Description
This book introduces the geometry of 3-D vision, that is, the reconstruction of 3-D models of objects from a collection of 2-D images. It details the classic theory of two view geometry and shows that a more proper tool for studying the geometry of multiple views is the so-called rank consideration of the multiple view matrix. It also develops practical reconstruction algorithms and discusses possible extensions of the theory. Preface 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 2.1 Three-dimensional Euclidean space 2.2 Rigid body motion 2.3 Rotational motion and its representations 2.4 Rigid body motion and its representations 2.5 Coordinate and velocity transformations 2.6 Summary 2.7 Exercises 2.A Quaternions and Euler angles for rotations 3 Image formation 3.1 Representation of images 3.2 Lenses, light, and basic photometry 3.3 A geometric model of image formation 3.4 Summary 3.5 Exercises 3.A Basic photometry with light sources and surfaces 3.B Image formation in the language of projective geometry 4 Image primitives and correspondence 4.1 Correspondence of geometric features 4.2 Local deformation models 4.3 Matching point features 4.4 Tracking line features 4.5 Summary 4.6 Exercises 4.A Computing image gradients II Geometry of two views 5 Reconstruction from two calibrated views 5.1 Epipolar geometry 5.2 Basic reconstruction algorithms 5.3 Planar scenes and homography 5.4 Continuous motion case 5.5 Summary 5.6 Exercises 5.A Optimization subject to epipolar constraint 6 Reconstruction from two uncalibrated views 6.1 Uncalibrated camera or distorted space? 6.2 Uncalibrated epipolar geometry 6.3 Ambiguities and constraints in image formation 6.4 Stratified reconstruction 6.5 Calibration with scene knowledge 6.6 Dinner with Kruppa 6.7 Summary 6.8 Exercises 6.A From images to Fundamental matrices 6.B Properties of Kruppa’s equations 7 Segmentation of multiple moving objects from two views 7.1 Multibody epipolar constraint and Fundamental matrix 7.2 A rank condition for the number of motions 7.3 Geometric properties of the multibody Fundamental matrix 7.4 Multibody motion estimation and segmentation 7.5 Multibody structure from motion
