Modern Mathematics And Applications In Computer Graphics And Vision

Author : Hongyu Guo
Publisher : World Scientific Publishing Company
Page : 524 pages
File Size : 51,9 Mb
Release : 2014-04-01
Category : Computers
ISBN : 9789814449359

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Modern Mathematics And Applications In Computer Graphics And Vision by Hongyu Guo Pdf

This book presents a concise exposition of modern mathematical concepts, models and methods with applications in computer graphics, vision and machine learning. The compendium is organized in four parts — Algebra, Geometry, Topology, and Applications. One of the features is a unique treatment of tensor and manifold topics to make them easier for the students. All proofs are omitted to give an emphasis on the exposition of the concepts. Effort is made to help students to build intuition and avoid parrot-like learning.There is minimal inter-chapter dependency. Each chapter can be used as an independent crash course and the reader can start reading from any chapter — almost. This book is intended for upper level undergraduate students, graduate students and researchers in computer graphics, geometric modeling, computer vision, pattern recognition and machine learning. It can be used as a reference book, or a textbook for a selected topics course with the instructor's choice of any of the topics.

Author : Hongyu Guo
Publisher : Unknown
Page : 128 pages
File Size : 42,5 Mb
Release : 2014
Category : Electronic
ISBN : 9814449342

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Modern Mathematics and Applications in Computer Graphics and Vision by Hongyu Guo Pdf

Author : Luiz Velho,Alejandro C. Frery,Jonas Gomes
Publisher : Springer Science & Business Media
Page : 476 pages
File Size : 53,5 Mb
Release : 2009-04-29
Category : Computers
ISBN : 9781848001930

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Image Processing for Computer Graphics and Vision by Luiz Velho,Alejandro C. Frery,Jonas Gomes Pdf

Image processing is concerned with the analysis and manipulation of images by computer. Providing a thorough treatment of image processing with an emphasis on those aspects most used in computer graphics, the authors concentrate on describing and analyzing the underlying concepts rather than on presenting algorithms or pseudocode. As befits a modern introduction to this topic, a good balance is struck between discussing the underlying mathematics and the main topics: signal processing, data discretization, the theory of colour and different colour systems, operations in images, dithering and half-toning, warping and morphing and image processing. This second edition reflects recent trends in science andtechnology that exploit image processing in computer graphics and vision applications. Stochastic image models and statistical methods for image processing are covered as are: A modern approach and new developments in the area, Probability theory for image processing, Applications in image analysis and computer vision.

Author : Luiz Velho,Paulo Carvalho,Jonas Gomes,Luiz de Figueiredo
Publisher : Morgan Kaufmann
Page : 304 pages
File Size : 55,7 Mb
Release : 2011-08-09
Category : Computers
ISBN : 008087858X

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Mathematical Optimization in Computer Graphics and Vision by Luiz Velho,Paulo Carvalho,Jonas Gomes,Luiz de Figueiredo Pdf

Mathematical optimization is used in nearly all computer graphics applications, from computer vision to animation. This book teaches readers the core set of techniques that every computer graphics professional should understand in order to envision and expand the boundaries of what is possible in their work. Study of this authoritative reference will help readers develop a very powerful tool- the ability to create and decipher mathematical models that can better realize solutions to even the toughest problems confronting computer graphics community today. *Distills down a vast and complex world of information on optimization into one short, self-contained volume especially for computer graphics *Helps CG professionals identify the best technique for solving particular problems quickly, by categorizing the most effective algorithms by application *Keeps readers current by supplementing the focus on key, classic methods with special end-of-chapter sections on cutting-edge developments

Author : John Vince
Publisher : Springer Nature
Page : 519 pages
File Size : 43,9 Mb
Release : 2023-01-24
Category : Computers
ISBN : 9783031174117

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Foundation Mathematics for Computer Science by John Vince Pdf

In this third edition of Foundation Mathematics for Computer Science, John Vince has reviewed and edited the second edition, and added chapters on systems of counting, area and volume. These subjects complement the existing chapters on visual mathematics, numbers, algebra, logic, combinatorics, probability, modular arithmetic, trigonometry, coordinate systems, determinants, vectors, complex numbers, matrices, geometric matrix transforms, differential and integral calculus. During this journey, the author touches upon more esoteric topics such as quaternions, octonions, Grassmann algebra, Barrycentric coordinates, transfinite sets and prime numbers. John Vince describes a range of mathematical topics that provide a solid foundation for an undergraduate course in computer science, starting with a review of number systems and their relevance to digital computers, and finishing with calculating area and volume using calculus. Readers will find that the author’s visual approach should greatly improve their understanding as to why certain mathematical structures exist, together with how they are used in real-world applications. This third edition includes new, full-colour illustrations to clarify the mathematical descriptions, and in some cases, equations are also coloured to reveal vital algebraic patterns. The numerous worked examples will help consolidate the understanding of abstract mathematical concepts. Whether you intend to pursue a career in programming, scientific visualisation, artificial intelligence, systems design, or real-time computing, you should find the author’s literary style refreshingly lucid and engaging, and prepare you for more advanced texts.

Author : Yi Ma,Stefano Soatto,Jana Kosecká,S. Shankar Sastry
Publisher : Springer Science & Business Media
Page : 542 pages
File Size : 48,8 Mb
Release : 2012-11-06
Category : Computers
ISBN : 9780387217796

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An Invitation to 3-D Vision by Yi Ma,Stefano Soatto,Jana Kosecká,S. Shankar Sastry Pdf

This book introduces the geometry of 3-D vision, that is, the reconstruction of 3-D models of objects from a collection of 2-D images. It details the classic theory of two view geometry and shows that a more proper tool for studying the geometry of multiple views is the so-called rank consideration of the multiple view matrix. It also develops practical reconstruction algorithms and discusses possible extensions of the theory.

Author : Tania Pouli,Erik Reinhard,Douglas W. Cunningham
Publisher : CRC Press
Page : 374 pages
File Size : 48,6 Mb
Release : 2013-12-13
Category : Computers
ISBN : 9781568817255

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Image Statistics in Visual Computing by Tania Pouli,Erik Reinhard,Douglas W. Cunningham Pdf

To achieve the complex task of interpreting what we see, our brains rely on statistical regularities and patterns in visual data. Knowledge of these regularities can also be considerably useful in visual computing disciplines, such as computer vision, computer graphics, and image processing. The field of natural image statistics studies the regularities to exploit their potential and better understand human vision. With numerous color figures throughout, Image Statistics in Visual Computing covers all aspects of natural image statistics, from data collection to analysis to applications in computer graphics, computational photography, image processing, and art. The authors keep the material accessible, providing mathematical definitions where appropriate to help readers understand the transforms that highlight statistical regularities present in images. The book also describes patterns that arise once the images are transformed and gives examples of applications that have successfully used statistical regularities. Numerous references enable readers to easily look up more information about a specific concept or application. A supporting website also offers additional information, including descriptions of various image databases suitable for statistics. Collecting state-of-the-art, interdisciplinary knowledge in one source, this book explores the relation of natural image statistics to human vision and shows how natural image statistics can be applied to visual computing. It encourages readers in both academic and industrial settings to develop novel insights and applications in all disciplines that relate to visual computing.

Author : Li M. Chen
Publisher : Springer
Page : 325 pages
File Size : 49,9 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 : Michael E. Mortenson
Publisher : Industrial Press Inc.
Page : 372 pages
File Size : 45,9 Mb
Release : 1999
Category : Computers
ISBN : 083113111X

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Mathematics for Computer Graphics Applications by Michael E. Mortenson Pdf

"Mathematics for Computer Graphics Applications is written for several audiences: for college students majoring in computer science, engineering, or applied mathematics and science, whose special interests are in computer graphics, CAD/CAM, geometric modeling, visualization, or related subjects; for industry and government on-the-job training of employees whose skills can be profitably expanded into these areas; and for the professional working in these fields in need of a comprehensive reference and skills refresher."--BOOK JACKET.

Author : Neeta Nain
Publisher : Vikas Publishing House
Page : 128 pages
File Size : 55,8 Mb
Release : 2024-06-25
Category : Computers
ISBN : 9789325972612

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Computer Graphics by Neeta Nain Pdf

This book adopts a conceptual approach to computer graphics, with emphasis on mathematical concepts and their applications. It introduces an abstract paradigm that relates the mathematical concepts with computer graphic techniques and implementation methods. This model is intended to help the reader understand the mathematical concepts and their practical use. However, mathematical complexity has not been allowed to dominate. The haul mark of the book is its profuse solved examples which aid in the understanding of mathematical concepts.The text is supplemented with introduction to various graphics standards, animation, multimedia techniques and fractals. These topics are of immense use in each of the three visual disciplines: modeling transformations, projections and multi-view geometry for computer vision. Geometry of lines, vectors and planes is essential for any geometric computation problem, light and illumination for image-based rendering, and hidden surface removal. Almost every chapter has the working source code to illustrate the concepts, which could be written and used as small programs for better understanding of the topics. A concise appendix of open source OpenGL is also included to showcase programming concepts of computer graphics and visualization.The text is completely platform-independent and the only prerequisite is the knowledge of coordinate geometry and basic algebra. It will be useful both as a text and reference, thus it can easily be used by novices and experienced practitioners alike.

Author : Yanxi Liu,Hagit Hel-Or,Craig S. Kaplan
Publisher : Now Publishers Inc
Page : 209 pages
File Size : 43,6 Mb
Release : 2010
Category : Computers
ISBN : 9781601983640

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Computational Symmetry in Computer Vision and Computer Graphics by Yanxi Liu,Hagit Hel-Or,Craig S. Kaplan Pdf

In the arts and sciences, as well as in our daily lives, symmetry has made a profound and lasting impact. Likewise, a computational treatment of symmetry and group theory (the ultimate mathematical formalization of symmetry) has the potential to play an important role in computational sciences. Though the term Computational Symmetry was formally defined a decade ago by the first author, referring to algorithmic treatment of symmetries, seeking symmetry from digital data has been attempted for over four decades. Computational symmetry on real world data turns out to be challenging enough that, after decades of effort, a fully automated symmetry-savvy system remains elusive for real world applications. The recent resurging interests in computational symmetry for computer vision and computer graphics applications have shown promising results. Recognizing the fundamental relevance and potential power that computational symmetry affords, we offer this survey to the computer vision and computer graphics communities. This survey provides a succinct summary of the relevant mathematical theory, a historic perspective of some important symmetry-related ideas, a partial yet timely report on the state of the arts symmetry detection algorithms along with its first quantitative benchmark, a diverse set of real world applications, suggestions for future directions and a comprehensive reference list.

Author : Ron Kimmel
Publisher : Springer Science & Business Media
Page : 222 pages
File Size : 55,6 Mb
Release : 2012-09-07
Category : Computers
ISBN : 9780387216379

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Numerical Geometry of Images by Ron Kimmel Pdf

Numerical Geometry of Images examines computational methods and algorithms in image processing. It explores applications like shape from shading, color-image enhancement and segmentation, edge integration, offset curve computation, symmetry axis computation, path planning, minimal geodesic computation, and invariant signature calculation. In addition, it describes and utilizes tools from mathematical morphology, differential geometry, numerical analysis, and calculus of variations. Graduate students, professionals, and researchers with interests in computational geometry, image processing, computer graphics, and algorithms will find this new text / reference an indispensable source of insight of instruction.

Author : John Vince
Publisher : Springer
Page : 303 pages
File Size : 51,6 Mb
Release : 2019-03-12
Category : Computers
ISBN : 9783030113766

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Calculus for Computer Graphics by John Vince Pdf

Students studying different branches of computer graphics have to be familiar with geometry, matrices, vectors, rotation transforms, quaternions, curves and surfaces and as computer graphics software becomes increasingly sophisticated, calculus is also being used to resolve its associated problems. In this 2nd edition, the author extends the scope of the original book to include applications of calculus in the areas of arc-length parameterisation of curves, geometric continuity, tangent and normal vectors, and curvature. The author draws upon his experience in teaching mathematics to undergraduates to make calculus appear no more challenging than any other branch of mathematics. He introduces the subject by examining how functions depend upon their independent variables, and then derives the appropriate mathematical underpinning and definitions. This gives rise to a function’s derivative and its antiderivative, or integral. Using the idea of limits, the reader is introduced to derivatives and integrals of many common functions. Other chapters address higher-order derivatives, partial derivatives, Jacobians, vector-based functions, single, double and triple integrals, with numerous worked examples, and over a hundred and seventy colour illustrations. This book complements the author’s other books on mathematics for computer graphics, and assumes that the reader is familiar with everyday algebra, trigonometry, vectors and determinants. After studying this book, the reader should understand calculus and its application within the world of computer graphics, games and animation.

Author : Hongyu Guo
Publisher : World Scientific
Page : 246 pages
File Size : 41,9 Mb
Release : 2021-06-16
Category : Mathematics
ISBN : 9789811241031

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What Are Tensors Exactly? by Hongyu Guo Pdf

Tensors have numerous applications in physics and engineering. There is often a fuzzy haze surrounding the concept of tensor that puzzles many students. The old-fashioned definition is difficult to understand because it is not rigorous; the modern definitions are difficult to understand because they are rigorous but at a cost of being more abstract and less intuitive.The goal of this book is to elucidate the concepts in an intuitive way but without loss of rigor, to help students gain deeper understanding. As a result, they will not need to recite those definitions in a parrot-like manner any more. This volume answers common questions and corrects many misconceptions about tensors. A large number of illuminating illustrations helps the reader to understand the concepts more easily.This unique reference text will benefit researchers, professionals, academics, graduate students and undergraduate students.

Author : Stanley Osher,Nikos Paragios
Publisher : Springer Science & Business Media
Page : 513 pages
File Size : 55,7 Mb
Release : 2007-05-08
Category : Computers
ISBN : 9780387218106

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Geometric Level Set Methods in Imaging, Vision, and Graphics by Stanley Osher,Nikos Paragios Pdf

Here is, for the first time, a book that clearly explains and applies new level set methods to problems and applications in computer vision, graphics, and imaging. It is an essential compilation of survey chapters from the leading researchers in the field. The applications of the methods are emphasized.