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Ⅰ IMAGE FORMATION 1

1 Geometric Camera Models 3

1.1 Image Formation 4

1.1.1 Pinhole Perspective 4

1.1.2 Weak Perspective 6

1.1.3 Cameras with Lenses 8

1.1.4 The Human Eye 12

1.2 Intrinsic and Extrinsic Parameters 14

1.2.1 Rigid Transformations and Homogeneous Coordinates 14

1.2.2 Intrinsic Parameters 16

1.2.3 Extrinsic Parameters 18

1.2.4 Perspective Projection Matrices 19

1.2.5 Weak-Perspective Projection Matrices 20

1.3 Geometric Camera Calibration 22

1.3.1 A Linear Approach to Camera Calibration 23

1.3.2 A Nonlinear Approach to Camera Calibration 27

1.4 Notes 29

2 Light and Shading 32

2.1 Modelling Pixel Brightness 32

2.1.1 Reflection at Surfaces 33

2.1.2 Sources and Their Effects 34

2.1.3 The Lambertian＋Specular Model 36

2.1.4 Area Sources 36

2.2 Inference from Shading 37

2.2.1 Radiometric Calibration and High Dynamic Range Images 38

2.2.2 The Shape of Specularities 40

2.2.3 Inferring Lightness and Illumination 43

2.2.4 Photometric Stereo：Shape from Multiple Shaded Images 46

2.3 Modelling Interreflection 52

2.3.1 The Illumination at a Patch Due to an Area Source 52

2.3.2 Radiosity and Exitance 54

2.3.3 An Interreflection Model 55

2.3.4 Qualitative Properties of Interreflections 56

2.4 Shape from One Shaded Image 59

2.5 Notes 61

3 Color 68

3.1 Human Color Perception 68

3.1.1 Color Matching 68

3.1.2 Color Receptors 71

3.2 The Physics of Color 73

3.2.1 The Color of Light Sources 73

3.2.2 The Color of Surfaces 76

3.3 Representing Color 77

3.3.1 Linear Color Spaces 77

3.3.2 Non-linear Color Spaces 83

3.4 A Model of Image Color 86

3.4.1 The Diffuse Term 88

3.4.2 The Specular Term 90

3.5 Inference from Color 90

3.5.1 Finding Specularities Using Color 90

3.5.2 Shadow Removal Using Color 92

3.5.3 Color Constancy：Surface Color from Image Color 95

3.6 Notes 99

Ⅱ EARLY VISION：JUST ONE IMAGE 105

4 Linear Filters 107

4.1 Linear Filters and Convolution 107

4.1.1 Convolution 107

4.2 Shift Invariant Linear Systems 112

4.2.1 Discrete Convolution 113

4.2.2 Continuous Convolution 115

4.2.3 Edge Effects in Discrete Convolutions 118

4.3 Spatial Frequency and Fourier Transforms 118

4.3.1 Fourier Transforms 119

4.4 Sampling and Aliasing 121

4.4.1 Sampling 122

4.4.2 Aliasing 125

4.4.3 Smoothing and Resampling 126

4.5 Filters as Templates 131

4.5.1 Convolution as a Dot Product 131

4.5.2 Changing Basis 132

4.6 Technique：Normalized Correlation and Finding Patterns 132

4.6.1 Controlling the Television by Finding Hands by Normalized Correlation 133

4.7 Technique：Scale and Image Pyramids 134

4.7.1 The Gaussian Pyramid 135

4.7.2 Applications of Scaled Representations 136

4.8 Notes 137

5 Local Image Features 141

5.1 Computing the Image Gradient 141

5.1.1 Derivative of Gaussian Filters 142

5.2 Representing the Image Gradient 144

5.2.1 Gradient-Based Edge Detectors 145

5.2.2 Orientations 147

5.3 Finding Corners and Building Neighborhoods 148

5.3.1 Finding Corners 149

5.3.2 Using Scale and Orientation to Build a Neighborhood 151

5.4 Describing Neighborhoods with SIFT and HOG Features 155

5.4.1 SIFT Features 157

5.4.2 HOG Features 159

5.5 Computing Local Features in Practice 160

5.6 Notes 160

6 Texture 164

6.1 Local Texture Representations Using Filters 166

6.1.1 Spots and Bars 167

6.1.2 From Filter Outputs to Texture Representation 168

6.1.3 Local Texture Representations in Practice 170

6.2 Pooled Texture Representations by Discovering Textons 171

6.2.1 Vector Quantization and Textons 172

6.2.2 K-means Clustering for Vector Quantization 172

6.3 Synthesizing Textures and Filling Holes in Images 176

6.3.1 Synthesis by Sampling Local Models 176

6.3.2 Filling in Holes in Images 179

6.4 Image Denoising 182

6.4.1 Non-local Means 183

6.4.2 Block Matching 3D （BM3D） 183

6.4.3 Learned Sparse Coding 184

6.4.4 Results 186

6.5 Shape from Texture 187

6.5.1 Shape from Texture for Planes 187

6.5.2 Shape from Texture for Curved Surfaces 190

6.6 Notes 191

Ⅲ EARLY VISION：MULTIPLE IMAGES 195

7 Stereopsis 197

7.1 Binocular Camera Geometry and the Epipolar Constraint 198

7.1.1 Epipolar Geometry 198

7.1.2 The Essential Matrix 200

7.1.3 The Fundamental Matrix 201

7.2 Binocular Reconstruction 201

7.2.1 Image Rectification 202

7.3 Human Stereopsis 203

7.4 Local Methods for Binocular Fusion 205

7.4.1 Correlation 205

7.4.2 Multi-Scale Edge Matching 207

7.5 Global Methods for Binocular Fusion 210

7.5.1 Ordering Constraints and Dynamic Programming 210

7.5.2 Smoothness and Graphs 211

7.6 Using More Cameras 214

7.7 Application：Robot Navigation 215

7.8 Notes 216

8 Structure from Motion 221

8.1 Internally Calibrated Perspective Cameras 221

8.1.1 Natural Ambiguity of the Problem 223

8.1.2 Euclidean Structure and Motion from Two Images 224

8.1.3 Euclidean Structure and Motion from Multiple Images 228

8.2 Uncalibrated Weak-Perspective Cameras 230

8.2.1 Natural Ambiguity of the Problem 231

8.2.2 Affine Structure and Motion from Two Images 233

8.2.3 Affine Structure and Motion from Multiple Images 237

8.2.4 From Affine to Euclidean Shape 238

8.3 Uncalibrated Perspective Cameras 240

8.3.1 Natural Ambiguity of the Problem 241

8.3.2 Projective Structure and Motion from Two Images 242

8.3.3 Projective Structure and Motion from Multiple Images 244

8.3.4 From Projective to Euclidean Shape 246

8.4 Notes 248

Ⅳ MID-LEVEL VISION 253

9 Segmentation by Clustering 255

9.1 Human Vision：Grouping and Gestalt 256

9.2 Important Applications 261

9.2.1 Background Subtraction 261

9.2.2 Shot Boundary Detection 264

9.2.3 Interactive Segmentation 265

9.2.4 Forming Image Regions 266

9.3 Image Segmentation by Clustering Pixels 268

9.3.1 Basic Clustering Methods 269

9.3.2 The Watershed Algorithm 271

9.3.3 Segmentation Using K-means 272

9.3.4 Mean Shift：Finding Local Modes in Data 273

9.3.5 Clustering and Segmentation with Mean Shift 275

9.4 Segmentation，Clustering，and Graphs 277

9.4.1 Terminology and Facts for Graphs 277

9.4.2 Agglomerative Clustering with a Graph 279

9.4.3 Divisive Clustering with a Graph 281

9.4.4 Normalized Cuts 284

9.5 Image Segmentation in Practice 285

9.5.1 Evaluating Segmenters 286

9.6 Notes 287

10 Grouping and Model Fitting 290

10.1 The Hough Transform 290

10.1.1 Fitting Lines with the Hough Transform 290

10.1.2 Using the Hough Transform 292

10.2 Fitting Lines and Planes 293

10.2.1 Fitting a Single Line 294

10.2.2 Fitting Planes 295

10.2.3 Fitting Multiple Lines 296

10.3 Fitting Curved Structures 297

10.4 Robustness 299

10.4.1 M-Estimators 300

10.4.2 RANSAC：Searching for Good Points 302

10.5 Fitting Using Probabilistic Models 306

10.5.1 Missing Data Problems 307

10.5.2 Mixture Models and Hidden Variables 309

10.5.3 The EM Algorithm for Mixture Models 310

10.5.4 Difficulties with the EM Algorithm 312

10.6 Motion Segmentation by Parameter Estimation 313

10.6.1 Optical Flow and Motion 315

10.6.2 Flow Models 316

10.6.3 Motion Segmentation with Layers 317

10.7 Model Selection：Which Model Is the Best Fit？ 319

10.7.1 Model Selection Using Cross-Validation 322

10.8 Notes 322

11 Tracking 326

11.1 Simple Tracking Strategies 327

11.1.1 Tracking by Detection 327

11.1.2 Tracking Translations by Matching 330

11.1.3 Using Affine Transformations to Confirm a Match 332

11.2 Tracking Using Matching 334

11.2.1 Matching Summary Representations 335

11.2.2 Tracking Using Flow 337

11.3 Tracking Linear Dynamical Models with Kalman Filters 339

11.3.1 Linear Measurements and Linear Dynamics 340

11.3.2 The Kalman Filter 344

11.3.3 Forward-backward Smoothing 345

11.4 Data Association 349

11.4.1 Linking Kalman Filters with Detection Methods 349

11.4.2 Key Methods of Data Association 350

11.5 Particle Filtering 350

11.5.1 Sampled Representations of Probability Distributions 351

11.5.2 The Simplest Particle Filter 355

11.5.3 The Tracking Algorithm 356

11.5.4 A Workable Particle Filter 358

11.5.5 Practical Issues in Particle Filters 360

11.6 Notes 362

Ⅴ HIGH-LEVEL VISION 365

12 Registration 367

12.1 Registering Rigid Objects 368

12.1.1 Iterated Closest Points 368

12.1.2 Searching for Transformations via Correspondences 369

12.1.3 Application：Building Image Mosaics 370

12.2 Model-based Vision：Registering Rigid Objects with Projection 375

12.2.1 Verification：Comparing Transformed and Rendered Source to Target 377

12.3 Registering Deformable Objects 378

12.3.1 Deforming Texture with Active Appearance Models 378

12.3.2 Active Appearance Models in Practice 381

12.3.3 Application：Registration in Medical Imaging Systems 383

12.4 Notes 388

13 Smooth Surfaces and Their Outlines 391

13.1 Elements of Differential Geometry 393

13.1.1 Curves 393

13.1.2 Surfaces 397

13.2 Contour Geometry 402

13.2.1 The Occluding Contour and the Image Contour 402

13.2.2 The Cusps and Inflections of the Image Contour 403

13.2.3 Koenderink’s Theorem 404

13.3 Visual Events：More Differential Geometry 407

13.3.1 The Geometry of the Gauss Map 407

13.3.2 Asymptotic Curves 409

13.3.3 The Asymptotic Spherical Map 410

13.3.4 Local Visual Events 412

13.3.5 The Bitangent Ray Manifold 413

13.3.6 Multilocal Visual Events 414

13.3.7 The Aspect Graph 416

13.4 Notes 417

14 Range Data 422

14.1 Active Range Sensors 422

14.2 Range Data Segmentation 424

14.2.1 Elements of Analytical Differential Geometry 424

14.2.2 Finding Step and Roof Edges in Range Images 426

14.2.3 Segmenting Range Images into Planar Regions 431

14.3 Range Image Registration and Model Acquisition 432

14.3.1 Quaternions 433

14.3.2 Registering Range Images 434

14.3.3 Fusing Multiple Range Images 436

14.4 Object Recognition 438

14.4.1 Matching Using Interpretation Trees 438

14.4.2 Matching Free-Form Surfaces Using Spin Images 441

14.5 Kinect 446

14.5.1 Features 447

14.5.2 Technique：Decision Trees and Random Forests 448

14.5.3 Labeling Pixels 450

14.5.4 Computing Joint Positions 453

14.6 Notes 453

15 Learning to Classify 457

15.1 Classification，Error，and Loss 457

15.1.1 Using Loss to Determine Decisions 457

15.1.2 Training Error，Test Error，and Overfitting 459

15.1.3 Regularization 460

15.1.4 Error Rate and Cross-Validation 463

15.1.5 Receiver Operating Curves 465

15.2 Major Classification Strategies 467

15.2.1 Example：Mahalanobis Distance 467

15.2.2 Example：Class-Conditional Histograms and Naive Bayes 468

15.2.3 Example：Classification Using Nearest Neighbors 469

15.2.4 Example：The Linear Support Vector Machine 470

15.2.5 Example：Kernel Machines 473

15.2.6 Example：Boosting and Adaboost 475

15.3 Practical Methods for Building Classifiers 475

15.3.1 Manipulating Training Data to Improve Performance 477

15.3.2 Building Multi-Class Classifiers Out of Binary Classifiers 479

15.3.3 Solving for SVMS and Kernel Machines 480

15.4 Notes 481

16 Classifying Images 482

16.1 Building Good Image Features 482

16.1.1 Example Applications 482

16.1.2 Encoding Layout with GIST Features 485

16.1.3 Summarizing Images with Visual Words 487

16.1.4 The Spatial Pyramid Kernel 489

16.1.5 Dimension Reduction with Principal Components 493

16.1.6 Dimension Reduction with Canonical Variates 494

16.1.7 Example Application：Identifying Explicit Images 498

16.1.8 Example Application：Classifying Materials 502

16.1.9 Example Application：Classifying Scenes 502

16.2 Classifying Images of Single Objects 504

16.2.1 Image Classification Strategies 505

16.2.2 Evaluating Image Classification Systems 505

16.2.3 Fixed Sets of Classes 508

16.2.4 Large Numbers of Classes 509

16.2.5 Flowers，Leaves，and Birds：Some Specialized Problems 511

16.3 Image Classification in Practice 512

16.3.1 Codes for Image Features 513

16.3.2 Image Classification Datasets 513

16.3.3 Dataset Bias 515

16.3.4 Crowdsourcing Dataset Collection 515

16.4 Notes 517

17 Detecting Objects in Images 519

17.1 The Sliding Window Method 519

17.1.1 Face Detection 520

17.1.2 Detecting Humans 525

17.1.3 Detecting Boundaries 527

17.2 Detecting Deformable Objects 530

17.3 The State of the Art of Object Detection 535

17.3.1 Datasets and Resources 538

17.4 Notes 539

18 Topics in Object Recognition 540

18.1 What Should Object Recognition Do？ 540

18.1.1 What Should an Object Recognition System Do？ 540

18.1.2 Current Strategies for Object Recognition 542

18.1.3 What Is Categorization？ 542

18.1.4 Selection：What Should Be Described？ 544

18.2 Feature Questions 544

18.2.1 Improving Current Image Features 544

18.2.2 Other Kinds of Image Feature 546

18.3 Geometric Questions 547

18.4 Semantic Questions 549

18.4.1 Attributes and the Unfamiliar 550

18.4.2 Parts，Poselets and Consistency 551

18.4.3 Chunks of Meaning 554

Ⅵ APPLICATIONS AND TOPICS 557

19 Image-Based Modeling and Rendering 559

19.1 Visual Hulls 559

19.1.1 Main Elements of the Visual Hull Model 561

19.1.2 Tracing Intersection Curves 563

19.1.3 Clipping Intersection Curves 566

19.1.4 Triangulating Cone Strips 567

19.1.5 Results 568

19.1.6 Going Further：Carved Visual Hulls 572

19.2 Patch-Based Multi-View Stereopsis 573

19.2.1 Main Elements of the PMVS Model 575

19.2.2 Initial Feature Matching 578

19.2.3 Expansion 579

19.2.4 Filtering 580

19.2.5 Results 581

19.3 The Light Field 584

19.4 Notes 587

20 Looking at People 590

20.1 HMM’s，Dynamic Programming，and Tree-Structured Models 590

20.1.1 Hidden Markov Models 590

20.1.2 Inference for an HMM 592

20.1.3 Fitting an HMM with EM 597

20.1.4 Tree-Structured Energy Models 600

20.2 Parsing People in Images 602

20.2.1 Parsing with Pictorial Structure Models 602

20.2.2 Estimating the Appearance of Clothing 604

20.3 Tracking People 606

20.3.1 Why Human Tracking Is Hard 606

20.3.2 Kinematic Tracking by Appearance 608

20.3.3 Kinematic Human Tracking Using Templates 609

20.4 3D from 2D：Lifting 611

20.4.1 Reconstruction in an Orthographic View 611

20.4.2Exploiting Appearance for Unambiguous Reconstructions 613

20.4.3Exploiting Motion for Unambiguous Reconstructions 615

20.5Activity Recognition 617

20.5.1 Background：Human Motion Data 617

20.5.2 Body Configuration and Activity Recognition 621

20.5.3 Recognizing Human Activities with Appearance Features 622

20.5.4 Recognizing Human Activities with Compositional Models 624

20.6Resources 624

20.7Notes 626

21 Image Search and Retrieval 627

21.1 The Application Context 627

21.1.1 Applications 628

21.1.2 User Needs 629

21.1.3 Types of Image Query 630

21.1.4 What Users Do with Image Collections 631

21.2 Basic Technologies from Information Retrieval 632

21.2.1 Word Counts 632

21.2.2 Smoothing Word Counts 633

21.2.3 Approximate Nearest Neighbors and Hashing 634

21.2.4 Ranking Documents 638

21.3 Images as Documents 639

21.3.1 Matching Without Quantization 640

21.3.2 Ranking Image Search Results 641

21.3.3 Browsing and Layout 643

21.3.4 Laying Out Images for Browsing 644

21.4 Predicting Annotations for Pictures 645

21.4.1 Annotations from Nearby Words 646

21.4.2 Annotations from the Whole Image 646

21.4.3 Predicting Correlated Words with Classifiers 648

21.4.4 Names and Faces 649

21.4.5 Generating Tags with Segments 651

21.5 The State of the Art of Word Prediction 654

21.5.1 Resources 655

21.5.2 Comparing Methods 655

21.5.3 Open Problems 656

21.6 Notes 659

Ⅶ BACKGROUND MATERIAL 661

22 Optimization Techniques 663

22.1 Linear Least-Squares Methods 663

22.1.1 Normal Equations and the Pseudoinverse 664

22.1.2 Homogeneous Systems and Eigenvalue Problems 665

22.1.3 Generalized Eigenvalues Problems 666

22.1.4 An Example：Fitting a Line to Points in a Plane 666

22.1.5 Singular Value Decomposition 667

22.2 Nonlinear Least-Squares Methods 669

22.2.1 Newton’s Method：Square Systems of Nonlinear Equations 670

22.2.2 Newton’s Method for Overconstrained Systems 670

22.2.3 The Gauss-Newton and Levenberg-Marquardt Algorithms 671

22.3 Sparse Coding and Dictionary Learning 672

22.3.1 Sparse Coding 672

22.3.2 Dictionary Learning 673

22.3.3 Supervised Dictionary Learning 675

22.4 Min-Cut/Max-Flow Problems and Combinatorial Optimization 675

22.4.1 Min-Cut Problems 676

22.4.2 Quadratic Pseudo-Boolean Functions 677

22.4.3 Generalization to Integer Variables 679

22.5 Notes 682

Bibliography 684

Index 737

List of Algorithms 760