Page : 462 pages
File Size : 40,9 Mb
Release : 2024-06-25
Category : Electronic
ISBN : 9783031577932

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Discrete Geometry and Mathematical Morphology by Sara Brunetti Pdf

Author : Walter G. Kropatsch,Nicole M. Artner,Ines Janusch
Publisher : Springer
Page : 400 pages
File Size : 47,6 Mb
Release : 2017-09-01
Category : Computers
ISBN : 9783319662725

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Discrete Geometry for Computer Imagery by Walter G. Kropatsch,Nicole M. Artner,Ines Janusch Pdf

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 : Tim Hoffmann,Martin Kilian,Katrin Leschke,Francisco Martin
Publisher : Springer Nature
Page : 280 pages
File Size : 41,7 Mb
Release : 2021-05-06
Category : Mathematics
ISBN : 9783030685416

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Minimal Surfaces: Integrable Systems and Visualisation by Tim Hoffmann,Martin Kilian,Katrin Leschke,Francisco Martin Pdf

This book collects original peer-reviewed contributions to the conferences organised by the international research network “Minimal surfaces: Integrable Systems and Visualization” financed by the Leverhulme Trust. The conferences took place in Cork, Granada, Munich and Leicester between 2016 and 2019. Within the theme of the network, the presented articles cover a broad range of topics and explore exciting links between problems related to the mean curvature of surfaces in homogeneous 3-manifolds, like minimal surfaces, CMC surfaces and mean curvature flows, integrable systems and visualisation. Combining research and overview articles by prominent international researchers, the book offers a valuable resource for both researchers and students who are interested in this research area.

Author : Michael Günther,Wil Schilders
Publisher : Springer Nature
Page : 348 pages
File Size : 44,7 Mb
Release : 2022-03-30
Category : Mathematics
ISBN : 9783030961732

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Novel Mathematics Inspired by Industrial Challenges by Michael Günther,Wil Schilders Pdf

This contributed volume convenes a rich selection of works with a focus on innovative mathematical methods with applications in real-world, industrial problems. Studies included in this book are all motivated by a relevant industrial challenge, and demonstrate that mathematics for industry can be extremely rewarding, leading to new mathematical methods and sometimes even to entirely new fields within mathematics. The book is organized into two parts: Computational Sciences and Engineering, and Data Analysis and Finance. In every chapter, readers will find a brief description of why such work fits into this volume; an explanation on which industrial challenges have been instrumental for their inspiration; and which methods have been developed as a result. All these contribute to a greater unity of the text, benefiting not only practitioners and professionals seeking information on novel techniques but also graduate students in applied mathematics, engineering, and related fields.

Author : Parvaneh Joharinad,Jürgen Jost
Publisher : Springer Nature
Page : 287 pages
File Size : 45,9 Mb
Release : 2023-07-29
Category : Mathematics
ISBN : 9783031334405

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Mathematical Principles of Topological and Geometric Data Analysis by Parvaneh Joharinad,Jürgen Jost Pdf

This book explores and demonstrates how geometric tools can be used in data analysis. Beginning with a systematic exposition of the mathematical prerequisites, covering topics ranging from category theory to algebraic topology, Riemannian geometry, operator theory and network analysis, it goes on to describe and analyze some of the most important machine learning techniques for dimension reduction, including the different types of manifold learning and kernel methods. It also develops a new notion of curvature of generalized metric spaces, based on the notion of hyperconvexity, which can be used for the topological representation of geometric information. In recent years there has been a fascinating development: concepts and methods originally created in the context of research in pure mathematics, and in particular in geometry, have become powerful tools in machine learning for the analysis of data. The underlying reason for this is that data are typically equipped with some kind of notion of distance, quantifying the differences between data points. Of course, to be successfully applied, the geometric tools usually need to be redefined, generalized, or extended appropriately. Primarily aimed at mathematicians seeking an overview of the geometric concepts and methods that are useful for data analysis, the book will also be of interest to researchers in machine learning and data analysis who want to see a systematic mathematical foundation of the methods that they use.

Author : Anne Bourlioux,Martin Gander
Publisher : Springer Science & Business Media
Page : 503 pages
File Size : 44,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401005104

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Modern Methods in Scientific Computing and Applications by Anne Bourlioux,Martin Gander Pdf

When we first heard in the spring of 2000 that the Seminaire de matMmatiques superieures (SMS) was interested in devoting its session of the summer of 200l-its 40th-to scientific computing the idea of taking on the organizational work seemed to us somewhat remote. More immediate things were on our minds: one of us was about to go on leave to the Courant Institute, the other preparing for a research summer in Paris. But the more we learned about the possibilities of such a seminar, the support for the organization and also the great history of the SMS, the more we grew attached to the project. The topics we planned to cover were intended to span a wide range of theoretical and practical tools for solving problems in image processing, thin films, mathematical finance, electrical engineering, moving interfaces, and combustion. These applications alone show how wide the influence of scientific computing has become over the last two decades: almost any area of science and engineering is greatly influenced by simulations, and the SMS workshop in this field came very timely. We decided to organize the workshop in pairs of speakers for each of the eight topics we had chosen, and we invited the leading experts worldwide in these fields. We were very fortunate that every speaker we invited accepted to come, so the program could be realized as planned.

Author : Haiqin Yang,Kitsuchart Pasupa,Andrew Chi-Sing Leung,James T. Kwok,Jonathan H. Chan,Irwin King
Publisher : Springer Nature
Page : 844 pages
File Size : 51,6 Mb
Release : 2020-11-19
Category : Computers
ISBN : 9783030638337

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Neural Information Processing by Haiqin Yang,Kitsuchart Pasupa,Andrew Chi-Sing Leung,James T. Kwok,Jonathan H. Chan,Irwin King Pdf

The three-volume set of LNCS 12532, 12533, and 12534 constitutes the proceedings of the 27th International Conference on Neural Information Processing, ICONIP 2020, held in Bangkok, Thailand, in November 2020. Due to COVID-19 pandemic the conference was held virtually. The 187 full papers presented were carefully reviewed and selected from 618 submissions. The papers address the emerging topics of theoretical research, empirical studies, and applications of neural information processing techniques across different domains. The second volume, LNCS 12533, is organized in topical sections on computational intelligence; machine learning; robotics and control.

Author : Joakim Lindblad,Filip Malmberg,Nataša Sladoje
Publisher : Springer Nature
Page : 553 pages
File Size : 49,5 Mb
Release : 2021-05-15
Category : Computers
ISBN : 9783030766573

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Discrete Geometry and Mathematical Morphology by Joakim Lindblad,Filip Malmberg,Nataša Sladoje Pdf

This book constitutes the proceedings of the First IAPR International Conference on Discrete Geometry and Mathematical Morphology, DGMM 2021, which was held during May 24-27, 2021, in Uppsala, Sweden. The conference was created by joining the International Conference on Discrete Geometry for computer Imagery, DGCI, with the International Symposium on Mathematical Morphology, ISMM. The 36 papers included in this volume were carefully reviewed and selected from 59 submissions. They were organized in topical sections as follows: applications in image processing, computer vision, and pattern recognition; discrete and combinatorial topology; discrete geometry - models, transforms, visualization; discrete tomography and inverse problems; hierarchical and graph-based models, analysis and segmentation; learning-based approaches to mathematical morphology; multivariate and PDE-based mathematical morphology, morphological filtering. The book also contains 3 invited keynote papers.

Author : Federico Battiston,Giovanni Petri
Publisher : Springer Nature
Page : 436 pages
File Size : 47,7 Mb
Release : 2022-04-26
Category : Science
ISBN : 9783030913748

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Higher-Order Systems by Federico Battiston,Giovanni Petri Pdf

The book discusses the potential of higher-order interactions to model real-world relational systems. Over the last decade, networks have emerged as the paradigmatic framework to model complex systems. Yet, as simple collections of nodes and links, they are intrinsically limited to pairwise interactions, limiting our ability to describe, understand, and predict complex phenomena which arise from higher-order interactions. Here we introduce the new modeling framework of higher-order systems, where hypergraphs and simplicial complexes are used to describe complex patterns of interactions among any number of agents. This book is intended both as a first introduction and an overview of the state of the art of this rapidly emerging field, serving as a reference for network scientists interested in better modeling the interconnected world we live in.