An Introduction to 3D Computer Vision Techniques and Algorithms

Cover\r......Page 1
AN INTRODUCTION TO 3D COMPUTER VISION TECHNIQUES AND ALGORITHMS......Page 2
ISBN 9780470017043......Page 4
Contents......Page 6
Preface......Page 14
Acknowledgements......Page 15
Notation and Abbreviations......Page 17
Color Plates\r......Page 19
Part I......Page 27
1 Introduction......Page 28
1.2 3D Vision Systems......Page 29
1.3 3D Vision Applications......Page 30
1.4 Contents Overview: The 3D Vision Task in Stages......Page 31
2.2 Retrospective of Vision Research......Page 33
2.3.1 Further Reading......Page 38
Part II......Page 39
3.1 Abstract......Page 40
3.2 Human Visual System......Page 41
3.3 Geometry and Acquisition of a Single Image......Page 46
3.3.2 Simple Camera System: the Pin-hole Model......Page 47
3.3.3 Projective Transformation of the Pin-hole Camera......Page 51
3.3.4 Special Camera Setups......Page 52
3.3.5 Parameters of Real Camera Systems......Page 53
3.4.1 Epipolar Geometry......Page 54
3.4.2 Canonical Stereoscopic System......Page 59
3.4.3 Disparity in the General Case......Page 61
3.4.4 Bifocal, Trifocal and Multifocal Tensors......Page 62
3.4.5 Finding the Essential and Fundamental Matrices......Page 64
3.4.6 Dealing with Outliers......Page 72
3.4.7 Catadioptric Stereo Systems......Page 77
3.4.8 Image Rectificatio......Page 78
3.4.9 Depth Resolution in Stereo Setups......Page 82
3.4.10 Stereo Images and Reference Data......Page 84
3.5 Stereo Matching Constraints......Page 89
3.6 Calibration of Cameras......Page 93
3.6.1 Standard Calibration Methods......Page 94
3.6.3 Self-calibration......Page 96
3.6.4 Calibration of the Stereo Setup......Page 97
3.7.1 Image Representation and Basic Structures......Page 98
3.8 Appendix: Derivation of the Pin-hole Camera Transformation......Page 114
3.9.1 Further Reading......Page 116
3.9.2 Problems and Exercises......Page 117
4.2.1 Convolution and Filtering......Page 118
4.2.2 Filter Separability......Page 120
4.3 Discrete Averaging......Page 122
4.3.1 Gaussian Filter......Page 123
4.3.2 Binomial Filter......Page 124
4.4.1 Optimized Differentiating Filters......Page 128
4.4.2 Savitzky–Golay Filters......Page 131
4.5 Edge Detection......Page 138
4.5.1 Edges from Signal Gradient......Page 140
4.5.2 Edges from the Savitzky–Golay Filter......Page 142
4.5.3 Laplacian of Gaussian......Page 143
4.5.4 Difference of Gaussians......Page 149
4.6 Structural Tensor......Page 150
4.6.1 Locally Oriented Neighbourhoods in Images......Page 151
4.6.2 Tensor Representation of Local Neighbourhoods......Page 156
4.6.3 Multichannel Image Processing with Structural Tensor......Page 166
4.7.1 The Most Common Corner Detectors......Page 167
4.7.2 Corner Detection with the Structural Tensor......Page 172
4.8.1 C++ Implementations......Page 174
4.8.2 Implementation of the Morphological Operators......Page 180
4.8.3 Examples in Matlab: Computation of the SVD......Page 184
4.9 Closure......Page 185
4.9.2 Problems and Exercises......Page 186
5.2.1 Context......Page 188
5.2.3 Image Matching Over Scale......Page 189
5.3.1 Gaussian Scale-space......Page 191
5.3.2 Differential Scale-space......Page 193
5.4.1 Introducing Multi-resolution Pyramids......Page 195
5.4.3 Constructing Regular Gaussian Pyramids......Page 198
5.4.4 Laplacian of Gaussian Pyramids......Page 200
5.4.5 Expanding Pyramid Levels......Page 201
5.4.6 Semi-pyramids......Page 202
5.5.1 C++ Examples......Page 204
5.5.2 Matlab Examples......Page 209
5.6.2 Further Reading......Page 214
5.6.3 Problems and Exercises......Page 215
6.2 Basic Concepts......Page 216
6.3.1 Distances of Image Regions......Page 217
6.3.2 Matching Distances for Bit Strings......Page 221
6.3.3 Matching Distances for Multichannel Images......Page 222
6.3.4 Measures Based on Theory of Information......Page 225
6.3.5 Histogram Matching......Page 228
6.3.6 Ef cient Computations of Distances......Page 229
6.3.7 Nonparametric Image Transformations......Page 232
6.3.8 Log-polar Transformation for Image Matching......Page 241
6.4.1 Occlusions......Page 245
6.4.2 Disparity Estimation with Subpixel Accuracy......Page 247
6.4.3 Evaluation Methods for Stereo Algorithms......Page 249
6.5 Diversity of Stereo Matching Methods......Page 252
6.5.1 Structure of Stereo Matching Algorithms......Page 256
6.6 Area-based Matching......Page 261
6.6.1 Basic Search Approach......Page 262
6.6.2 Interpreting Match Cost......Page 264
6.6.3 Point-oriented Implementation......Page 268
6.6.4 Disparity-oriented Implementation......Page 273
6.6.5 Complexity of Area-based Matching......Page 279
6.6.6 Disparity Map Cross-checking......Page 280
6.6.7 Area-based Matching in Practice......Page 282
6.7.1 Elastic Matching at a Single Scale......Page 296
6.7.2 Elastic Matching Concept......Page 301
6.7.3 Scale-based Search......Page 303
6.7.4 Coarse-tone Matching Over Scale......Page 306
6.7.5 Scale Subdivision......Page 307
6.7.6 Con dence Over Scale......Page 308
6.7.7 Final Multi-resolution Matcher......Page 309
6.8 Feature-based Image Matching......Page 311
6.8.1 Zero-crossing Matching......Page 312
6.8.2 Corner-based Matching......Page 315
6.8.3 Edge-based Matching: The Shirai Method......Page 318
6.9 Gradient-based Matching......Page 319
6.10 Method of Dynamic Programming......Page 321
6.10.1 Dynamic Programming Formulation of the Stereo Problem......Page 324
6.11.1 Graph Cut Algorithm......Page 329
6.11.2 Stereo as a Voxel Labelling Problem......Page 334
6.11.3 Stereo as a Pixel Labelling Problem......Page 335
6.12 Optical Flow......Page 337
6.13.1 Stereo Matching Hierarchy in C++......Page 341
6.13.2 Log-polar Transformation......Page 342
6.14.1 Further Reading......Page 344
6.14.2 Problems and Exercises......Page 345
7.2 General 3D Reconstruction......Page 346
7.2.1 Triangulation......Page 347
7.2.2 Reconstruction up to a Scale......Page 348
7.2.3 Reconstruction up to a Projective Transformation......Page 350
7.3 Multiview Integration......Page 352
7.3.1 Implicit Surfaces and Marching Cubes......Page 353
7.3.2 Direct Mesh Integration......Page 361
7.4.1 Further Reading......Page 365
8.2 3D System for Vision-Impaired Persons......Page 366
8.3.1 Development of Face and Body Capture Systems......Page 368
8.3.2 Imaging Resolution, 3D Resolution and Implications for Applications......Page 369
8.3.3 3D Capture and Analysis Pipeline for Constructing Virtual Humans......Page 373
8.4.1 Development of 3D Clinical Photography......Page 375
8.4.3 Clinical Assessment Based on 3D Surface Anatomy......Page 376
8.4.4 Extraction of Basic 3D Anatomic Measurements......Page 377
8.4.5 Vector Field Surface Analysis by Means of Dense Correspondences......Page 380
8.4.6 Eigenspace Methods......Page 382
8.4.7 Clinical and Veterinary Examples......Page 385
8.4.8 Multimodal 3D Imaging......Page 390
8.5 Movie Restoration......Page 393
8.6.1 Further Reading......Page 397
Part III......Page 398
9.2 Homogeneous Coordinates......Page 399
9.3 Point, Line and the Rule of Duality......Page 401
9.4 Point and Line at Infinit......Page 402
9.5.1 Conics in P2......Page 404
9.5.2 Conics in P3......Page 406
9.6.1 Projective Base......Page 407
9.6.3 Projective Homographies......Page 408
9.7 Projective Invariants......Page 409
9.8 Closure......Page 410
9.8.1 Further Reading......Page 411
10.2 Basic Concepts......Page 412
10.2.1 Linear Operators......Page 413
10.2.2 Change of Coordinate Systems: Jacobians......Page 414
10.3 Change of a Base......Page 415
10.4 Laws of Tensor Transformations......Page 417
10.5.1 Covariant and Contravariant Components in a Curvilinear Coordinate System......Page 418
10.6.1 Tensor Summation......Page 420
10.6.4 Reduction to Principal Axes......Page 421
10.7.1 Further Reading......Page 422
11.2 Types and Models of Noise......Page 423
11.3 Generating Noisy Test Images......Page 425
11.4 Generating Random Numbers with Normal Distributions......Page 427
11.5.1 Further Reading......Page 428
12.2 Architecture of the Warping System......Page 429
12.3.1 Projective and Affin Transformations of a Plane......Page 430
12.3.2 Polynomial Transformations......Page 431
12.4.1 Bilinear Interpolation......Page 432
12.5 The Warp Engine......Page 434
12.6.1 Coordinate Transformation Hierarchy......Page 435
12.6.3 Image Warp Hierarchy......Page 436
12.7 Warp Examples......Page 439
12.8 Finding the Linear Transformation from Point Correspondences......Page 440
12.8.1 Linear Algebra on Images......Page 444
12.9 Closure......Page 447
12.9.1 Further Reading......Page 448
13.1 Abstract......Page 449
13.2.1 Design and Implementation......Page 450
13.2.2 Template Classes......Page 456
13.2.3 Asserting Code Correctness......Page 458
13.2.4 Debugging Issues......Page 460
13.3.1 Template Function Objects......Page 461
13.3.2 Handle-body or Bridge......Page 462
13.3.3 Composite......Page 465
13.3.4 Strategy......Page 467
13.3.5 Class Policies and Traits......Page 468
13.3.7 Proxy......Page 470
13.3.8 Factory Method......Page 471
13.3.9 Prototype......Page 472
13.4 Object Lifetime and Memory Management......Page 473
13.5.2 Writing Software for Different Platforms......Page 475
13.6.1 Further Reading......Page 476
14 Image Processing Library......Page 477
References......Page 478
Index......Page 494