计算机视觉(英文版)

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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 Radio
3.6.1 Trichromacy and Colour Spaces 3.6.2 Lightness and Colour Constancy 3.6.3 Colour in recognition 91 3.7 Assignments 91 II IMAGE MODELS 94 4 GEOMETRIC IMAGE FEATURES 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 4.2. 1 The Occluding Contour and the Iimlage Contour 113 4.2.2 The Cusps and Inflections of the Image Contour 114 4.2.3 Koenderink,s Theorem 4.3 Notes 117 4.士 assignments 118 5 ANALYTICAL IMAGE FEATURES 120 5.1 Elements of Analytical Euclidean Geometry 120 5.1.1 Coordinate Systems and Ilomogeneous 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 5.3Ca allbraglon ethos 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 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 6.1.3 Choosing P 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 6.5.3 Bayesian Inference 170 6.5.4 Open issues 177 6.6 Discussion 178 II EARLY VISION: ONE IMAGE 180 T LINEAR FILTERS 82 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 7. 4.2 Aliasing 201 7.4.3 Smoothing and resampling 202 7.5 Tcchniquc: Scalc and Imagc Pyramids 204 7.5. 1 The Gaussian pyramid 205 7.5.2 Applications of Scaled Representations 7.5.3 Scale Space 208 7.6 Discussion 7.6.1 Real Imaging Systems vs shift-Invariant Linear Systems 21l 7.6.2 Scale 8 EDGE DETECTION 214 8.1 Estimating Derivatives with finite Differences 214 8.1.1 Differentiation and noise 8.1.2 Laplacians and edges 217 8.2 Noise 8.2.1 Additive Stationary gaussian noise 219 8.3 Edges alld 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 Edgc Points from Filtor 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 HuIllall Visio: 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 9.2.4 The Lateral Geniculate Nucleus 242 9.2.5 Thc 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 Ilands by Normalised Correlation 248 9. 4 Corners and Orientation Representations 249 9.5 Advanced Smoothing Strategies and Non-linear Filters 252 9.5.1 Morc Noisc modcls 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 Cor nta 259 10 TEXTURE 261 10.1 Representing Texture 10.1.1 Extracting Image Structure with Filter Banks 10.2 Analysis(and Synthesis) Using Oriented Pyramids 268 10.2.1 The Laplacian Pyramid 269 10.2.2 Oriented Pyrainlids 272 10.3 Application: Synthesizing Textures for Rendering 272 10.3.1 Homogeneit 27生 10.3.2 Synthesis by Matching Histograms of Filter Responses 10.3.3 Synthesis by Sainpling ConditioNal Densities of Filter Responses 280 10.3.4 Synthesis by Sampling Local Models 284 10.4 Shape from Texture: Planes and Isotropy 10.4.1 Recovering the Orientation of a Plane from an isotropic Texture 288 10.4.2 Recovering the Orientation of a Plane froin all Hoinlogenleity assumptin 10.4.3 Shape from Texture for Curved Surfaces 10.5 Not 10.5.1 Shape from Texture IV EARLY VISION: MULTIPLE IMAGES 295 11 THE GEOMETRY OF MULTIPLE VIEWS 297 11.1 Two V 298 11.1.1 Epipolar geometry 298 11.1.2 The Calibrated Case 11.1.3 Small motions 300 11.1.4 The Uncalibrated Case 301 11.1.5 Weak Calibration 302 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 Estination of the Trifocal tensor 310 11. 3 More Views 11.5 Assignments 12 STEREOPSIS 321 12.1 Reconstruction 323 12.1.1 Camera Calibration 324 12.1.2 Image rectification 325 Human Vision: Stcrcopsis 327 12.2 Binocular fusion 331 12.2.1 Correlation 331 12.2.2 Multi-Scale Edge Matching 12.2.3 Dynamic Programming 12.3 USing More Camera.s 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 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 13.3.2 A Factorization Approach to Affine Motion Analysis 353 13.4 From Affine to euclidean images 13.4. 1 Euclidean Projection Model 357 13.4.2 From Affine to euclidean motion 358 13.5 Affine Motion Segmentation 360 3.5.1 The Reduced Echelon Form of the Data matrix 360 13.5.2 The Shape Interaction Matrix 360 13.6 Notes 362 13.7 Assignments 363 14 PROJECTIVE STRUCTURE FROM MOTION 365 14.1 Flements of Projective Geometry 14.1.1 Projective Bases and Projective Coordinates 366 14.1.2 Projective Transformations 368 14.1.3 Affine and Projective Spaces 14.1.4 Hyperplanes and Duality 14.1.5 CroSS-Ratios 14.1.6 Application: Parameterizing the Fundamental Matrix 14.2 Projective Scene Reconstruction from Two views 14.2.1 Analytical Scene Reconstruction 376 14.2.2 Geonletric Scene Reconstruction 378 14.3 Motion Estimation from Two or Three Views 379 14.3.1 Motion estimation from fundamental matrices 14.3.2 Motion estimation from trifocal tensors 381 14.4 Motion Estimation fronn Multiple views 14.4.1 A Factorization Approach to Projective Motion Analysis 383 14.4.2 Bundle Adjustment 14.5 From Projective to Euclidean Structure and Motion 14.5.1 Metric Upgrades froIn(Partial) Calera CalibratiOn 387 14.5.2 Metric Upgrades from Minimal Assumptions 14.6 Notes 14.7 Assignments 394 V MID-LEVEL VISION 399 15 SEG MENTATION 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 Dctection 408 15.2.3 Finding Skin Using Image Colour 15.3 Image Segmentation by Clustering Pixels 411 15.3.1 Simple clustering Methods 411 15.3.2 Segmentation Using Simple Clustering Methods 15.3.3 Clustcring and Segmentation by K-mcans 15.4 Segmentation by Graph-Theoretic Clustering 4 15.4.1 Basic Graph 15.4.2 The Overall Approach 420 15.4.3 Affinity Measures 420 15.4.4 Eigenvectors and Segmenta tion 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 lough Transform 437 16.1.2 Practical Problems with the Hough Transform 438 16.2 Fitting Lines 440 16. 2.1 Least Squares, MaxiIluIn Likelihood alld Paraineter Estination441 16.2.2 Which point is on which L Ine 16.3 Fitting Curves 445 16.3.1 Implicit Curves 16.3.2 Parametric Curves 449 16.4 Fitting to thc 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 PROBABILISTIC METH ODS 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 Ilow Many Lines are There? 474 17.2 Robustness 17.2.1 Explicit Outliers 475 17.2.2 M-estimators 477 17.2.3 RANSAC 17.3 How Many are There? 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 1 8 TRACKING 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 Ovcrvicw 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 p ties of Linear d 508 18.3.2 Difficulties with Likelihoods 509 18 4 Particle Filtering 18.4. 1 Sampled Representations of Probability Distributions 511 18.4.2 The Simplest Particle Filter 18.4.4 If's, And, s and But's- Practical Issues in Building Particle 518 18. 4.3 A Workable particle Filter Filters 18.5 Data Association 523 18.5.1 Choosing the Nearest- Global Nearest Neighbours 523 18.5.2 Gating and Probabilistic Dat a. Association 524 18.6 Applications alld Examples 527 18.6.1 Vehicle Tracking 528 18.6.2 Finding and Tracking People 532 18.7 Discussion 538 I Appendix: The Extended Kalman Filter, or EKF 540

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