Multiple View Geometry in Computer Vision

Front Cover
Cambridge University Press, 2003 - Computers - 655 pages
18 Reviews
A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Techniques for solving this problem are taken from projective geometry and photogrammetry. Here, the authors cover the geometric principles and their algebraic representation in terms of camera projection matrices, the fundamental matrix and the trifocal tensor. The theory and methods of computation of these entities are discussed with real examples, as is their use in the reconstruction of scenes from multiple images. The new edition features an extended introduction covering the key ideas in the book (which itself has been updated with additional examples and appendices) and significant new results which have appeared since the first edition. Comprehensive background material is provided, so readers familiar with linear algebra and basic numerical methods can understand the projective geometry and estimation algorithms presented, and implement the algorithms directly from the book.
  

What people are saying - Write a review

User ratings

5 stars
16
4 stars
2
3 stars
0
2 stars
0
1 star
0

Great book - ok delivery

User Review  - ndwork - Overstock.com

The book is phenomenol. It explains how to accomplish things that look like magic. One can create a 3d geometry of a scene with only three images of that scene. It's amazing. The delivery of the ... Read full review

User Review - Flag as inappropriate

vfgssssssssssssss

Contents

Projective Geometry and Transformations of 2D
25
22 The 2D projective plane
26
23 Projective transformations
32
24 A hierarchy of transformations
37
25 The projective geometry of ID
44
26 Topology of the projective plane
46
27 Recovery of affine and metric properties from images
47
28 More properties of conics
58
126 Probability distribution of the estimated 3D point
321
128 Closure
323
Scene planes and homographies
325
131 Homographies given the plane and vice versa
326
132 Plane induced homographies given F and image correspondences
329
133 Computing F given the homography induced by a plane
334
134 The infinite homography H
338
135 Closure
340

29 Fixed points and lines
61
210 Closure
62
Projective Geometry and Transformations of 3D
65
32 Representing and transforming planes lines and quadrics
66
33 Twisted cubics
75
34 The hierarchy of transformations
77
35 The plane at infinity
79
36 The absolute conic
81
37 The absolute dual quadric
83
38 Closure
85
Estimation 2D Projective Transformations
87
41 The Direct Linear Transformation DLT algorithm
88
42 Different cost functions
93
43 Statistical cost functions and Maximum Likelihood estimation
102
44 Transformation invariance and normalization
104
45 Iterative minimization methods
110
46 Experimental comparison of the algorithms
115
47 Robust estimation
116
48 Automatic computation of a homography
123
49 Closure
127
Algorithm Evaluation and Error Analysis
132
52 Covariance of the estimated transformation
138
53 Monte Carlo estimation of covariance
149
54 Closure
150
Camera Geometry and Single View Geometry
151
Outline
152
Camera Models
153
62 The projective camera
158
63 Cameras at infinity
166
64 Other camera models
174
65 Closure
176
Computation of the Camera Matrix P
178
72 Geometric error
180
73 Restricted camera estimation
184
74 Radial distortion
189
75 Closure
193
More Single View Geometry
195
82 Images of smooth surfaces
200
83 Action of a projective camera on quadrics
201
84 The importance of the camera centre
202
85 Camera calibration and the image of the absolute conic
208
86 Vanishing points and vanishing lines
213
87 Affine 3D measurements and reconstruction
220
88 Determining camera calibration K from a single view
223
89 Single view reconstruction
229
810 The calibrating conic
231
811 Closure
233
TwoView Geometry
237
Outline
238
Epipolar Geometry and the Fundamental Matrix
239
92 The fundamental matrix F
241
93 Fundamental matrices arising from special motions
247
94 Geometric representation of the fundamental matrix
250
95 Retrieving the camera matrices
253
96 The essential matrix
257
97 Closure
259
3D Reconstruction of Cameras and Structure
262
102 Reconstruction ambiguity
264
103 The projective reconstruction theorem
266
104 Stratified reconstruction
267
105 Direct reconstruction using ground truth
275
106 Closure
276
Computation of the Fundamental Matrix F
279
112 The normalized 8point algorithm
281
113 The algebraic minimization algorithm
282
114 Geometric distance
284
115 Experimental evaluation of the algorithms
288
116 Automatic computation of F
290
117 Special cases of Fcomputation
293
118 Correspondence of other entities
294
119 Degeneracies
295
1110 A geometric interpretation of Fcomputation
297
1111 The envelope of epipolar lines
298
1112 Image rectification
302
1113 Closure
308
Structure Computation
310
122 Linear triangulation methods
312
123 Geometric error cost function
313
124 Sampson approximation firstorder geometric correction
314
125 An optimal solution
315
Affine Epipolar Geometry
344
142 The affine fundamental matrix
345
143 Estimating F from image point correspondences
347
144 Triangulation
353
146 Necker reversal and the basrelief ambiguity
355
147 Computing the motion
357
148 Closure
360
ThreeView Geometry
363
Outline
364
The Trifocal Tensor
365
152 The trifocal tensor and tensor notation
376
153 Transfer
379
154 The fundamental matrices for three views
383
155 Closure
387
Computation of the Trifocal Tensor T
391
162 The normalized linear algorithm
393
163 The algebraic minimization algorithm
395
164 Geometric distance
396
165 Experimental evaluation of the algorithms
399
166 Automatic computation of T
400
167 Special cases of Tcomputation
404
168 Closure
406
NView Geometry
409
Outline
410
NLinearities and Multiple View Tensors
411
172 Trilinear relations
414
173 Quadrilinear relations
418
17 A Intersections of four planes
421
175 Counting arguments
422
176 Number of independent equations
428
177 Choosing equations
431
178 Closure
432
NView Computational Methods
434
182 Affine reconstruction the factorization algorithm
436
183 Nonrigid factorization
440
184 Projective factorization
444
185 Projective reconstruction using planes
447
186 Reconstruction from sequences
452
187 Closure
456
AutoCalibration
458
192 Algebraic framework and problem statement
459
193 Calibration using the absolute dual quadric
462
194 The Kruppa equations
469
195 A stratified solution
473
196 Calibration from rotating cameras
481
197 Autocalibration from planes
485
198 Planar motion
486
199 Single axis rotation turntable motion
490
1910 Autocalibration of a stereo rig
493
1911 Closure
497
Duality
502
202 Reduced reconstruction
508
203 Closure
513
Cheirality
515
212 Front and back of a camera
518
213 Threedimensional point sets
519
214 Obtaining a quasiaffine reconstruction
520
215 Effect of transformations on cheirality
521
216 Orientation
523
217 The cheiral inequalities
525
218 Which points are visible in a third view
528
219 Which points are in front of which
530
2110 Closure
531
Degenerate Configurations
533
222 Degeneracies in two views
539
223 CarlssonWeinshall duality
546
224 Threeview critical configurations
553
225 Closure
558
Appendices
561
Tensor Notation
562
Gaussian Normal and 𝓧˛ Distributions
565
Parameter Estimation
568
Matrix Properties and Decompositions
578
Leastsquares Minimization
588
Iterative Estimation Methods
597
Some Special Plane Projective Transformations
628
Bibliography
634
Index
646
Copyright

Common terms and phrases

Popular passages

Page 641 - CJ Poelman and T. Kanade. A paraperspective factorization method for shape and motion recovery.
Page 637 - Self-calibration of a ID projective camera and its application to the self-calibration of a 2D projective camera.
Page 637 - RI Hartley. Lines and points in three views and the trifocal tensor.
Page 637 - Lee, K. Ottenberg, and M. Nolle, "Analysis and solutions of the three point perspective pose estimation problem," in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp.
Page 634 - Chengke, editors, EuropeChina workshop on Geometrical Modelling and Invariants for Computer Vision, pages 214-221. Xidan University Press, Xi'an, China, 1995. [4] F.
Page 638 - Hartley. In defense of the eight-point algorithm. IEEE Transactions on Pattern Analysis and Machine Intelligence, 19(6):580-593, June 1997.
Page 638 - A. Heyden. Projective structure and motion from image sequences using subspace methods. In Scandinavian Conference on Image Analysis.
Page 636 - Vision, pages 269-275, 1995. 3. R. Cipolla and A. Blake. Surface shape from the deformation of apparent contours. Int. Journal of Computer Vision, 9(2):83-112, 1992.

References to this book

All Book Search results »

About the author (2003)

Hartley-General Electric, Schenectady

Andrew Zisserman is a Science and Engineering Research Council (SERC) Research Fellow in the Department of Computer Science at the University of Edinburgh.

Bibliographic information