Uncertain Projective Geometry
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Uncertain Projective Geometry
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Author : Stephan Heuel
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-04-29
Uncertain Projective Geometry written by Stephan Heuel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-04-29 with Mathematics categories.
Algebraic projective geometry, with its multilinear relations and its embedding into Grassmann-Cayley algebra, has become the basic representation of multiple view geometry, resulting in deep insights into the algebraic structure of geometric relations, as well as in efficient and versatile algorithms for computer vision and image analysis. This book provides a coherent integration of algebraic projective geometry and spatial reasoning under uncertainty with applications in computer vision. Beyond systematically introducing the theoretical foundations from geometry and statistics and clear rules for performing geometric reasoning under uncertainty, the author provides a collection of detailed algorithms. The book addresses researchers and advanced students interested in algebraic projective geometry for image analysis, in statistical representation of objects and transformations, or in generic tools for testing and estimating within the context of geometric multiple-view analysis.
Uncertain Projective Geometry
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Author : Stephan Heuel
language : en
Publisher: Springer
Release Date : 2004-04-22
Uncertain Projective Geometry written by Stephan Heuel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-04-22 with Mathematics categories.
Algebraic projective geometry, with its multilinear relations and its embedding into Grassmann-Cayley algebra, has become the basic representation of multiple view geometry, resulting in deep insights into the algebraic structure of geometric relations, as well as in efficient and versatile algorithms for computer vision and image analysis. This book provides a coherent integration of algebraic projective geometry and spatial reasoning under uncertainty with applications in computer vision. Beyond systematically introducing the theoretical foundations from geometry and statistics and clear rules for performing geometric reasoning under uncertainty, the author provides a collection of detailed algorithms. The book addresses researchers and advanced students interested in algebraic projective geometry for image analysis, in statistical representation of objects and transformations, or in generic tools for testing and estimating within the context of geometric multiple-view analysis.
Projective Geometry And Projective Metrics
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Author : Herbert Busemann
language : en
Publisher: Courier Corporation
Release Date : 2012-11-14
Projective Geometry And Projective Metrics written by Herbert Busemann and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-14 with Mathematics categories.
This text examines the 3 classical geometries and their relationship to general geometric structures, with particular focus on affine geometry, projective metrics, non-Euclidean geometry, and spatial geometry. 1953 edition.
Linear Algebra And Projective Geometry
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Author : Reinhold Baer
language : en
Publisher: Courier Corporation
Release Date : 2012-06-11
Linear Algebra And Projective Geometry written by Reinhold Baer and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-11 with Mathematics categories.
Geared toward upper-level undergraduates and graduate students, this text establishes that projective geometry and linear algebra are essentially identical. The supporting evidence consists of theorems offering an algebraic demonstration of certain geometric concepts. 1952 edition.
Projective Geometry
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Author : H.S.M. Coxeter
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-10-09
Projective Geometry written by H.S.M. Coxeter and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-10-09 with Mathematics categories.
In Euclidean geometry, constructions are made with ruler and compass. Projective geometry is simpler: its constructions require only a ruler. In projective geometry one never measures anything, instead, one relates one set of points to another by a projectivity. The first two chapters of this book introduce the important concepts of the subject and provide the logical foundations. The third and fourth chapters introduce the famous theorems of Desargues and Pappus. Chapters 5 and 6 make use of projectivities on a line and plane, respectively. The next three chapters develop a self-contained account of von Staudt's approach to the theory of conics. The modern approach used in that development is exploited in Chapter 10, which deals with the simplest finite geometry that is rich enough to illustrate all the theorems nontrivially. The concluding chapters show the connections among projective, Euclidean, and analytic geometry.
The Real Projective Plane
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Author : H.S.M. Coxeter
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Real Projective Plane written by H.S.M. Coxeter and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Along with many small improvements, this revised edition contains van Yzeren's new proof of Pascal's theorem (§1.7) and, in Chapter 2, an improved treatment of order and sense. The Sylvester-Gallai theorem, instead of being introduced as a curiosity, is now used as an essential step in the theory of harmonic separation (§3.34). This makes the logi cal development self-contained: the footnotes involving the References (pp. 214-216) are for comparison with earlier treatments, and to give credit where it is due, not to fill gaps in the argument. H.S.M.C. November 1992 v Preface to the Second Edition Why should one study the real plane? To this question, put by those who advocate the complex plane, or geometry over a general field, I would reply that the real plane is an easy first step. Most of the prop erties are closely analogous, and the real field has the advantage of intuitive accessibility. Moreover, real geometry is exactly what is needed for the projective approach to non· Euclidean geometry. Instead of introducing the affine and Euclidean metrics as in Chapters 8 and 9, we could just as well take the locus of 'points at infinity' to be a conic, or replace the absolute involution by an absolute polarity.
Projective Geometry
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Author : Oswald Veblen
language : en
Publisher:
Release Date : 1938
Projective Geometry written by Oswald Veblen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1938 with Geometry, Projective categories.
Photogrammetric Computer Vision
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Author : Wolfgang Förstner
language : en
Publisher: Springer
Release Date : 2016-10-04
Photogrammetric Computer Vision written by Wolfgang Förstner and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-04 with Computers categories.
This textbook offers a statistical view on the geometry of multiple view analysis, required for camera calibration and orientation and for geometric scene reconstruction based on geometric image features. The authors have backgrounds in geodesy and also long experience with development and research in computer vision, and this is the first book to present a joint approach from the converging fields of photogrammetry and computer vision. Part I of the book provides an introduction to estimation theory, covering aspects such as Bayesian estimation, variance components, and sequential estimation, with a focus on the statistically sound diagnostics of estimation results essential in vision metrology. Part II provides tools for 2D and 3D geometric reasoning using projective geometry. This includes oriented projective geometry and tools for statistically optimal estimation and test of geometric entities and transformations and their relations, tools that are useful also in the context of uncertain reasoning in point clouds. Part III is devoted to modelling the geometry of single and multiple cameras, addressing calibration and orientation, including statistical evaluation and reconstruction of corresponding scene features and surfaces based on geometric image features. The authors provide algorithms for various geometric computation problems in vision metrology, together with mathematical justifications and statistical analysis, thus enabling thorough evaluations. The chapters are self-contained with numerous figures and exercises, and they are supported by an appendix that explains the basic mathematical notation and a detailed index. The book can serve as the basis for undergraduate and graduate courses in photogrammetry, computer vision, and computer graphics. It is also appropriate for researchers, engineers, and software developers in the photogrammetry and GIS industries, particularly those engaged with statistically based geometric computer vision methods.
Symmetry And Pattern In Projective Geometry
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Author : Abby Enger
language : en
Publisher:
Release Date : 2016-10-01
Symmetry And Pattern In Projective Geometry written by Abby Enger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-01 with categories.
We are all familiar with Euclidean geometry and with the fact that it describes our three dimensional world so well. In Euclidean geometry, the sides of objects have lengths, intersecting lines determine angles between them, and two lines are said to be parallel if they lie in the same plane and never meet. Moreover, these properties do not change when the Euclidean transformations (translation and rotation) are applied. Since Euclidean geometry describes our world so well, it is at first tempting to think that it is the only type of geometry. However, when we consider the imaging process of a camera, it becomes clear that Euclidean geometry is insufficient: Lengths and angles are no longer preserved, and parallel lines may intersect. Euclidean geometry is actually a subset of what is known as projective geometry. Projective geometry exists in any number of dimensions, just like Euclidean geometry. Projective geometry has its origins in the early Italian Renaissance, particularly in the architectural drawings of Filippo Brunelleschi (1377-1446) and Leon Battista Alberti (1404-72), who invented the method of perspective drawing. Projective geometry deals with the relationships between geometric figures and the images, or mappings that result from projecting them onto another surface. Common examples of projections are the shadows cast by opaque objects and motion pictures displayed on a screen.First of all, projective geometry is a jewel of mathematics, one of the outstanding achievements of the nineteenth century, a century of remarkable mathematical achievements such as non-Euclidean geometry, abstract algebra, and the foundations of calculus. Projective geometry is as much a part of a general education in mathematics as differential equations and Galois theory. Moreover, projective geometry is a prerequisite for algebraic geometry, one of today's most vigorous and exciting branches of mathematics. Secondly, for more than fifty years projective geometry has been propelled in a new direction by its combinatorial connections. The challenge of describing a classical geometric structure by its parameters - properties that at first glance might seem superficial - provided much of the impetus for finite geometry, another of today's flourishing branches of mathematics.
Projective And Cayley Klein Geometries
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Author : Arkadij L. Onishchik
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-11-22
Projective And Cayley Klein Geometries written by Arkadij L. Onishchik and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-22 with Mathematics categories.
This book offers an introduction into projective geometry. The first part presents n-dimensional projective geometry over an arbitrary skew field; the real, the complex, and the quaternionic geometries are the central topics, finite geometries playing only a minor part. The second deals with classical linear and projective groups and the associated geometries. The final section summarizes selected results and problems from the geometry of transformation groups.