Statistical Learning and Pattern Analysis for Image and Video Processing (eBook)

Preface 5
Why are We Writing This Book? 5
Acknowledgments 8
Contents 9
Chapter 1 Pattern Analysis and Statistical Learning 15
1.1 Introduction 15
1.1.1 Statistical Pattern Recognition 16
1.1.2 Pattern Theory 18
1.2 Statistical Classification 20
1.2.1 Feature Extraction and Selection 20
1.2.2 Classifier 21
1.3 Visual Pattern Representation 22
1.3.1 The Curse of Dimensionality 23
1.3.2 Dimensionality Reduction Techniques 23
1.4 Statistical Learning 24
1.4.1 Prediction Risk 25
1.4.2 Supervised, Unsupervised, and Others 26
1.5 Summary 28
References 28
Chapter 2 Unsupervised Learning for Visual Pattern Analysis 29
2.1 Introduction 2.1.1 Unsupervised Learning 29
2.1.2 Visual Pattern Analysis 30
2.1.3 Outline 31
2.2 Cluster Analysis 31
2.3 Clustering Algorithms 35
2.3.1 Partitional Clustering 35
2.3.2 Hierarchical Clustering 44
2.4 Perceptual Grouping 47
2.4.1 Hierarchical Perceptual Grouping 47
2.4.2 Gestalt Grouping Principles 49
2.4.3 Contour Grouping 53
2.4.4 Region Grouping 59
2.5 Learning Representational Models for Visual Patterns 61
2.6 Summary 62
Appendix 62
References 62
Chapter 3 Component Analysis 64
3.1 Introduction 64
3.2 Overview of Component Analysis 67
3.3 Generative Models 68
3.3.1 Principal Component Analysis 68
3.3.2 Nonnegative Matrix Factorization 79
3.3.3 Independent Component Analysis 85
3.4 Discriminative Models 89
3.4.1 Linear Discriminative Analysis 89
3.4.2 Oriented Component Analysis 92
3.4.3 Canonical Correlation Analysis 92
3.4.4 Relevant Component Analysis 94
3.5 Standard Extensions of the Linear Model 3.5.1 Latent Variable Analysis 96
3.5.2 Kernel Method 96
3.6 Summary 96
References 97
Chapter 4 Manifold Learning 99
4.1 Introduction 99
4.2 Mathematical Preliminaries 103
4.2.1 Manifold Related Terminologies 103
4.2.2 Graph Related Terminologies 104
4.3 Global Methods 106
4.3.1 Multidimensional Scaling 106
4.3.2 Isometric Feature Mapping 107
4.3.3 Variants of the Isomap 108
4.4 Local Methods 112
4.4.1 Locally Linear Embedding 112
4.4.2 Laplacian Eigenmaps 115
4.4.3 Hessian Eigenmaps 119
4.4.4 Diffusion Maps 121
4.5 Hybrid Methods: Global Alignment of Local Models 125
4.5.1 Global Coordination of Local Linear Models 125
4.5.2 Charting a Manifold 127
4.5.3 Local Tangent Space Alignment 129
4.6 Summary 129
Appendix 130
References 130
Chapter 5 Functional Approximation 132
5.1 Introduction 132
5.2 Modeling and Approximating the Visual Data 135
5.2.1 On Statistical Analysis 136
5.2.2 On Harmonic Analysis 137
5.2.3 Issues of Approximation and Compression 138
5.3 Wavelet Transform and Lifting Scheme 5.3.1 Wavelet Transform 140
5.3.2 Constructing a Wavelet Filter Bank 141
5.3.3 Lifting Scheme 143
5.3.4 Lifting-Based Integer Wavelet Transform 144
5.4 Optimal IntegerWavelet Transform 145
5.5 Introducing Adaptability into the Wavelet Transform 147
5.5.1 Curve Singularities in an Image 148
5.5.2 Anisotropic Basis 148
5.5.3 Adaptive Lifting-Based Wavelet 150
5.6 Adaptive Lifting Structure 151
5.6.1 Adaptive Prediction Filters 151
5.6.2 Adaptive Update Filters 153
5.7 Adaptive Directional Lifting Scheme 154
5.7.1 ADL Framework 155
5.7.2 Implementation of ADL 156
5.8 Motion Compensation Temporal Filtering in Video Coding 159
5.8.1 Overview of MCTF 159
5.8.2 MC in MCTF 162
5.8.3 Adaptive Lifting-Based Wavelets in MCTF 163
5.9 Summary and Discussions 164
References 165
Chapter 6 Supervised Learning for Visual Pattern Classification 170
6.1 Introduction 170
6.2 An Example of Supervised Learning 171
6.3 Support Vector Machine 174
6.3.1 Optimal Separating Hyper-plane 174
6.3.2 Realization of SVM 178
6.3.3 Kernel Function 180
6.4 Boosting Algorithm 182
6.4.1 AdaBoost Algorithm 183
6.4.2 Theoretical Analysis of AdaBoost 184
6.4.3 AdaBoost Algorithm as an Additive Model 187
6.5 Summary 189
Appendix 189
References 190
Chapter 7 Statistical Motion Analysis 191
7.1 Introduction 191
7.1.1 Problem Formulation 191
7.1.2 Overview of Computing Techniques 193
7.2 Bayesian Estimation of Optical Flow 196
7.2.1 Problem Formulation 196
7.2.2 MAP Estimation 200
7.2.3 Occlusion 202
7.3 Model-Based Motion Analysis 203
7.3.1 Motion Models 204
7.3.2 Statistical Model Selection 205
7.3.3 Learning Parameterized Models 206
7.4 Motion Segmentation 211
7.4.1 Layered Model: Multiple Motion Models 212
7.4.2 Clustering Optical Flow Field into Layers 214
7.4.3 Mixture Estimation for Layer Extraction 215
7.5 Statistics of Optical Flow 218
7.5.1 Statistics of Optical Flow 218
7.5.2 Motion Prior Modeling 220
7.5.3 Contrastive Divergence Learning 221
7.6 Summary 222
Appendix Graph and Neighborhood 222
Steerable Filter Design 223
References 224
Chapter 8 Bayesian Tracking of Visual Objects 226
8.1 Introduction 226
8.2 Sequential Bayesian Estimation 228
8.2.1 Problem Formulation of Bayesian Tracking 229
8.2.2 Kalman Filter 230
8.2.3 Grid-Based Methods 231
8.2.4 Sub-optimal Filter 231
8.3 Monte Carlo Filtering 233
8.3.1 Problem Formulation 233
8.3.2 Sequential Importance Sampling 235
8.3.3 Sequential Monte Carlo Filtering 240
8.3.4 Particle Filter 241
8.4 Object Representation Model 244
8.4.1 Visual Learning for Object Representation 245
8.4.2 Active Contour 246
8.4.3 Appearance Model 250
8.5 Summary 252
References 253
Chapter 9 Probabilistic Data Fusion for Robust Visual Tracking 254
9.1 Introduction 254
9.2 Earlier Work on Robust Visual Tracking 257
9.3 Data Fusion-Based Visual Tracker 260
9.3.1 Sequential Bayesian Estimator 260
9.3.2 The Four-Layer Data Fusion Visual Tracker 262
9.4 Layer 1: Visual Cue Fusion 264
9.4.1 Fusion Rules: Product Versus Weighted Sum 264
9.4.2 Adaptive Fusion Rule 266
9.4.3 Online Approach to Determining the Reliability of a Visual cue 267
9.5 Layer 2: Model Fusion 269
9.5.1 Pseudo-Measurement-Based Multiple Model Method 270
9.5.2 Likelihood Function 272
9.6 Layer 3: Tracker Fusion 273
9.6.1 Problem Formulation 274
9.6.2 Interactive Multiple Trackers 275
9.6.3 Practical Issues 276
9.7 Sensor Fusion 278
9.8 Implementation Issues and Empirical Results 280
9.8.1 Visual Cue Fusion Layer 280
9.8.2 Model Fusion Layer 283
9.8.3 Tracker Fusion Layer 285
9.8.4 Bottom-Up Fusion with a Three-Layer Structure 290
9.8.5 Multi-Sensor Fusion Tracking System Validation 290
9.9 Summary 292
References 293
Chapter 10 Multitarget Tracking in Video-Part I 295
10.1 Introduction 295
10.2 Overview of MTTV Methods 298
10.3 Static Model for Multitarget 300
10.3.1 Problem formulation 300
10.3.2 Observation Likelihood Function 302
10.3.3 Prior Model 303
10.4 Approximate Inference 304
10.4.1 Model Approximation 304
10.4.2 Algorithm Approximation 307
10.5 Fusing Information from Temporal and Bottom-Up Detectors 310
10.6 Experiments and Discussions 312
10.6.1 Proof-of-Concept 313
10.6.2 Comparison with Other Trackers 316
10.6.3 The Efficiency of the Gibbs Sampler 323
10.7 Summary 323
References 323
Chapter 11 Multi-Target Tracking in Video – Part II 326
11.1 Introduction 326
11.2 Overview of the MTTV Data Association Mechanism 329
11.2.1 Handing Data Association Explicitly 329
11.2.2 Handing Data Association Implicitly 331
11.2.3 Detection and Tracking 332
11.3 The Generative Model for MTT 333
11.3.1 Problem Formulation 333
11.3.2 The Generative Model 334
11.4 Approximating The Marginal Term 336
11.4.1 The State Prediction 337
11.4.2 Existence and Association Posterior 339
11.5 Approximating the Interactive Term 341
11.6 Hybrid Measurement Process 342
11.7 Experiments and Discussion 342
11.7.1 Tracking Soccer Players 343
11.7.2 Tracking Pedestrians in a Dynamic Scene 344
11.7.3 Discussion 344
11.8 Summary 347
References 347
Chapter 12 Information Processing in Cognition Process and New Artificial Intelligent Systems 349
12.1 Introduction 349
12.2 Cognitive Model: A Prototype of Intelligent System 351
12.3 Issues in Theories and Methodologies of Current Brain Research and Vision Science 353
12.4 Interactive Behaviors and Selective Attention in the Process of Visual Cognition 357
12.5 Intelligent Information Processing and Modeling Based on Cognitive Mechanisms 12.5.1 Cognitive Modeling and Behavioral Control in Complex Systems in an Information Environment 359
12.5.2 Distributed Cognition 362
12.5.3 Neurophysiological Mechanism of Learning and Memory and Information Processing Model 364
12.6 Cognitive Neurosciences and Computational Neuroscience 365
12.6.1 Consciousness and Intention Reading 366
12.6.2 The Core of Computational Neuroscience Is to Compute and Interpret the States of Nervous System 366
12.7 Soft Computing Method 366
12.8 Summary 367
References 368
Index 369