计算机视觉中的多视图几何

计算机视觉中的多视图几何Multiple view geometry in Computer visionSecond editionRichard hartleyAustralian National universityCanberra. australiaAndrew zissermanUniversity of Oxford, UKF CNAVERSRY PRGSCAMBRIDGE UNIVERSITY PRESSCambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao PauloCambridge University PressThe Edinburgh Building, Cambridge CB2 2RU, UKPublished in the United States of America by Cambridge University Press, New Yorkwww.cambridge.orgInformationonthistitlewww.cambridgeorg/9780521540513o Cambridge University Press 2000, 2003This publication is in copyright. Subject to statutory exception and to the provision ofrelevant collective licensing agreements, no reproduction of any part may take placewithout the written permission of Cambridge University PressFirst published in print format 2004ISBN-13 978-0-5II-I8618-9 eBook(EBLISBN-I0 0-51I-I8618-5 eBook(EBLISBN-13 978-0-521-54051-3 paperbackISBN-I0 0-52I-5405I-8 paperbackCambridge University Press has no responsibility for the persistence or accuracy of urlsfor external or third-party internet websites referred to in this publication and does notguarantee that any content on such websites is, or will remain, accurate or appropriateDedicationThis book is dedicated to Joe Mundy whose vision and conslant search for new ideasled us into this fieldContentsforewordefaceXI1 Introduction-a Tour of Multiple view geometryII Introduction-the ubiquitous projective geometry1.2 Camera projections61. 3 Reconstruction from more than one view1.4 Three-view geometry121. 5 Four view geometry and n-view reconstruction1.6 Transfe141.7 Euclidean reconstruction16l 8 Auto-calibration171.9 The reward I: 3D graphical models181.10 The reward Il: video augmentation19PART U: The background: Projective Geometry, Transformations and esti-mation23Outline242 Projective Geometry and Transformations of 2D252.1 Planar geometr252.2 The 2D projective plar262.3 Projective transformations322.4 A hierarchy of transformations372.5 The projective geometry of ID442.6 Topology of the projective plane462.7 Recovery of affine and metric properties from images472.8 More properties of conics58Fixed points and lines612.10 Closure623 Projective geometry and Transformations of 3D653.1 Points and projective transformations653.2 RepresenTing and transforming planes, lines and quadricsContents3.3 Twisted cubics3.4 The hierarchy of transformations773.5 The plane at infinity793. 6 The absolute conic83.7 The absolute dual quadric833. 8 Closure854 Estimation- 2D Projective Transformations874.1 The Direct Linear Transformation(Dlt)algorithm884.2 Different cost functions9343 Statistical cost functions and maximum likelihood estimation 1024.4 Transformation invariance and normalization1044.5 Iterative minimization methods1104.6 Experimental comparison of the algorithms1154.7 Robust estimation1164.8 Automatic computation of a homography1234.9 Closure1275 Algorithm Evaluation and Error Analysis1325.1 Bounds on performance1325.2 Covariance of the estimated transformation1385.3 Monte carlo estimation of covariance1495.4 Closure150PART I: Camera geometry and single view geometr151Outline1526 Camera models1536.1 Finite cameras1536.2 The projective camera1586.3 Cameras at infin1666.4 Other camera models1746.5 Closure1767 Computation of the Camera matrix P1787.1 Basic equations1787.2 Geometric error1807.3 Restricted camera estimation18474 Radial distortion1897.5 Closure1938 More Single view Geometry1958.1 Action of a projective camera on planes, lines, and conics1958.2 Images of smooth surfaces8.3 Action of a projective camera on quadrics2018.4 The importance of the camera centre2028.5 Camera calibration and the image of the absolule conic208Contents8.6 Vanishing points and vanishing lines8. 7 Affine 3D measurements and reconstruction2208.8 Determining camera calibration K from a single vier2238.9 Single view reconstruction2298.10 The calibrating conic2318.1 Closure233PART I: Two-View Geometry37Outline2389 Epipolar Geometry and the Fundamental Matrix2399.1 Epipolar geometry2399.2 The fundamental matrix F2419.3 Fundamental matrices arising from special motions2479.4 Geometric representation of the fundamental matrix2509.5 Retrieving the camera matrices2539.6 The essential matrix2579.7 Closure25910 3D Reconstruction of Cameras and Structure26210.1 Outline of reconstruction method26210.2 Reconstruction ambiguity26410. 3 The projective reconstruction theorem2660. 4 Stratified reconstruction26710.5 Direct reconstruction -using ground truth27510.6 Closure27611 Computation of the Fundamental Matrix FIl. Basic equations27911.2 The normalized 8-point algorithm28111. 3 The algebraic minimization algorithm28211. 4 Geometric distanc28411.5 Experimental evaluation of the algorithms28811.6 Automatic computation of F29011.7 Special cases of F-computalion29311. 8 Correspondence of other entities29411.9 Degeneracies29511.10 A geometric interpretation of F-computation297I11I The envelope of epipolar lines298I. 12 Image rectification30211.13 Closure30812 Structure Computation31012.1 Problem statement31012.2 Linear triangulation methods31212. 3 Geometric error cost function31312.4 Sampson approximation(first-order geometric correction)14v11Contents12.5An31512.6 Probability distribution of the estimated 3d point32112.7 Line reconstruction32112.8 Closure32313 Scene planes and homographie32513. 1 Homographies given the plane and vice versa32613.2 Plane induced homographies given F and image correspondences 32913.3 Computing F given the homography induced by a plane33413. 4 The infinite homography Ho33813.5 Closure34014 Affine Epipolar Geometry34414.1 Affine epipolar geometry34414.2 The affine fundamental matrix34514.3 Estimating F from image point correspondences34714.4 Triangulation35314.5 Affine reconstruction35314.6 Necker reversal and the bas-relief ambiguity35514.7 Computing the motion35714. 8 Closure360PART III: Three- View Geometry363Outline36415 The Trifocal tensor36515. 1 The geometric basis for the trifocal tensor36515.2 The trifocal tensor and tensor notation37615.3 Transfer37915. 4 The fundamental matrices for three views38315.5 Closure38716 Computation of the Trifocal Tensor T39116.1 Basic equations39116.2 The normalized linear algorithm39316.3 The algebraic minimization algorithm39516.4 Geometric distance39616.5 Experimental evaluation of the algorithms39916.6 Automatic computation of T40016.7 Special cases of T-computation40416.8 Closure406PARTIV:N-View Geometry409Outline41017 N-Linearities and multiple view tensors41117.1 Bilinear relations41117.2 Trilinear relalions414