Author | Ma, Yi. author |
---|---|
Title | An Invitation to 3-D Vision [electronic resource] : From Images to Geometric Models / by Yi Ma, Stefano Soatto, Jana Koลกeckรก, S. Shankar Sastry |
Imprint | New York, NY : Springer New York : Imprint: Springer, 2004 |
Connect to | http://dx.doi.org/10.1007/978-0-387-21779-6 |
Descript | XX, 528 p. online resource |
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