Multiple view geometry in computer vision
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
eBook, English, 2003
Cambridge University Press, Cambridge, UK, 2003
1 online resource (1 electronic recource (xvi, 655 pages)) : illustrations (some color)
9786610458127, 9780511185359, 9780521540513, 9780511313332, 9780511811685, 661045812X, 0511185359, 0521540518, 0511313330, 0511811683
1018083819
Cover
Title
Copyright
Dedication
Contents
Foreword
Preface
1 Introduction ... a Tour of Multiple View Geometry
1.1 Introduction ... the ubiquitous projective geometry
1.1.1 Affine and Euclidean Geometry
1.2 Camera projections
1.3 Reconstruction from more than one view
1.4 Three-view geometry
1.5 Four view geometry and n-view reconstruction
1.6 Transfer
1.7 Euclidean reconstruction
1.8 Auto-calibration
1.9 The reward I : 3D graphical models
1.10 The reward II: video augmentation
Part 0 The Background: Projective Geometry, Transformations and Estimation
Outline
2 Projective Geometry and Transformations of 2D
2.1 Planar geometry
2.2 The 2D projective plane
2.3 Projective transformations
2.4 A hierarchy of transformations
2.5 The projective geometry of 1D
2.6 Topology of the projective plane
2.7 Recovery of affine and metric properties from images
2.8 More properties of conics
2.9 Fixed points and lines
2.10 Closure
3 Projective Geometry and Transformations of 3D
3.1 Points and projective transformations
3.2 Representing and transforming planes, lines and quadrics
3.3 Twisted cubics
3.4 The hierarchy of transformations
3.5 The plane at infinity
3.6 The absolute conic
3.7 The absolute dual quadric
3.8 Closure
4 Estimation ... 2D Projective Transformations
4.1 The Direct Linear Transformation (DLT) algorithm
4.2 Different cost functions
4.3 Statistical cost functions and Maximum Likelihood estimation
4.4 Transformation invariance and normalization
4.5 Iterative minimization methods
4.6 Experimental comparison of the algorithms
4.7 Robust estimation
4.8 Automatic computation of a homography
4.9 Closure
5 Algorithm Evaluation and Error Analysis
5.1 Bounds on performance
5.2 Covariance of the estimated transformation
5.3 Monte Carlo estimation of covariance
5.4 Closure
Part I Camera Geometry and Single View Geometry
Outline
6 Camera Models
6.1 Finite cameras
6.2 The projective camera
6.3 Cameras at infinity
6.4 Other camera models
6.5 Closure
7 Computation of the Camera Matrix P
7.1 Basic equations
7.2 Geometric error
7.3 Restricted camera estimation
7.4 Radial distortion
7.5 Closure
8 More Single View Geometry
8.1 Action of a projective camera on planes, lines, and conics
8.2 Images of smooth surfaces
8.3 Action of a projective camera on quadrics
8.4 The importance of the camera centre
8.5 Camera calibration and the image of the absolute conic
8.6 Vanishing points and vanishing lines
8.7 Affine 3D measurements and reconstruction
8.8 Determining camera calibration K from a single view
8.9 Single view reconstruction
8.10 The calibrating conic
8.11 Closure
Part II Two-View Geometry
Outline
9 Epipolar Geometry and the Fundamental Matrix
9.1 Epipolar geometry
9.2 The fundamental matrix F
9.3 Fundamental matrices arising from special mot