计算机视觉_一种现代方法.英文版

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计算机视觉_一种现代方法 英文版
3.7.4 Alternative Shading Representations 3.8 Assignments 3.8. 1 Exercises 3.8.2 Programming Assignments 4 COLOUR 80 4.1 The Physics of Colour 4.1.1 Radiometry for Coloured Lights: Spcctral Quantities 4.1.2 The Colour of Surfaces 4.1.3 The Colour of sources 4.2 Human Colour Perception 4.2. 1 Colour Matching 4.2.2 Colour Receptors 4.3 Representing Colour 4.3.1 Linear Colour Spaces 4.3.2 Non-linear Colour Spaces 95 4.3.3 Spatial and Temporal Effects 100 4.4 A Model for Image Colour 100 4.4.1 Cameras 100 4.4.2 A Model for Image Colour 101 4.4.3 Application: Finding Specularities 105 4.5 Surface Colour from Image Colour 108 4.5.1 Surface Colour Perception in People 109 4.5.2 Inferring Lightness 4.5.3 Surface colour from Finite dimensional linear models 4.6 Notes 4.6.1 Trichromacy and Colour Spaces 118 4.6.2 Specularity Finding 119 4.6.3 Lightness 119 4.6. 4 Colour Constancy 120 4.6.5 Colour in Recognition 121 4.7 Assignments 121 II IMAGE MODELS 125 5 GEOMETRIC CAMERA MODELS 127 5.1 Elements of Analytical Euclidean Geometry 128 vIll 5.1.1 Coordinate Systems and Homogeneous Coordinates 128 5.1.2 Coordinate System Changes and Rigid Transformations 132 5.2 Geometric Camera parameters 137 5.2.1 trinsic parameters 138 5.2.2 ExTrinsic Parameters 140 5.2.3 A Characterization of Perspective Projection Matrices 141 5.3 Straight Lines and their Projections 142 5.3.1 Elements of Line geometry 142 5.3.2 Projection Equation 144 5.4 Notes 144 5.5 Assignments l45 G GEOMETRIC CAMERA CALIBRATION 148 6.1 Lcast-Squares Paramctcr Estimation 149 6.1.1 Linear Least-Squares Methods 149 6.1.2 Non-Linear Least-Squares methods 153 6.2 A Linear Approach to Camera Calibration 6.2.1 Estimation of the Projection Matrix 157 6.2.2 Estimation of the intrinsic and extrinsic parameters 6.2. 3 Degenerate point Configurations 158 6.3 Taking Radial Distortion into Account 159 6.3.1 Estimation of the Projection Matrix 160 6.3.2 Estimation of the Intrinsic and extrinsic Parameters 160 6.3.3 Degenerate point Configurations 162 6.4 Using Straight Lines for Calibration 162 6.5 Analytica. Photogrammetry 164 6.6 An Applicalion: Mobile robot Localization 166 6.7 Note 167 6.8 Assignments 168 7 AN INTRODUCTION TO PROBABILITY 170 7. 1 Probability in Discrete Spaces 171 7.1.1 Probability: the P-function 172 7. 1.2 Conditional Probability 173 7.1.3 Choosing P 174 7.2 Probability in Continuous Spacc 179 7.2.1 Event Structures for Continuous Spaces 179 7.2.2 Representing P-functions 181 7.2.3 Representing P-functions with Probability Density Functions 182 7.3 RandonⅤ ariables 182 7.3. 1 Conditional Probability and Independence 183 7.3.2 Expectatio 7.3.3 Joint Distributions and marginalization 185 D d de 187 7. 4.1 The Normal Distribution 188 7. 5 Probabilistic Inference 7.5. 1 The Maximum Likelihood Principle 189 7.5.2 Priors, Posteriors and Bayes'rule 189 7.5.3 Bayesian Inference 7.5.4 Open Iss 198 7.6 Discussion 198 III EARLY VISION: ONE IMAGE 201 8 LINEAR FILTERS 203 8.1 Linear Filters and Convolution 203 8.1.1 Convolution 204 8.2 Shift invariant linear systems 210 8.2.1 Discrete Convolution 8.2.2 Continuous Convolution 2 8.2.3 Edge Eects in Discrete Convolutions 215 8.3 Spatial Frcqucncy and Fouricr Transforms 8.3.1 Fourier Transforms 216 8.4 Sampling and Aliasing 8.4.1 Sampling 220 8.4.2 Aliasing 223 8.4.3 Smoothing and resampling 224 8.5 Technique: Scale and Image Pyramids 226 8.5. 1 The Gaussian Pyramid 227 8.5.2 Applications of Scaled Representations 228 8.5.3 Scale Space 231 8.6 Discussion 8.6.1 Real Imaging Systems vs Shift-Invariant Lincar Systems 234 8.6.2 Scale 235 8.6.3 Anisotropic Scaling 235 9 EDGE DETECTION 238 9. 1 noise 238 9.1.1 Additive Stationary Gaussian Noisc 239 9.1.2 Why Finite Differences Respond to Noise 24⊥ 9.2 Estimating Derivatives 9.2.1 Choosing a Smoothing Filter 245 9.2.2 Why Smooth with a Gaussian? 9.2.3 Derivative of Gaussian Filters 249 9.3 Detecting Edges 249 9.3.1 Using the Laplacian to Detect Edges 250 9.3.2 Gradient Based Edge Detectors 251 9.3.3 Technique: Orientation Representations and Corners 255 9.4 Commentary 10 FILTERS AND FEATURES 266 10.1 Filters as Templates 266 10.1.1 Convolution as a Dot product 266 10.1.2 Changing Basis 267 10.2 Technique: Normalised Correlation and Finding Patterns 268 10.2.1 Controlling the Television by Finding Hands by normalised Correlation 10.3 Human Vision: Filters and Primate early vision 269 10.3.1 The Visual Pathway 10.3.2 The Rcsponsc of Retinal Cclls 272 10.3.3 The Lateral Geniculate Nucleus 274 10.3.4 The Visual Cortex 275 10.3.5 A Model of early Spatial vision 278 10.4 Advanced Smoothing Strategies and Non-linear Filters 280 10.4.1 More Noise models 10.4.2 Robust estimates 281 10.4.3 Median Filters 282 10.4.4 Mathematical morphology: erosion and dilation 10.5 Commentary 287 11 TEXURE 289 11.1 Representing Texture ll 1.1 Extracting Image Structure with Filter Banks 291 11.2 Analysis(and Synthesis) Using Oriented Pyramids 294 11.2.1 The Laplacian Pyramid 296 11.2.2 Filters in the Spatial frequency Domain 298 11.2.3 Oricnted Pyramids 302 11.3 Application: Synthesizing Textures for Rendering 304 11.3.1 Homogeneity 306 11.3.2 Synthesis by Matching Histograms of Filter Responses 306 11.3.3 Synthesis by Sampling Conditional Densities of Filter Responses 309 11.3.4 Synthesis by sampling local models 314 11.4 Shape from Texture 11.4. 1 Shape from Texture for Planes 317 11.4.2 Shape from Texture for Curved Surfaces 321 11.5 Note 322 11.5.1 Fillers, Pyramids and Eficiency 323 11.5.2 Texture Synthesis 323 11.5.3 Shape from Texture 323 IV EARLY VISION: MULTIPLE IMAGES 326 12 THE GEOMETRY OF MULTIPLE VIEWS 328 12.1 Two Views 329 12.1.1 Epipolar geometry 329 12.1.2 The Calibrated Case 330 12.1.3 Small motions 331 12.1.4 The uncalibrated case 12.1.5 Weak Calibration 12.2 Thrcc Vicws 336 12.2.1 Trifocal Geometry 338 12. 2.2 The calibrated Case 338 12.2.3 The Uncalibrated Case 340 12.2.4 Estimation of the Trifocal Tensor 341 12. 3 More views 342 12.4 Notes 348 12.5 Assignments 350 13 STEREOPSIS 352 13.1 Reconstruction 354 13.1.1 Camera Calibration 355 13.1.2 Image rectification Human Vision: Stereopsis 13.2 Binocular Fusion 362 13.2.1 Correlation 362 13.2.2 Multi-Scale Edge Matching 364 13.2.3 Dynamic Programming 367 13.3 Using More Cameras 369 13.3.1 Trinocular stereo 369 13.3.2 Multiple-Baseline Stereo 371 13. 4 Notes 372 13.5 Assignments 374 14 AFFINE STRUCTURE FROM MOTION 377 14.1 Elcments of Affine Gcomctry 14.2 Affine Structure from Two Images 381 14.2.1 The Affine Structure-from-Motion Theorem 14.2.2 Rigidity and Metric Constraints 14.3 Affine Structure from Multiple Images 384 14.3.1 The Affine Structure of Affine Image Sequences 385 Technique: Singular value Decomposition 385 14.3.2 A Factorization Approach to Affine Motion Analysis 387 14.4 From Affine to Euclidean Images 388 14.4.1 Euclidean Projection Models 389 14.4.2 From Affine to Euclidean motion 390 14.5 Affine Motion Segmentation 391 14.5.1 The reduced echelon form of the data Matrix 391 14.5.2 The Shape Interaction Matrix 392 14.6 Note 394 14.7 Assignments 395 15 PROJECTIVE STRUCTURE FROM MOTION 397 15. 1 Elements of Projective Geometry 15.1.1 Projective Bases and Projective Coordinates 398 15. 1.2 Projective Transformations 400 15. 1.3 Affine and Projective Spaces 402 15.1.4 Hyperplanes and Duality 403 15.1.5 Cross-Ratios 404 15. 1.6 Application: Parameterizing the Fundamental Matrix 407 15.2 Projective Scene Reconstruction from Two Views 15.2.1 Analytical Scene Reconstruction 408 15.2.2 Gcomctric Sccnc Reconstruction 410 15.3 Motion estimation from two or Three views 4l⊥ 15.3.1 Motion estimation froi fundamental matrices 15.3.2 Motion Estimation from Trifocal Tensors 15. 4 Motion Estimation from Multiple Views 415 15.4.1 A Factorization Approach to Projective Motion Analysis 415 15.4.2 Bundle adjustment 418 15.5 From Projective to Euclidean Structure and Motion 15.5.1 Metric Upgrades from(Partial) Camera Calibration 15.5.2 Metric Upgrades from Minimal Assumptions 421 15.6 Notes 424 15.7 Assignments 426 VMID-LEⅤ EL VISION 431 16 SEGMENTATION BY CLUSTERING 433 16.1 What is Segmentation 433 16.1.1 Four model problems 435 16.1.2 Segmentation as Clustering 16.2 Human vision: Grouping and gestalt 437 16.3 Applicalions: Shot Boundary Delection and Background SubtractiON 442 16.3.1 Background subtraction 442 16.3.2 Shot Boundary Detection 444 16.4 Image Segmentation by Clustering Pixels 16.4. 1 Segmentation Using Simple Clustering Methods 447 16.4.2 Clustering and Segmentation by K-means 150 16.5 Segmentation by Graph-Theoretic Clustering 451 16.5.1 Terminology for Graphs 452 16.5.2 The Overall Approach 454 16.5.3 Affinity Measures 454 16.5.4 Eigenvectors and Segmentation 457 16.5.5 Normalised CT 16.6 Discussion 463 16.6.1 Segmentation and grouping in People 465 16.6.2 Perceptual grouping 466 XIV 17 SEGMENTATION BY FITTING A MODEL 469 17.1 Fitting Lines 469 17.1.1 The Hough Transform 470 17.1.2 Line Fitting with Least Squares 474 17.1.3 Which Poinl is on Wllich Line? 476 17.2 Fitting Curves 478 17.2.1 Implicit Curves 478 17.2.2 Parametric Curves 481 17.3 Example: Finding Body Segments by Fitting 482 17.3.1 Some relations between Surfaces and outlines 482 17.3.2 Using Constraints to Fit SOR Outlines 484 17.4 Fitting as a Probabilistic Inference Problem 486 17.5 Robustness 488 17.5.⊥ M-estimators 17.5.2 RANSAC 492 17.6 Example: Using RANSaC to Fit Fundamental Matrices 496 17.6.1 An Expression for Fitting Error 17.6.2 Correspondence as noise 497 17.6. 3 Applying RANSAc 497 17.7 Discussion 198 1 8 SEGMENTATION AND FITTING USING PROBABILISTIC METH- ODS 501 18.1 Missing Data Problems, Fitting and Segmentation 502 18.1.1 Missing Data Problems 18.1.2 The EM Algorithm 506 18.1.3 The EM Algorithm in the General Case 507 18.2 The EM AlgorithIn in Practice 507 18.2.1 Example: Image Segmentation, Revisited 507 18.2.2 Example: Line Fitting with EM 18.2.3 Example: Motion Segmentation and EM 510 18.2.4 Example: Using em to Identify Outliers 516 18.2.5 Example: Background Subtraction using EM 517 18.2.6 Example: Finding Body Segments with eM 18.2.7 Example: EM and the Fundamental matrix 18.2. 8 Difficultics with the EM algorithm 18.3 How Many are There? 18.3.1 Basic Ideas 520

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