Multiple View Geometry 计算机视觉中的多视图几何.pdf

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计算机视觉经典教程,计算机视觉中的多视图几何,英文原版。
Multiple View Geometry in Computer Vision Second edition Richard hartley Australian National University, Canberra. australia Andrew Zisserman University of Oxford, UK S CAMBRIDGE 沙 UNIVERSITY PRESS CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, sao paulo Cambridge university press The Edinburgh Building, Cambridge CB2 2RU, UK Published in the United States of america by cambridge University Press, New york www.cambridge.org Informationonthistitlewww.cambridgeorg/9780521540513 O Cambridge University Press 2000, 2003 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press First published in print format 2004 ISBN-13 978-0-5II-I8618-9 eBook(EBL) ISBN-10 0-511-18618-5 eBook(EBL) ISBN-I3978-0-52I-5405I-3 paperback ISBN-I0 0-52I-5405I-8 paperback Cambridge university press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate Dedication This book is dedicated to Joe Mundy whose vision and constant search for new ideas led us into this field Contents Foreword page xl Preface XIlI 1 Introduction-a Tour of Multiple view Geometry 1.1 Introduction-the ubiquitous projective geometry 1.2 Camera projections 1. 3 Reconstruction from more than one view 10 1.4 Three-view geometry 12 1.5 Four view geometry and n-view reconstruction 13 1. 6 Transfer 14 1.7 Euclidean reconstruction 16 1. 8 Auto-calibration 17 1.9 The reward I: 3D graphical models 18 1. 10 The reward I video augmentation 19 PART O: The Background: Projective Geometry, Transformations and esti mation 23 Outline 4 2 Projective Geometry and Transformations of 2D 2.1 Planar geometry 5 2.2 The 2D projective plane 26 2.3 Projective transformations 32 2.4 a hierarchy of transformations 37 2. 5 The projective geometry of lD 44 2.6 Topology of the projective plane 46 2.7 Recovery of affine and metric properties from images 47 2.8 More properties of conics 58 2.9 Fixed points and lines 61 2.10 Closure 62 3 Projective Geometry and Transformations of 3D 65 3.1 Points and projective transformations 65 3.2 Representing and transforming planes, lines and quadrics Contents 3. 3 Twisted cubics 75 3.4 The hierarchy of transformations 77 3.5 The plane at infinit 79 3.6 The absolute conic 81 3.7 The absolute dual quadric 83 3.8 Closure 85 4 Estimation- 2D Projective Transformations 87 4.1 The Direct Linear Transformation DLt) algorithm 88 4.2 Different cost functions 93 4.3 Statistical cost functions and maximum Likelihood estimation 102 4.4 Transformation invariance and normalization 104 4.5 Iterative minimization methods 110 4.6 Experimental comparison of the algorithms 115 4.7 Robust estimation 116 4.8 Automatic computation of a homography 123 4.9 Closure 127 5 Algorithm Evaluation and Error analysis 132 5.1 Bounds on performance 132 5.2 Covariance of the estimated transformation 138 5.3 Monte Carlo estimation of covariance 149 5.4 Closure 150 PARTI: Camera Geometry and Single view Geometry 151 Outline 152 6 Camera models 153 6.1 Finite cameras 153 6.2 The projective camera 158 6.3 Cameras at infinity 166 6.4 Other camera models 174 6.5 Closure 176 7 Computation of the camera matrix P 178 7.1 Basic equations 178 7.2 Geometric error 180 7. 3 Restricted camera estimation 184 7. 4 Radial distortion 189 7.5 Closure 193 8 More single view geometry 195 8. Action of a projective camera on planes, lines, and conics 195 8.2 mages of smooth surfaces 200 8.3 Action of a projective camera on quadrics 201 8.4 The importance of the camera centre 202 8.5 Camera calibration and the image of the absolute conic Contents 8.6 Vanishing points and vanishing lines 213 8.7 Affine 3d measurements and reconstruction 220 8. 8 Determining camera calibration k from a single view 223 8.9 Single view reconstruction 229 8.10 The calibrating conic 31 8.11 Clost 233 PART II: Two-View Geometry 237 Outline 238 9 Epipolar geometry and the Fundamental matrix 239 9.1 Epipolar geometry 239 9.2 The fundamental matrix F 241 9.3 Fundamental matrices arising from special motions 247 9.4 Geometric representation of the fundamental matrix 250 9. 5 Retrieving the camera matrices 253 9.6 The essential matrix 257 9.7 Closure 10 3D Reconstruction of Cameras and structure 262 10.1 Outline of reconstruction method 262 10.2 Reconstruction ambiguity 264 10.3 The projective reconstruction theorem 266 10.4 Stratified reconstruction 267 10.5 Direct reconstruction-using ground truth 275 10.6 Closure 276 11 Computation of the Fundamental Matrix F 279 11.1 Basic equations 279 11.2 The normalized 8-point algorithm 81 11.3 The algebraic minimization algorithm 282 11. 4 Geometric distance 284 11.5 Experimental evaluation of the algorithms 11.6 Automatic computation of F 290 11.7 Special cases of F-computation 293 11.8 Correspondence of other entities 294 11.9 Degeneracies 295 11.10 A geometric interpretation of F-computation 297 11. 11 The envelope of epipolar lines 298 11.12 Image rectification 302 11.13 Closure 12 Structure Computation 310 12.1 Problem statement 310 12.2 Linear triangulation methods 312 12. 3 Geometric error cost function 313 12.4 Sampson approximation(first-order geometric correction) 314 Contents 12.5 An optimal solution 315 12.6 Probability distribution of the estimated 3d point 321 12.7 Line reconstruction 321 12. 8 Closure 323 13 Scene planes and homographies 325 13.1 Homographies given the plane and vice versa 326 13.2 Plane induced homographies given F and image correspondences 329 13.3 Computing F given the homography induced by a plane 334 13. 4 The infinite homography Hoo 338 13.5 Closure 340 14 Affine Epipolar Geometry 344 14.1 Affine epipolar geometry 344 14.2 The affine fundamental matrix 345 14.3 Estimating Fa from image point correspondences 347 14.4 Triangulation 353 14.5 Affine reconstruction 353 14.6 Necker reversal and the bas-relief ambiguity 355 14.7 Computing the motion 357 14.8 Closure 360 PART III: Three- View Geometry 363 Outline 364 15 The Trifocal Tensor 365 15.1 The geometric basis for the trifocal tensor 365 15.2 The trifocal tensor and tensor notation 376 15.3 Transfer 379 15. 4 The fundamental matrices for three views 383 15.5 Closure 387 16 Computation of the Trifocal Tensor T 391 16.1 Basic equations 391 16.2 The normalized linear algorithm 393 16. 3 The algebraic minimization algorithm 395 16.4 Geometric distance 396 16.5 Experimental evaluation of the algorithms 399 16.6 Automatic computation of T 400 16.7 Special cases of T-computation 404 16. 8 Closure 406 PART IV: N-View Geometry 409 Outline 410 17 N-Linearities and multiple view Tensors 411 17.1 Bilinear relations 411 17.2 Trilinear relations 414

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