Multiple view geometry in computer vision 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 2.2.1 Points and lines 2.2.2 Ideal points and the line at infinity 2.2.3 Conics and dual conics 2.3 Projective transformations 2.3.1 Transformations of lines and conics 2.4 A hierarchy of transformations 2.4.1 Class I: Isometries 2.4.2 Class II: Similarity transformations 2.4.3 Class III: Affine transformations 2.4.4 Class IV: Projective transformations 2.4.5 Summary and comparison 2.4.6 Decomposition of a projective transformation 2.4.7 The number of invariants 2.5 The projective geometry of 1D 2.6 Topology of the projective plane 2.7 Recovery of affine and metric properties from images 2.7.1 The line at infinity 2.7.2 Recovery of affine properties from images 2.7.3 The circular points and their dual 2.7.4 Angles on the projective plane 2.7.5 Recovery of metric properties from images 2.8 More properties of conics 2.8.1 The pole polar relationship 2.8.2 Classification of conics 2.9 Fixed points and lines 2.10 Closure 2.10.1 The literature 2.10.2 Notes and exercises 3 Projective Geometry and Transformations of 3D. How to reconstruct scenes from images using geometry and algebra with applications to computer vision.