Photogrammetric Computer Vision

Statistics, Geometry, Orientation and Reconstruction

Author: Wolfgang Förstner,Bernhard P. Wrobel

Publisher: Springer

ISBN: 3319115502

Category: Computers

Page: 816

View: 1408


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.

Applications of Linear and Nonlinear Models

Fixed Effects, Random Effects, and Total Least Squares

Author: Erik Grafarend,Joseph L. Awange

Publisher: Springer Science & Business Media

ISBN: 3642222412

Category: Science

Page: 1016

View: 4396


Here we present a nearly complete treatment of the Grand Universe of linear and weakly nonlinear regression models within the first 8 chapters. Our point of view is both an algebraic view as well as a stochastic one. For example, there is an equivalent lemma between a best, linear uniformly unbiased estimation (BLUUE) in a Gauss-Markov model and a least squares solution (LESS) in a system of linear equations. While BLUUE is a stochastic regression model, LESS is an algebraic solution. In the first six chapters we concentrate on underdetermined and overdeterimined linear systems as well as systems with a datum defect. We review estimators/algebraic solutions of type MINOLESS, BLIMBE, BLUMBE, BLUUE, BIQUE, BLE, BIQUE and Total Least Squares. The highlight is the simultaneous determination of the first moment and the second central moment of a probability distribution in an inhomogeneous multilinear estimation by the so called E-D correspondence as well as its Bayes design. In addition, we discuss continuous networks versus discrete networks, use of Grassmann-Pluecker coordinates, criterion matrices of type Taylor-Karman as well as FUZZY sets. Chapter seven is a speciality in the treatment of an overdetermined system of nonlinear equations on curved manifolds. The von Mises-Fisher distribution is characteristic for circular or (hyper) spherical data. Our last chapter eight is devoted to probabilistic regression, the special Gauss-Markov model with random effects leading to estimators of type BLIP and VIP including Bayesian estimation. A great part of the work is presented in four Appendices. Appendix A is a treatment, of tensor algebra, namely linear algebra, matrix algebra and multilinear algebra. Appendix B is devoted to sampling distributions and their use in terms of confidence intervals and confidence regions. Appendix C reviews the elementary notions of statistics, namely random events and stochastic processes. Appendix D introduces the basics of Groebner basis algebra, its careful definition, the Buchberger Algorithm, especially the C. F. Gauss combinatorial algorithm.

Multiple View Geometry in Computer Vision

Author: Richard Hartley,Andrew Zisserman

Publisher: Cambridge University Press

ISBN: 1139449141

Category: Computers

Page: N.A

View: 7014


A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Techniques for solving this problem are taken from projective geometry and photogrammetry. Here, the authors cover the geometric principles and their algebraic representation in terms of camera projection matrices, the fundamental matrix and the trifocal tensor. The theory and methods of computation of these entities are discussed with real examples, as is their use in the reconstruction of scenes from multiple images. The new edition features an extended introduction covering the key ideas in the book (which itself has been updated with additional examples and appendices) and significant new results which have appeared since the first edition. Comprehensive background material is provided, so readers familiar with linear algebra and basic numerical methods can understand the projective geometry and estimation algorithms presented, and implement the algorithms directly from the book.

Uncertain Projective Geometry

Statistical Reasoning for Polyhedral Object Reconstruction

Author: Stephan Heuel

Publisher: Springer Science & Business Media

ISBN: 3540220291

Category: Mathematics

Page: 210

View: 3371


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.

Advanced Research and Trends in New Technologies, Software, Human-Computer Interaction, and Communicability

Author: Cipolla-Ficarra, Francisco Vicente

Publisher: IGI Global

ISBN: 1466644915

Category: Computers

Page: 696

View: 3245


"This book presents scientific, theoretical, and practical insight on the software and technology of social networks and the factors that boost communicability, highlighting different disciplines in the computer and social sciences fields"--Provided by publisher.

Manual of Photogrammetry

Author: J. Chris McGlone,Edward M. Mikhail,James S. Bethel,American Society for Photogrammetry and Remote Sensing

Publisher: Asprs Publications


Category: Photography

Page: 1151

View: 1644



Introduction to modern photogrammetry

Author: Edward M. Mikhail,James S. Bethel,J. Chris McGlone

Publisher: John Wiley & Sons Inc

ISBN: 9780471309246

Category: Mathematics

Page: 479

View: 1604


This book is designed to give the reader a strong grounding in the mathematical basis of photogrammetry while introducing them to the related fields, such as remote sensing and digital image processing, which are increasingly important to photogrammetric research and practice.


Author: N.A

Publisher: Society of Photo Optical

ISBN: 9780819425966

Category: Information display systems

Page: 336

View: 9556