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  • 1
    UID:
    almahu_9947362734802882
    Umfang: XX, 528 p. , online resource.
    ISBN: 9780387217796
    Serie: Interdisciplinary Applied Mathematics, 26
    Inhalt: Endowing machines with a sense of vision has been a dream of scientists and engineers alike for over half a century. Only in the past decade, however, has the geometry of vision been understood to the point where this dream becomes attainable, thanks also to the remarkable progress in imaging and computing hardware. This book addresses a central problem in computer vision -- how to recover 3-D structure and motion from a collection of 2-D images -- using techniques drawn mainly from linear algebra and matrix theory. The stress is on developing a unified framework for studying the geometry of multiple images of a 3-D scene and reconstructing geometric models from those images. The book also covers relevant aspects of image formation, basic image processing, and feature extraction. The authors bridge the gap between theory and practice by providing step-by-step instructions for the implementation of working vision algorithms and systems. Written primarily as a textbook, the aim of this book is to give senior undergraduate and beginning graduate students in computer vision, robotics, and computer graphics a solid theoretical and algorithmic foundation for future research in this burgeoning field. It is entirely self-contained with necessary background material covered in the beginning chapters and appendices, and plenty of exercises, examples, and illustrations given throughout the text.
    Anmerkung: 1 Introduction -- 1.1 Visual perception from 2-D images to 3-D models -- 1.2 A mathematical approach -- 1.3 A historical perspective -- I Introductory Material -- 2 Representation of a Three-Dimensional Moving Scene -- 3 Image Formation -- 4 Image Primitives and Correspondence -- II Geometry of Two Views -- 5 Reconstruction from Two Calibrated Views -- 6 Reconstruction from Two Uncalibrated Views -- 7 Estimation of Multiple Motions from Two Views -- III Geometry of Multiple Views -- 8 Multiple-View Geometry of Points and Lines -- 9 Extension to General Incidence Relations -- 10 Geometry and Reconstruction from Symmetry -- IV Applications -- 11 Step-by-Step Building of a 3-D Model from Images -- 12 Visual Feedback -- V Appendices -- A Basic Facts from Linear Algebra -- A.1 Basic notions associated with a linear space -- A.1.1 Linear independence and change of basis -- A.1.2 Inner product and orthogonality -- A.1.3 Kronecker product and stack of matrices -- A.2 Linear transformations and matrix groups -- A.3 Gram-Schmidt and the QR decomposition -- A.4 Range, null space (kernel), rank and eigenvectors of a matrix -- A.5 Symmetric matrices and skew-symmetric matrices -- A.6 Lyapunov map and Lyapunov equation -- A.7 The singular value decomposition (SVD) -- A.7.1 Algebraic derivation -- A.7.2 Geometric interpretation -- A.7.3 Some properties of the SVD -- B Least-Variance Estimation and Filtering -- B.1 Least-variance estimators of random vectors -- B.1.1 Projections onto the range of a random vector -- B.1.2 Solution for the linear (scalar) estimator -- B.1.3 Affine least-variance estimator -- B.1.4 Properties and interpretations of the least-variance estimator -- B.2 The Kalman-Bucy filter -- B.2.1 Linear Gaussian dynamical models -- B.2.2 A little intuition -- B.2.3 Observability -- B.2.4 Derivation of the Kalman filter -- B.3 The extended Kalman filter -- C Basic Facts from Nonlinear Optimization -- C.1 Unconstrained optimization: gradient-based methods -- C.1.1 Optimality conditions -- C.1.2 Algorithms -- C.2 Constrained optimization: Lagrange multiplier method. -- C.2.1 Optimality conditions -- C.2.2 Algorithms -- References -- Glossary of Notation.
    In: Springer eBooks
    Weitere Ausg.: Printed edition: ISBN 9781441918468
    Sprache: Englisch
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 2
    UID:
    gbv_1655452541
    Umfang: Online-Ressource (XX, 527 p, online resource)
    ISBN: 9780387217796
    Serie: Interdisciplinary Applied Mathematics 26
    Inhalt: Endowing machines with a sense of vision has been a dream of scientists and engineers alike for over half a century. Only in the past decade, however, has the geometry of vision been understood to the point where this dream becomes attainable, thanks also to the remarkable progress in imaging and computing hardware. This book addresses a central problem in computer vision -- how to recover 3-D structure and motion from a collection of 2-D images -- using techniques drawn mainly from linear algebra and matrix theory. The stress is on developing a unified framework for studying the geometry of multiple images of a 3-D scene and reconstructing geometric models from those images. The book also covers relevant aspects of image formation, basic image processing, and feature extraction. The authors bridge the gap between theory and practice by providing step-by-step instructions for the implementation of working vision algorithms and systems. Written primarily as a textbook, the aim of this book is to give senior undergraduate and beginning graduate students in computer vision, robotics, and computer graphics a solid theoretical and algorithmic foundation for future research in this burgeoning field. It is entirely self-contained with necessary background material covered in the beginning chapters and appendices, and plenty of exercises, examples, and illustrations given throughout the text
    Weitere Ausg.: ISBN 9781441918468
    Weitere Ausg.: Erscheint auch als Druck-Ausgabe An invitation to 3-D vision New York : Springer, 2004 ISBN 9780387008936
    Weitere Ausg.: ISBN 0387008934
    Weitere Ausg.: ISBN 9781441918468
    Sprache: Englisch
    Fachgebiete: Informatik , Mathematik
    RVK:
    RVK:
    Schlagwort(e): Computergrafik ; Algorithmische Geometrie
    URL: Volltext  (lizenzpflichtig)
    URL: Cover
    Mehr zum Autor: Sastry, Shankar 1956-
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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