Multiple View Geometry in Computer VisionCambridge University Press, 2003 - 655 pagine 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. |
Sommario
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 𝓧² Distributions | 565 |
Parameter Estimation | 568 |
Matrix Properties and Decompositions | 578 |
Leastsquares Minimization | 588 |
Iterative Estimation Methods | 597 |
Some Special Plane Projective Transformations | 628 |
634 | |
646 | |
Altre edizioni - Visualizza tutto
Multiple View Geometry in Computer Vision Richard Hartley,Andrew Zisserman Anteprima non disponibile - 2000 |
Parole e frasi comuni
3-space 3D points absolute conic affine camera affine reconstruction affine transformation algebraic algorithm ambiguity auto-calibration axis back-projected calibration camera centre camera matrices chapter circular points columns Computer Vision configuration consider constraints coordinate frame corresponding points cost function covariance matrix defined degrees of freedom determined distance entries epipolar geometry epipolar line epipole equivalent Euclidean Euclidean transformation example fundamental matrix Gaussian geometric error given homogeneous homography image plane image points inliers internal parameters intersection iterative linear mapping matches matrix F measured method metric reconstruction minimization motion normal null-space obtained orthogonal outliers pair parallel pixels planar plane at infinity point correspondences problem projective camera projective geometry projective reconstruction projective transformation quadric rank RANSAC ratio represented result rotation rows scale scene screw axis set of points solution space three views transformation H trifocal tensor twisted cubic vanishing line vanishing point vector zero
Brani popolari
Pagina 637 - Self-calibration of a ID projective camera and its application to the self-calibration of a 2D projective camera.
Pagina 637 - RI Hartley. Lines and points in three views and the trifocal tensor.
Pagina 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.
Pagina 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.
Pagina 638 - Hartley. In defense of the eight-point algorithm. IEEE Transactions on Pattern Analysis and Machine Intelligence, 19(6):580-593, June 1997.
Pagina 638 - A. Heyden. Projective structure and motion from image sequences using subspace methods. In Scandinavian Conference on Image Analysis.
Pagina 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.
Riferimenti a questo libro
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