计算机视觉 CONTENTS I IMAGEFORMATION 1 1 RADIOMETRY

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详细说明： CONTENTS I IMAGEFORMATION 1 1 RADIOMETRY — MEASURING LIGHT 3 1.1 Light in Space 3 1.1.1 Foreshortening 3 1.1.2 Solid Angle 4 1.1.3 Radiance 6 1.2 Light at Surfaces 8 1.2.1 Simplifying Assumptions 9 1.2.2 The Bidirectional Reflectance Distribution Function 9 1.3 Important Special Cases 11 1.3.1 Radiosity 11 1.3.2 Directional Hemispheric Reflectance 12 1.3.3 Lambertian Surfaces and Albedo 12 1.3.4 Specular Surfaces 13 1.3.5 The Lambertian + Specular Model 14 1.4 Quick Reference: Radiometric Terminology for Light 16 1.5 Quick Refer ence: Radiometric Properties of Surfaces 17 1.6 Quick Reference: Important Types of Surface 18 1.7 Notes 19 1.8 Assignments 19 2 SOURCES, SHADOWS AND SHADING 21 2.1 Radiometric Properties of Light Sources 21 2.2 Qualitative Radiometry 22 2.3 Sources and their Effects 23 2.3.1 Point Sources 24 v vi 2.3.2 Line Sources 26 2.3.3 Area Sources 27 2.4 Local Shading Models 28 2.4.1 Local Shading Models for Point Sources 28 2.4.2 Area Sources and their Shadows 31 2.4.3 Ambient Illumination 31 2.5 Application: Photometric Stereo 33 2.5.1 Normal and Albedo from Many Views 36 2.5.2 Shape from Normals 37 2.6 Interreflections: Global Shading Models 40 2.6.1 An Interreflection Model 42 2.6.2 Solving for Radiosity 43 2.6.3 The qualitative effects of interreflections 45 2.7 Notes 47 2.8 Assignments 50 2.8.1 Exercises 50 2.8.2 Programming Assignments 51 3 COLOUR 53 3.1 The Physics of Colour 53 3.1.1 Radiometry for Coloured Lights: Spectral Quantities 53 3.1.2 The Colour of Surfaces 54 3.1.3 The Colour of Sources 55 3.2 Human Colour Perception 58 3.2.1 Colour Matching 58 3.2.2 Colour Receptors 61 3.3 Representing Colour 63 3.3.1 Linear Colour Spaces 63 3.3.2 Non-linear Colour Spaces 68 3.3.3 Spatial and Temporal Effects 73 3.4 Application: Finding Specularities 73 3.5 Surface Colour from Image Colour 77 3.5.1 Surface Colour Perception in People 77 3.5.2 Inferring Lightness 80 3.5.3 A Model for Image Colour 83 3.5.4 Surface Colour from Finite Dimensional Linear Models 86 3.6 Notes 89 vii 3.6.1 Trichromacy and Colour Spaces 89 3.6.2 Lightness and Colour Constancy 90 3.6.3 Colour in Recognition 91 3.7 Assignments 91 II IMAGE MODELS 94 4 GEOMETRIC IMAGE FEATURES 96 4.1 Elements of Differential Geometry 100 4.1.1 Curves 100 4.1.2 Surfaces 105 Application: The shape of specularities 109 4.2 Contour Geometry 112 4.2.1 The Occluding Contour and the Image Contour 113 4.2.2 The Cusps and Inflections of the Image Contour 114 4.2.3 Koenderink’s Theorem 115 4.3 Notes 117 4.4 Assignments 118 5 ANALYTICAL IMAGE FEATURES 120 5.1 Elements of Analytical Euclidean Geometry 120 5.1.1 Coordinate Systems and Homogeneous Coordinates 121 5.1.2 Coordinate System Changes and Rigid Transformations 124 5.2 Geometric Camera Parameters 129 5.2.1 Intrinsic Parameters 129 5.2.2 Extrinsic Parameters 132 5.2.3 A Characterization of Perspective Projection Matrices 132 5.3 Calibration Methods 133 5.3.1 A Linear Approach to Camera Calibration 134 Technique: Linear Least Squares Methods 135 5.3.2 Taking Radial Distortion into Account 139 5.3.3 Using Straight Lines for Calibration 140 5.3.4 Analytical Photogrammetry 143 Technique: Non-Linear Least Squares Methods 145 5.4 Notes 147 5.5 Assignments 147 viii 6 AN INTRODUCTION TO PROBABILITY 150 6.1 Probability in Discrete Spaces 151 6.1.1 Probability: the P-function 151 6.1.2 Conditional Probability 153 6.1.3 Choosing P 153 6.2 Probability in Continuous Spaces 159 6.2.1 Event Structures for Continuous Spaces 159 6.2.2 Representing a P-function for the Real Line 160 6.2.3 Probability Densities 161 6.3 Random Variables 161 6.3.1 Conditional Probability and Independence 162 6.3.2 Expectations 163 6.3.3 Joint Distributions and Marginalization 165 6.4 Standard Distributions and Densities 165 6.4.1 The Normal Distribution 167 6.5 Probabilistic Inference 167 6.5.1 The Maximum Likelihood Principle 168 6.5.2 Priors, Posteriors and Bayes’ rule 170 6.5.3 Bayesian Inference 170 6.5.4 Open Issues 177 6.6 Discussion 178 III EARLY VISION: ONE IMAGE 180 7 LINEAR FILTERS 182 7.1 Linear Filters and Convolution 182 7.1.1 Convolution 182 7.1.2 Example: Smoothing by Averaging 183 7.1.3 Example: Smoothing with a Gaussian 185 7.2 Shift invariant linear systems 186 7.2.1 Discrete Convolution 188 7.2.2 Continuous Convolution 190 7.2.3 Edge Effects in Discrete Convolutions 192 7.3 Spatial Frequency and Fourier Transforms 193 7.3.1 Fourier Transforms 193 7.4 Sampling and Aliasing 197 7.4.1 Sampling 198 ix 7.4.2 Aliasing 201 7.4.3 Smoothing and Resampling 202 7.5 Technique: Scale and Image Pyramids 204 7.5.1 The Gaussian Pyramid 205 7.5.2 Applications of Scaled Representations 206 7.5.3 Scale Space 208 7.6 Discussion 211 7.6.1 Real Imaging Systems vs Shift-Invariant Linear Systems 211 7.6.2 Scale 212 8 EDGE DETECTION 214 8.1 Estimating Derivatives with Finite Differences 214 8.1.1 Differentiation and Noise 216 8.1.2 Laplacians and edges 217 8.2 Noise 217 8.2.1 Additive Stationary Gaussian Noise 219 8.3 Edges and Gradient-based Edge Detectors 224 8.3.1 Estimating Gradients 224 8.3.2 Choosing a Smoothing Filter 225 8.3.3 Why Smooth with a Gaussian? 227 8.3.4 Derivative of Gaussian Filters 229 8.3.5 Identifying Edge Points from Filter Outputs 230 8.4 Commentary 234 9 FILTERS AND FEATURES 237 9.1 Filters as Templates 237 9.1.1 Convolution as a Dot Product 237 9.1.2 Changing Basis 238 9.2 Human Vision: Filters and Primate Early Vision 239 9.2.1 The Visual Pathway 239 9.2.2 How the Visual Pathway is Studied 241 9.2.3 The Response of Retinal Cells 241 9.2.4 The Lateral Geniculate Nucleus 242 9.2.5 The Visual Cortex 243 9.2.6 A Model of Early Spatial Vision 246 9.3 Technique: Normalised Correlation and Finding Patterns 248 9.3.1 Controlling the Television by Finding Hands by Normalised Correlation 248 x 9.4 Corners and Orientation Representations 249 9.5 Advanced Smoothing Strategies and Non-linear Filters 252 9.5.1 More Noise Models 252 9.5.2 Robust Estimates 253 9.5.3 Median Filters 254 9.5.4 Mathematical morphology: erosion and dilation 257 9.5.5 Anisotropic Scaling 258 9.6 Commentary 259 10 TEXTURE 261 10.1 Representing Texture 263 10.1.1 Extracting Image Structure with Filter Banks 263 10.2 Analysis (and Synthesis) Using Oriented Pyramids 268 10.2.1 The Laplacian Pyramid 269 10.2.2 Oriented Pyramids 272 10.3 Application: Synthesizing Textures for Rendering 272 10.3.1 Homogeneity 274 10.3.2 Synthesis by Matching Histograms of Filter Responses 275 10.3.3 Synthesis by Sampling Conditional Densities of Filter Responses280 10.3.4 Synthesis by Sampling Local Models 284 10.4 Shape from Texture: Planes and Isotropy 286 10.4.1 Recovering the Orientation of a Plane from an Isotropic Texture288 10.4.2 Recovering the Orientation of a Plane from an Homogeneity Assumption 290 10.4.3 Shape from Texture for Curved Surfaces 291 10.5 Notes 292 10.5.1 Shape from Texture 293 IV EARLY VISION: MULTIPLE IMAGES 295 11 THE GEOMETRY OF MULTIPLE VIEWS 297 11.1 Two Views 298 11.1.1 Epipolar Geometry 298 11.1.2 The Calibrated Case 299 11.1.3 Small Motions 300 11.1.4 The Uncalibrated Case 301 11.1.5 Weak Calibration 302 xi 11.2 Three Views 305 11.2.1 Trifocal Geometry 307 11.2.2 The Calibrated Case 307 11.2.3 The Uncalibrated Case 309 11.2.4 Estimation of the Trifocal Tensor 310 11.3 More Views 311 11.4 Notes 317 11.5 Assignments 319 12 STEREOPSIS 321 12.1 Reconstruction 323 12.1.1 Camera Calibration 324 12.1.2 Image Rectification 325 Human Vision: Stereopsis 327 12.2 Binocular Fusion 331 12.2.1 Correlation 331 12.2.2 Multi-Scale Edge Matching 333 12.2.3 Dynamic Programming 336 12.3 Using More Cameras 338 12.3.1 Trinocular Stereo 338 12.3.2 Multiple-Baseline Stereo 340 12.4 Notes 341 12.5 Assignments 343 13 AFFINE STRUCTURE FROM MOTION 345 13.1 Elements of Affine Geometry 346 13.2 Affine Structure from Two Images 349 13.2.1 The Affine Structure-from-Motion Theorem 350 13.2.2 Rigidity and Metric Constraints 351 13.3 Affine Structure from Multiple Images 351 13.3.1 The Affine Structure of Affine Image Sequences 352 Technique: Singular Value Decomposition 353 13.3.2 A Factorization Approach to Affine Motion Analysis 353 13.4 From Affine to Euclidean Images 356 13.4.1 Euclidean Projection Models 357 13.4.2 From Affine to Euclidean Motion 358 13.5 Affine Motion Segmentation 360 13.5.1 The Reduced Echelon Form of the Data Matrix 360 xii 13.5.2 The Shape Interaction Matrix 360 13.6 Notes 362 13.7 Assignments 363 14 PROJECTIVE STRUCTURE FROM MOTION 365 14.1 Elements of Projective Geometry 366 14.1.1 Projective Bases and Projective Coordinates 366 14.1.2 Projective Transformations 368 14.1.3 Affine and Projective Spaces 370 14.1.4 Hyperplanes and Duality 371 14.1.5 Cross-Ratios 372 14.1.6 Application: Parameterizing the Fundamental Matrix 375 14.2 Projective Scene Reconstruction from Two Views 376 14.2.1 Analytical Scene Reconstruction 376 14.2.2 Geometric Scene Reconstruction 378 14.3 Motion Estimation from Two or Three Views 379 14.3.1 Motion Estimation from Fundamental Matrices 379 14.3.2 Motion Estimation from Trifocal Tensors 381 14.4 Motion Estimation from Multiple Views 382 14.4.1 A Factorization Approach to Projective Motion Analysis 383 14.4.2 Bundle Adjustment 386 14.5 From Projective to Euclidean Structure and Motion 386 14.5.1 Metric Upgrades from (Partial) Camera Calibration 387 14.5.2 Metric Upgrades from Minimal Assumptions 389 14.6 Notes 392 14.7 Assignments 394 V MID-LEVEL VISION 399 15 SEGMENTATION USING CLUSTERING METHODS 401 15.1 Human vision: Grouping and Gestalt 403 15.2 Applications: Shot Boundary Detection, Background Subtraction and Skin Finding 407 15.2.1 Background Subtraction 407 15.2.2 Shot Boundary Detection 408 15.2.3 Finding Skin Using Image Colour 410 15.3 Image Segmentation by Clustering Pixels 411 xiii 15.3.1 Simple Clustering Methods 411 15.3.2 Segmentation Using Simple Clustering Methods 413 15.3.3 Clustering and Segmentation by K-means 415 15.4 Segmentation by Graph-Theoretic Clustering 417 15.4.1 Basic Graphs 418 15.4.2 The Overall Approach 420 15.4.3 Affinity Measures 420 15.4.4 Eigenvectors and Segmentation 424 15.4.5 Normalised Cuts 427 15.5 Discussion 430 16 FITTING 436 16.1 The Hough Transform 437 16.1.1 Fitting Lines with the Hough Transform 437 16.1.2 Practical Problems with the Hough Transform 438 16.2 Fitting Lines 440 16.2.1 Least Squares, Maximum Likelihood and Parameter Estimation441 16.2.2 Which Point is on Which Line? 444 16.3 Fitting Curves 445 16.3.1 Implicit Curves 446 16.3.2 Parametric Curves 449 16.4 Fitting to the Outlines of Surfaces 450 16.4.1 Some Relations Between Surfaces and Outlines 451 16.4.2 Clustering to Form Symmetries 453 16.5 Discussion 457 17 SEGMENTATION AND FITTING USING PROBABILISTICMETHODS 460 17.1 Missing Data Problems, Fitting and Segmentation 461 17.1.1 Missing Data Problems 461 17.1.2 The EM Algorithm 463 17.1.3 Colour and Texture Segmentation with EM 469 17.1.4 Motion Segmentation and EM 470 17.1.5 The Number of Components 474 17.1.6 How Many Lines are There? 474 17.2 Robustness 475 17.2.1 Explicit Outliers 475 17.2.2 M-estimators 477 xiv 17.2.3 RANSAC 480 17.3 How Many are There? 483 17.3.1 Basic Ideas 484 17.3.2 AIC — An Information Criterion 484 17.3.3 Bayesian methods and Schwartz’ BIC 485 17.3.4 Description Length 486 17.3.5 Other Methods for Estimating Deviance 486 17.4 Discussion 487 18 TRACKING 489 18.1 Tracking as an Abstract Inference Problem 490 18.1.1 Independence Assumptions 490 18.1.2 Tracking as Inference 491 18.1.3 Overview 492 18.2 Linear Dynamic Models and the Kalman Filter 492 18.2.1 Linear Dynamic Models 492 18.2.2 Kalman Filtering 497 18.2.3 The Kalman Filter for a 1D State Vector 497 18.2.4 The Kalman Update Equations for a General State Vector 499 18.2.5 Forward-Backward Smoothing 500 18.3 Non-Linear Dynamic Models 505 18.3.1 Unpleasant Properties of Non-Linear Dynamics 508 18.3.2 Difficulties with Likelihoods 509 18.4 Particle Filtering 511 18.4.1 Sampled Representations of Probability Distributions 511 18.4.2 The Simplest Particle Filter 515 18.4.3 A Workable Particle Filter 518 18.4.4 If’s, And’s and But’s — Practical Issues in Building Particle Filters 519 18.5 Data Association 523 18.5.1 Choosing the Nearest — Global Nearest Neighbours 523 18.5.2 Gating and Probabilistic Data Association 524 18.6 Applications and Examples 527 18.6.1 Vehicle Tracking 528 18.6.2 Finding and Tracking People 532 18.7 Discussion 538 II Appendix: The Extended Kalman Filter, or EKF 540 xv VI HIGH-LEVEL VISION 542 19 CORRESPONDENCE AND POSE CONSISTENCY 544 19.1 Initial Assumptions 544 19.1.1 Obtaining Hypotheses 545 19.2 Obtaining Hypotheses by Pose Consistency 546 19.2.1 Pose Consistency for Perspective Cameras 547 19.2.2 Affine and Projective Camera Models 549 19.2.3 Linear Combinations of Models 551 19.3 Obtaining Hypotheses by Pose Clustering 553 19.4 Obtaining Hypotheses Using Invariants 554 19.4.1 Invariants for Plane Figures 554 19.4.2 Geometric Hashing 559 19.4.3 Invariants and Indexing 560 19.5 Verification 564 19.5.1 Edge Proximity 565 19.5.2 Similarity in Texture, Pattern and Intensity 567 19.5.3 Example: Bayes Factors and Verification 567 19.6 Application: Registration in Medical Imaging Systems 568 19.6.1 Imaging Modes 569 19.6.2 Applications of Registration 570 19.6.3 Geometric Hashing Techniques in Medical Imaging 571 19.7 Curved Surfaces and Alignment 573 19.8 Discussion 576 20 FINDING TEMPLATES USING CLASSIFIERS 581 20.1 Classifiers 582 20.1.1 Using Loss to Determine Decisions 582 20.1.2 Overview: Methods for Building Classifiers 584 20.1.3 Example: A Plug-in Classifier for Normal Class-conditional Densities 586 20.1.4 Example: A Non-Parametric Classifier using Nearest Neighbours 587 20.1.5 Estimating and Improving Performance 588 20.2 Building Classifiers from Class Histograms 590 20.2.1 Finding Skin Pixels using a Classifier 591 20.2.2 Face Finding Assuming Independent Template Responses 592 20.3 Feature Selection 595 xvi 20.3.1 Principal Component Analysis 595 20.3.2 Canonical Variates 597 20.4 Neural Networks 601 20.4.1 Key Ideas 601 20.4.2 Minimizing the Error 606 20.4.3 When to Stop Training 610 20.4.4 Finding Faces using Neural Networks 610 20.4.5 Convolutional Neural Nets 612 20.5 The Support Vector Machine 615 20.5.1 Support Vector Machines for Linearly Separable Datasets 616 20.5.2 Finding Pedestrians using Support Vector Machines 618 20.6 Conclusions 622 II Appendix: Support Vector Machines for Datasets that are not Linearly Separable 624 III Appendix: Using Support Vector Machines with Non-Linear Kernels 625 21 RECOGNITION BY RELATIONS BETWEEN TEMPLATES 627 21.1 Finding Objects by Voting on Relations between Templates 628 21.1.1 Describing Image Patches 628 21.1.2 Voting and a Simple Generative Model 629 21.1.3 Probabilistic Models for Voting 630 21.1.4 Voting on Relations 632 21.1.5 Voting and 3D Objects 632 21.2 Relational Reasoning using Probabilistic Models and Search 633 21.2.1 Correspondence and Search 633 21.2.2 Example: Finding Faces 636 21.3 Using Classifiers to Prune Search 639 21.3.1 Identifying Acceptable Assemblies Using Projected Classifiers 640 21.3.2 Example: Finding People and Horses Using Spatial Relations 640 21.4 Technique: Hidden Markov Models 643 21.4.1 Formal Matters 644 21.4.2 Computing with Hidden Markov Models 645 21.4.3 Varieties of HMM’s 652 21.5 Application: HiddenMarkovModels and Sign Language Understanding654 21.6 Application: Finding People with Hidden Markov Models 659 21.7 Frames and Probability Models 662 21.7.1 Representing Coordinate Frames Explicitly in a Probability Model 664 xvii 21.7.2 Using a Probability Model to Predict Feature Positions 666 21.7.3 Building Probability Models that are Frame-Invariant 668 21.7.4 Example: Finding Faces Using Frame Invariance 669 21.8 Conclusions 669 22 ASPECT GRAPHS 672 22.1 Differential Geometry and Visual Events 677 22.1.1 The Geometry of the Gauss Map 677 22.1.2 Asymptotic Curves 679 22.1.3 The Asymptotic Spherical Map 681 22.1.4 Local Visual Events 682 22.1.5 The Bitangent Ray Manifold 684 22.1.6 Multilocal Visual Events 686 22.1.7 Remarks 687 22.2 Computing the Aspect Graph 689 22.2.1 Step 1: Tracing Visual Events 690 22.2.2 Step 2: Constructing the Regions 691 22.2.3 Remaining Steps of the Algorithm 692 22.2.4 An Example 692 22.3 Aspect Graphs and Object Recognition 696 22.4 Notes 696 22.5 Assignments 697 VII APPLICATIONS AND TOPICS 699 23 RANGE DATA 701 23.1 Active Range Sensors 701 23.2 Range Data Segmentation 704 Technique: Analytical Differential Geometry 705 23.2.1 Finding Step and Roof Edges in Range Images 707 23.2.2 Segmenting Range Images into Planar Regions 712 23.3 Range Image Registration and Model Construction 714 Technique: Quaternions 715 23.3.1 Registering Range Images Using the Iterative Closest-Point Method 716 23.3.2 Fusing Multiple Range Images 719 23.4 Object Recognition 720 xviii 23.4.1 Matching Piecewise-Planar Surfaces Using Interpretation Trees721 23.4.2 Matching Free-Form Surfaces Using Spin Images 724 23.5 Notes 729 23.6 Assignments 730 24 APPLICATION: FINDING IN DIGITAL LIBRARIES 732 24.1 Background 733 24.1.1 What do users want? 733 24.1.2 What can tools do? 735 24.2 Appearance 736 24.2.1 Histograms and correlograms 737 24.2.2 Textures and textures of textures 738 24.3 Finding 745 24.3.1 Annotation and segmentation 748 24.3.2 Template matching 749 24.3.3 Shape and correspondence 751 24.4 Video 754 24.5 Discussion 756 25 APPLICATION: IMAGE-BASED RENDERING 758 25.1 Constructing 3D Models from Image Sequences 759 25.1.1 Scene Modeling from Registered Images 759 25.1.2 Scene Modeling from Unregistered Images 767 25.2 Transfer-Based Approaches to Image-Based Rendering 771 25.2.1 Affine View Synthesis 772 25.2.2 Euclidean View Synthesis 775 25.3 The Light Field 778 25.4 Notes 782 25.5 Assignments 784 ...展开收缩

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