Del 26 - Interdisciplinary Applied Mathematics

Invitation to 3-D Vision

From Images to Geometric Models

Inbunden, Engelska, 2003

Av Yi Ma, Stefano Soatto, Jana Kosecká, S. Shankar Sastry, S Shankar Sastry

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This book is intended to give students at the advanced undergraduate or introduc tory graduate level, and researchers in computer vision, robotics and computer graphics, a self-contained introduction to the geometry of three-dimensional (3- D) vision. This is the study of the reconstruction of 3-D models of objects from a collection of 2-D images. An essential prerequisite for this book is a course in linear algebra at the advanced undergraduate level. Background knowledge in rigid-body motion, estimation and optimization will certainly improve the reader's appreciation of the material but is not critical since the first few chapters and the appendices provide a review and summary of basic notions and results on these topics. Our motivation Research monographs and books on geometric approaches to computer vision have been published recently in two batches: The first was in the mid 1990s with books on the geometry of two views, see e. g. [Faugeras, 1993, Kanatani, 1993b, Maybank, 1993, Weng et aI. , 1993b]. The second was more recent with books fo cusing on the geometry of multiple views, see e. g. [Hartley and Zisserman, 2000] and [Faugeras and Luong, 2001] as well as a more comprehensive book on computer vision [Forsyth and Ponce, 2002]. We felt that the time was ripe for synthesizing the material in a unified framework so as to provide a self-contained exposition of this subject, which can be used both for pedagogical purposes and by practitioners interested in this field.

Produktinformation

Utgivningsdatum2003-11-14
Mått165 x 245 x 30 mm
Vikt880 g
FormatInbunden
SpråkEngelska
SerieInterdisciplinary Applied Mathematics
Antal sidor528
Upplaga2004
FörlagSpringer-Verlag New York Inc.
ISBN9780387008936

Tillhör följande kategorier

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 Kalmanfilter.- 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.

From the reviews:"Computer vision is invading our daily lives … . Covering all the aspects would be too vast an area to cover in one book, so here, the authors concentrated on the specific goal of recovering the geometry of a 3D object … . The 22 pages of references form a good guide to the literature. The authors found an excellent balance between a thorough mathematical treatment and the applications themselves. … the text will be a pleasure to read for students … ." (Adhemar Bultheel, Bulletin of the Belgian Mathematical Society, Vol. 12 (2), 2005)"This is primarily a textbook of core principles, taking the reader from the most basic concepts of machine vision … to detailed applications, such as autonomous vehicle navigation. … It is a clearly written book … . Everything that is required is introduced … . an entirely self-contained work. … The book is aimed at graduate or advanced undergraduate students in electrical engineering, computer science, applied mathematics, or indeed anyone interested in machine vision … . is highly recommended." (D.E. Holmgren, The Photogrammetric Record, 2004)"This very interesting book is a great book teaching how to go from two-dimensional (2D)-images to three-dimensional (3D)-models of the geometry of a scene. … A good part of this book develops the foundations of an appropriate mathematical approach necessary for solving those difficult problems. … Exercises (drill exercises, advanced exercises and programming exercises) are provided at the end of each chapter." (Hans-Dietrich Hecker, Zentralblatt MATH, Vol. 1043 (18), 2004)"This book gives senior undergraduate and beginning graduate students and researchers in computer vision, applied mathematics, computer graphics, and robotics a self-contained introduction to the geometry of 3D vision. That is the reconstruction of 3D models of objects from a collection of 2D images. … Exercises are provided at the endof each chapter. Software for examples and algorithms are available on the author’s website." (Daniel Leitner, Simulation News Europe, Vol. 16 (1), 2006)