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AuthorMa, Yi. author
TitleAn Invitation to 3-D Vision [electronic resource] : From Images to Geometric Models / by Yi Ma, Stefano Soatto, Jana Koลกeckรก, S. Shankar Sastry
ImprintNew York, NY : Springer New York : Imprint: Springer, 2004
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Descript XX, 528 p. online resource


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


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

Computer science Computers Computer graphics Applied mathematics Engineering mathematics Geometry Calculus of variations Control engineering Robotics Mechatronics Computer Science Theory of Computation Calculus of Variations and Optimal Control; Optimization Geometry Applications of Mathematics Computer Imaging Vision Pattern Recognition and Graphics Control Robotics Mechatronics


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