共享《An Invitation to 3d vision》电子书

This Printer: Opaque this This is page v Printer: Opaque this reface This book is intended to give students at the advanced undergraduate or introductory graduate level and researchers in computer vision, robotics and computer graphics a self-contained introduction to the geometry of 3-D vision: that is, the reconstruction of 3-D models of objects from a collection of 2-D images. The only prerequisite for this book is a course in linear algebra at the undergraduate level As timely research summary, two bursts of manuscripts were published the past on a geometric approach to computer vision: the ones that were published in mid 1990's on the geometry of two views(e. g, Faugeras 1993, Weng, Ahuja and Luang 1993, Maybank 1993), and the ones that were recently published on the geometry of multiple views(e.g, Hartley and Zisserman 2000, Faugeras, Luong and Papadopoulo 2001). While a majority of those manuscripts were to summarize up to date research re sults by the time they were published, we sense that now the time is ripe for putting a coherent part of that material in a unified and yet simplified amework which can be used for pedagogical purposes. Although the ap- proach we are to take here deviates frOIn those old ones and thhe techniques we use are mainly linear algebra this book nonet heless gives a comprehen- sive coverage of what is known todate on the geometry of 3-D ⅴ ISIoN It I To our knowledge, there are also two other books on computer vision currently in preparation: Ponce and Forsyth(expected in 2002), Pollefeys and van Gool(expected in2002) also builds on a homogeneous terminology a solid analytical foundation for future research in this young field This book is organized as follows. Following a brief introductiOn, Part I provides background materials for the rest of the book. Two fundament a. I transformations in multiple view geometry, namely the rigid-body motion and perspective projection, are introduced in Chapters 2 and 3 respectively Image formation and feature extraction are discussed in Chapter 4. The two chapters in Part Ii cover the classic theory of two view geometry based on the so-called epipolar constraint. Theory and algorithms are developed for ooth discrete and continuous Notions. alld for both calibrated and uncal- ibrated camera models. Although the epipolar constraint has been very succcssful in the two vicw casc, Part III shows that a morc propcr tool for studying the geometry of multiple views is the so-called rank condi tion on the multiple vieau matri, which trivia. ly implies all the constraints among multiple images that are known todate, in particular the epipolar constraint. The theory culminates in Chapter 10 with a unified theorem on a rank condition for arbitrarily mixed point, line and plane features. It captures all possible constraints among multiple images of these geometric primitives, and serves as a kcy to both geometric analysis and algorithmic development. Based on the theory and conceptual algorithms developed in early part of the book, Part iv develops practical reconstruction algorithms step by step, as well as discusses possible extensions of the theory covered in this book Different parts and chapters of this book have been taught as a one semester course at the University of California at Berkeley, the University of Illinois at Urbana-Champaign, and the george Mason University, and as a two-quater course at the University of California at Los Angles. There is apparantly adequate material for lectures of one and a half semester or two ters. Ad sted in Part Iv or chosen by the instruct can be added to the second half of the second semester if a two-semester course is offered Given below are some suggestions for course development. this b 1. A oTe-seTnesler course: Appendix A alld Chapters 1-7 and part of Chapters 8 and 13 2. A two-quater course: Chapters 1-6 for the first quater and Chapters 7-10 and 13 for the second quater 3. A two-semester course: Appendix A and Chapters 1-7 for the first semester: Chapters8-10 and the instructor's choice of some advanced topics froIn chapters in Part IV for the second selllester Exercises are provided at the end of each chapter. They consist of three types: 1. drill exercises that help student understand the theory covered each chapter; 2. prograIllIning exercises that help student grasp algorithms developed in each chapter: 3. exercises that guide student to Prca creatively develop a solution to a specialized case that is related to but not necessarily covered by the general theorems in the book. Solutions to IlloSt of the exercises will be imade available upon the publication of this book. Soft ware for examples and a lgorithms in this book will also be made available at a designated website Yi Ma Stefano soatto Jana kosecka Shankar sastr Cafe Nefeli, Berkeley Jnly 1, 200/ This is page x Printer: Opaque this Contents Preface 1 Introduction 1 1.1 Visual perception: from 2-D images to 3-D models 1.2 A historical perspective 1.3 A mathematical ap 4 1.4 Organization of the book 5 Introductory material 2 Representation of a three dimensional moving scene 2.1 Thrcc-dimcnsional Euclidean spacc 2.2 Rigid body InotiOn 12 2.3 Rotational motion and its representations 16 2.3.1 Canonical exponential coordinates 18 2.3.2 QuaterniOns and Lie-Cartan coordinates 2.4 Rigid body motion and its representations 2.4.1 Homogeneous representation 26 2.4.2 Canonical exponential coordi 2.5 Coordinates and velocity transformation 2.6 Summary 2.7 References 2. 8 Exercises 33 Contents 3 Image formation 36 3. 1 Representation of images 3.2 Lenses. surfaces alld light 3.2.1 Imaging through lenses 40 3.2.2 Imaging through pin 42 3.3 A first Inodel of ilage forinlatiol 43 3.3.1B phot 43 3.3.2 The basic model of imaging geometr 47 3.3.3 Ideal camera 48 3.3.4 Ca mera. with intrinsic parameters 50 33.6 Approximate camera mode,··. 3.3.5 Spherical projection 53 3.4 Summary 3.5卫ⅹ excises.. 54 4 Image primitives and correspondence 4.1 Correspondence between images 58 4.1.1 Transformations in the image domain 4.1.2 Transformations of the intensity value 60 4.2 Photometric anld geometric features 4.3 Optical flow and feature tracking 64 4.3.1 Translational modcl 4.3.2 Affine deforimation Inodel 4.4 Feature detection algorithms 4.4.1 Computing imagc gradicnt 4.4.2 Line features: edges 4.4.3 point features corners 4.5 Compensating for photometric factors 4.6 Exercises II Geometry of pairwise views 77 5 Reconstruction from two calibrated views 79 5.1 The epipolar const. 80 5.1.1 Discrete epipolar constraint and the essential matrix 80 5.1.2 Elementary properties of the essential matrix 5.2 Closed-form reconstruction 5.2.1 The eight-point linear algorithm 5.2.2 Euclidean constraints and structure reconstruction 89 5.3 Optimal reconstruction 90 5.4 continuo 5.4.1 Continuous epipolar constraint and the continuous 5.4.2 Properties of continuous essential matrices 96 5.4.3 The eight-point linear algorithm 100 5.4.4 Euclidean constraints and structure reconstruction 105 5.5 Summary 106 5.6 Exercises 107 6 Camera calibration and self-calibration 111 6.1 Calibration with a rig 112 6.2 The fundamental matrix 114 6.2.1 Gcomctric charactcrization of thc fundamcntal ma trix 115 6.2.2 The eight-point linear algorithm 6.3 Basics of uncalibrated geometry ....118 6.3.1 Kruppa's equations 121 6.4 Self-ca libration from special motions and chirality 127 6.4.1 Pure rotational motion 6.4.2 Translatic allel to rotation 6.4.3 Calibration with chiralitv 135 6.5 Calibration from continuous motion 138 6.6 Three st 6.6.1 Projective reconstruction ,142 6.6.2 Affine reconstruction 145 6.6.3 Euclidean reconstruction 147 6.7 Summary 148 6.8 Exercises 148 II Geometry of multiple views 151 7 Introduction to multiple view reconstruction 153 7. 1 Basic notions: pre-image and co-image of point and line. 154 7. 2 Preliminaries 157 7. 3 Pairwise view geometry revisited 7.4 Triple-wise view geometry 7.5 Summary 165 7.6Eⅹ excises. 165 8 Geometry and reconstruction from point features 168 8.1 Multiple views of a point 8.2 The multiple view matrix and its rank 170 8.3 Geometric interpretation of the rank condition 173 8.3.1 Uniqueness of the pre-image 8.3.2 Geometry of the multiple view matrix 177 8.4 Applications of the rank condition 178 8.4.1C 178 8.4.2 Reconstruction 179 Contents 8.5 Experiments 182 8.5.1Set 8.5. 2 Comparison with the 8 point algorithIll 8.5.3 Error as a function of the number of frames ... 184 8.5.4 Experiments on real images 184 8.6 SuillInary 186 8.7Ex 186 9 Geometry and reconstruction from line features 187 9.1 Multiple views of a line 187 9.2 The multiple view matrix and its rank 189 9.3 Geometric interpretation of the rank condition 191 9.3.1 Uniqueness of the pre-image 192 9.3.2 Geometry of the multiple view matrix 194 9.3.3 Relationships between rank conditions for line and point 196 9.4 Applications of the rank condition 197 9.4.1 Matching 197 9.4.2 Reconstruction 9.5 Experinents 201 9.5.1 Setup 201 9.5.2 Motion and structurc from four frames 9.5. 3 Error as a function of IluInber of fralnes 9.6 Summar 205 9.7 Exercises 205 10 Geometry and reconstruction with incidence relations 206 0.1 Image and CO-image of a point and line 206 10.2 Rank conditions for various incidence relations 208 10.2.1 Inclusion of features 209 10.2.2 Intersection of features 211 10.2.3 Features restricted to a plane 10.3 Rank conditions on the universal multiple view matrix 216 10.4 Geometric interpretation of the rank conditions 220 10.41Case2:0≤rank(M)≤1 220 10.4.2 Case 1: 1 rank(M)