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Object detection, tracking and recognition in images are key problems in computer vision. This book provides the reader with a balanced treatment between the theory and practice of selected methods in these areas to make the book accessible to a range of researchers, engineers, developers and postgraduate students working in computer vision and related fields. Key features: * Explains the main theoretical ideas behind each method (which are augmented with a rigorous mathematical derivation of the formulas), their implementation (in C++) and demonstrated working in real applications. * Places…mehr
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Object detection, tracking and recognition in images are key problems in computer vision. This book provides the reader with a balanced treatment between the theory and practice of selected methods in these areas to make the book accessible to a range of researchers, engineers, developers and postgraduate students working in computer vision and related fields. Key features: * Explains the main theoretical ideas behind each method (which are augmented with a rigorous mathematical derivation of the formulas), their implementation (in C++) and demonstrated working in real applications. * Places an emphasis on tensor and statistical based approaches within object detection and recognition. * Provides an overview of image clustering and classification methods which includes subspace and kernel based processing, mean shift and Kalman filter, neural networks, and k-means methods. * Contains numerous case study examples of mainly automotive applications. * Includes a companion website hosting full C++ implementation, of topics presented in the book as a software library, and an accompanying manual to the software platform.
Produktdetails
- Produktdetails
- Verlag: John Wiley & Sons
- Seitenzahl: 552
- Erscheinungstermin: 20. Mai 2013
- Englisch
- ISBN-13: 9781118618363
- Artikelnr.: 38483139
- Verlag: John Wiley & Sons
- Seitenzahl: 552
- Erscheinungstermin: 20. Mai 2013
- Englisch
- ISBN-13: 9781118618363
- Artikelnr.: 38483139
Boguslaw Cyganek received his M.Sc. degree in electronics in 1993, then in computer science in 1996 from the AGH University of Science and Technology, Krakow, Poland. He obtained his Ph.D. degree cum laude in 2001 with a thesis on correlation of stereo images, and D.Sc. degree in 2011 with a thesis on methods and algorithms of object recognition in digital images. During the recent years, Dr. Boguslaw Cyganek has been cooperating with many scientific centers in development of computer vision systems. He has also gained several years of practical experience working as a Software Development Manager and a Senior Software Engineer both in the USA and Poland. He is currently a researcher and lecturer at the Department of Electronics, AGH University of Science and Technology. His research interests include computer vision, pattern recognition, as well as development of programmable devices and embedded systems. He is an author or a co-author of over eighty conference and journal papers and four books including An Introduction to 3D Computer Vision Techniques and Algorithms published by Wiley. Dr. Cyganek is a member of the IEEE, IAPR and SIAM.
Preface xiii Acknowledgements xv Notations and Abbreviations xvii 1
Introduction 1 1.1 A Sample of Computer Vision 3 1.2 Overview of Book
Contents 6 References 8 2 Tensor Methods in Computer Vision 9 2.1 Abstract
9 2.2 Tensor - A Mathematical Object 10 2.2.1 Main Properties of Linear
Spaces 10 2.2.2 Concept of a Tensor 11 2.3 Tensor - A Data Object 13 2.4
Basic Properties of Tensors 15 2.4.1 Notation of Tensor Indices and
Components 16 2.4.2 Tensor Products 18 2.5 Tensor Distance Measures 20
2.5.1 Overview of Tensor Distances 22 2.5.1.1 Computation of Matrix
Exponent and Logarithm Functions 24 2.5.2 Euclidean Image Distance and
Standardizing Transform 29 2.6 Filtering of Tensor Fields 33 2.6.1 Order
Statistic Filtering of Tensor Data 33 2.6.2 Anisotropic Diffusion Filtering
36 2.6.3 IMPLEMENTATION of Diffusion Processes 40 2.7 Looking into Images
with the Structural Tensor 44 2.7.1 Structural Tensor in Two-Dimensional
Image Space 47 2.7.2 Spatio-Temporal Structural Tensor 50 2.7.3
Multichannel and Scale-Space Structural Tensor 52 2.7.4 Extended Structural
Tensor 54 2.7.4.1 IMPLEMENTATION of the Linear and Nonlinear Structural
Tensor 57 2.8 Object Representation with Tensor of Inertia and Moments 62
2.8.1 IMPLEMENTATION of Moments and their Invariants 65 2.9
Eigendecomposition and Representation of Tensors 68 2.10 Tensor Invariants
72 2.11 Geometry of Multiple Views: The Multifocal Tensor 72 2.12
Multilinear Tensor Methods 75 2.12.1 Basic Concepts of Multilinear Algebra
78 2.12.1.1 Tensor Flattening 78 2.12.1.2 IMPLEMENTATION Tensor
Representation 84 2.12.1.3 The k-mode Product of a Tensor and a Matrix 95
2.12.1.4 Ranks of a Tensor 100 2.12.1.5 IMPLEMENTATION of Basic Operations
on Tensors 101 2.12.2 Higher-Order Singular Value Decomposition (HOSVD) 112
2.12.3 Computation of the HOSVD 114 2.12.3.1 Implementation of the HOSVD
Decomposition 119 2.12.4 HOSVD Induced Bases 121 2.12.5 Tensor Best Rank-1
Approximation 123 2.12.6 Rank-1 Decomposition of Tensors 126 2.12.7 Best
Rank-(R1, R2, . . . , RP) Approximation 131 2.12.8 Computation of the Best
Rank-(R1, R2, . . . , RP) Approximations 134 2.12.8.1 IMPLEMENTATION - Rank
Tensor Decompositions 137 2.12.8.2 CASE STUDY - Data Dimensionality
Reduction 145 2.12.9 Subspace Data Representation 149 2.12.10 Nonnegative
Matrix Factorization 151 2.12.11 Computation of the Nonnegative Matrix
Factorization 155 2.12.12 Image Representation with NMF 160 2.12.13
Implementation of the Nonnegative Matrix Factorization 162 2.12.14
Nonnegative Tensor Factorization 169 2.12.15 Multilinear Methods of Object
Recognition 173 2.13 Closure 179 2.13.1 Chapter Summary 179 2.13.2 Further
Reading 180 2.13.3 Problems and Exercises 181 References 182 3
Classification Methods and Algorithms 189 3.1 Abstract 189 3.2
Classification Framework 190 3.2.1 IMPLEMENTATION Computer Representation
of Features 191 3.3 Subspace Methods for Object Recognition 194 3.3.1
Principal Component Analysis 195 3.3.1.1 Computation of the PCA 199 3.3.1.2
PCA for Multi-Channel Image Processing 210 3.3.1.3 PCA for Background
Subtraction 214 3.3.2 Subspace Pattern Classification 215 3.4 Statistical
Formulation of the Object Recognition 222 3.4.1 Parametric and
Nonparametric Methods 222 3.4.2 Probabilistic Framework 222 3.4.3 Bayes
Decision Rule 223 3.4.4 Maximum a posteriori Classification Scheme 224
3.4.5 Binary Classification Problem 226 3.5 Parametric Methods - Mixture of
Gaussians 227 3.6 The Kalman Filter 233 3.7 Nonparametric Methods 236 3.7.1
Histogram Based Techniques 236 3.7.2 Comparing Histograms 239 3.7.3
IMPLEMENTATION - Multidimensional Histograms 243 3.7.4 Parzen Method 246
3.7.4.1 Kernel Based Methods 248 3.7.4.2 Nearest-Neighbor Method 250 3.8
The Mean Shift Method 251 3.8.1 Introduction to the Mean Shift 251 3.8.2
Continuously Adaptive Mean Shift Method (CamShift) 257 3.8.3 Algorithmic
Aspects of the Mean Shift Tracking 259 3.8.3.1 Tracking of Multiple
Features 259 3.8.3.2 Tracking of Multiple Objects 260 3.8.3.3 Fuzzy
Approach to the CamShift 261 3.8.3.4 Discrimination with Background
Information 262 3.8.3.5 Adaptive Update of the Classifiers 263 3.8.4
IMPLEMENTATION of the CamShift Method 264 3.9 Neural Networks 267 3.9.1
Probabilistic Neural Network 267 3.9.2 IMPLEMENTATION - Probabilistic
Neural Network 270 3.9.3 Hamming Neural Network 274 3.9.4 IMPLEMENTATION of
the Hamming Neural Network 278 3.9.5 Morphological Neural Network 282
3.9.5.1 IMPLEMENTATION of the Morphological Neural Network 285 3.10 Kernels
in Vision Pattern Recognition 291 3.10.1 Kernel Functions 296 3.10.2
IMPLEMENTATION - Kernels 301 3.11 Data Clustering 306 3.11.1 The k-Means
Algorithm 308 3.11.2 Fuzzy c-Means 311 3.11.3 Kernel Fuzzy c-Means 313
3.11.4 Measures of Cluster Quality 315 3.11.5 IMPLEMENTATION Issues 317
3.12 Support Vector Domain Description 327 3.12.1 Implementation of Support
Vector Machines 333 3.12.2 Architecture of the Ensemble of One-Class
Classifiers 334 3.13 Appendix - MATLAB R and other Packages for Pattern
Classification 336 3.14 Closure 336 3.14.1 Chapter Summary 336 3.14.2
Further Reading 337 Problems and Exercises 338 References 339 4 Object
Detection and Tracking 346 4.1 Introduction 346 4.2 Direct Pixel
Classification 346 4.2.1 Ground-Truth Data Collection 347 4.2.2 CASE STUDY
- Human Skin Detection 348 4.2.3 CASE STUDY - Pixel Based Road Signs
Detection 352 4.2.3.1 Fuzzy Approach 353 4.2.3.2 SVM Based Approach 353
4.2.4 Pixel Based Image Segmentation with Ensemble of Classifiers 361 4.3
Detection of Basic Shapes 364 4.3.1 Detection of Line Segments 366 4.3.2
UpWrite Detection of Convex Shapes 367 4.4 Figure Detection 370 4.4.1
Detection of Regular Shapes from Characteristic Points 371 4.4.2 Clustering
of the Salient Points 375 4.4.3 Adaptive Window Growing Method 376 4.4.4
Figure Verification 378 4.4.5 CASE STUDY - Road Signs Detection System 380
4.5 CASE STUDY - Road Signs Tracking and Recognition 385 4.6 CASE STUDY -
Framework for Object Tracking 389 4.7 Pedestrian Detection 395 4.8 Closure
402 4.8.1 Chapter Summary 402 4.8.2 Further Reading 402 Problems and
Exercises 403 References 403 5 Object Recognition 408 5.1 Abstract 408 5.2
Recognition from Tensor Phase Histograms and Morphological Scale Space 409
5.2.1 Computation of the Tensor Phase Histograms in Morphological Scale 411
5.2.2 Matching of the Tensor Phase Histograms 413 5.2.3 CASE STUDY - Object
Recognition with Tensor Phase Histograms in Morphological Scale Space 415
5.3 Invariant Based Recognition 420 5.3.1 CASE STUDY - Pictogram
Recognition with Affine Moment Invariants 421 5.4 Template Based
Recognition 424 5.4.1 Template Matching for Road Signs Recognition 425
5.4.2 Special Distances for Template Matching 428 5.4.3 Recognition with
the Log-Polar and Scale-Spaces 429 5.5 Recognition from Deformable Models
436 5.6 Ensembles of Classifiers 438 5.7 CASE STUDY - Ensemble of
Classifiers for Road Sign Recognition from Deformed Prototypes 440 5.7.1
Architecture of the Road Signs Recognition System 442 5.7.2 Module for
Recognition of Warning Signs 446 5.7.3 The Arbitration Unit 452 5.8
Recognition Based on Tensor Decompositions 453 5.8.1 Pattern Recognition in
SubSpaces Spanned by the HOSVD Decomposition of Pattern Tensors 453 5.8.2
CASE STUDY - Road Sign Recognition System Based on Decomposition of Tensors
with Deformable Pattern Prototypes 455 5.8.3 CASE STUDY - Handwritten Digit
Recognition with Tensor Decomposition Method 462 5.8.4 IMPLEMENTATION of
the Tensor Subspace Classifiers 465 5.9 Eye Recognition for Driver's State
Monitoring 470 5.10 Object Category Recognition 476 5.10.1 Part-Based
Object Recognition 476 5.10.2 Recognition with Bag-of-Visual-Words 477 5.11
Closure 480 5.11.1 Chapter Summary 480 5.11.2 Further Reading 481 Problems
and Exercises 482 Reference 483 A Appendix 487 A.1 Abstract 487 A.2
Morphological Scale-Space 487 A.3 Morphological Tensor Operators 490 A.4
Geometry of Quadratic Forms 491 A.5 Testing Classifiers 492 A.5.1
Implementation of the Confusion Matrix and Testing Object Detection in
Images 496 A.6 Code Acceleration with OpenMP 499 A.6.1 Recipes for
Object-Oriented Code Design with OpenMP 501 A.6.2 Hints on Using and Code
Porting to OpenMP 507 A.6.3 Performance Analysis 511 A.7 Useful MATLAB R
Functions for Matrix and Tensor Processing 512 A.8 Short Guide to the
Attached Software 513 A.9 Closure 516 A.9.1 Chapter Summary 516 A.9.2
Further Reading 519 Problems and Exercises 520 References 520 Index 523
Introduction 1 1.1 A Sample of Computer Vision 3 1.2 Overview of Book
Contents 6 References 8 2 Tensor Methods in Computer Vision 9 2.1 Abstract
9 2.2 Tensor - A Mathematical Object 10 2.2.1 Main Properties of Linear
Spaces 10 2.2.2 Concept of a Tensor 11 2.3 Tensor - A Data Object 13 2.4
Basic Properties of Tensors 15 2.4.1 Notation of Tensor Indices and
Components 16 2.4.2 Tensor Products 18 2.5 Tensor Distance Measures 20
2.5.1 Overview of Tensor Distances 22 2.5.1.1 Computation of Matrix
Exponent and Logarithm Functions 24 2.5.2 Euclidean Image Distance and
Standardizing Transform 29 2.6 Filtering of Tensor Fields 33 2.6.1 Order
Statistic Filtering of Tensor Data 33 2.6.2 Anisotropic Diffusion Filtering
36 2.6.3 IMPLEMENTATION of Diffusion Processes 40 2.7 Looking into Images
with the Structural Tensor 44 2.7.1 Structural Tensor in Two-Dimensional
Image Space 47 2.7.2 Spatio-Temporal Structural Tensor 50 2.7.3
Multichannel and Scale-Space Structural Tensor 52 2.7.4 Extended Structural
Tensor 54 2.7.4.1 IMPLEMENTATION of the Linear and Nonlinear Structural
Tensor 57 2.8 Object Representation with Tensor of Inertia and Moments 62
2.8.1 IMPLEMENTATION of Moments and their Invariants 65 2.9
Eigendecomposition and Representation of Tensors 68 2.10 Tensor Invariants
72 2.11 Geometry of Multiple Views: The Multifocal Tensor 72 2.12
Multilinear Tensor Methods 75 2.12.1 Basic Concepts of Multilinear Algebra
78 2.12.1.1 Tensor Flattening 78 2.12.1.2 IMPLEMENTATION Tensor
Representation 84 2.12.1.3 The k-mode Product of a Tensor and a Matrix 95
2.12.1.4 Ranks of a Tensor 100 2.12.1.5 IMPLEMENTATION of Basic Operations
on Tensors 101 2.12.2 Higher-Order Singular Value Decomposition (HOSVD) 112
2.12.3 Computation of the HOSVD 114 2.12.3.1 Implementation of the HOSVD
Decomposition 119 2.12.4 HOSVD Induced Bases 121 2.12.5 Tensor Best Rank-1
Approximation 123 2.12.6 Rank-1 Decomposition of Tensors 126 2.12.7 Best
Rank-(R1, R2, . . . , RP) Approximation 131 2.12.8 Computation of the Best
Rank-(R1, R2, . . . , RP) Approximations 134 2.12.8.1 IMPLEMENTATION - Rank
Tensor Decompositions 137 2.12.8.2 CASE STUDY - Data Dimensionality
Reduction 145 2.12.9 Subspace Data Representation 149 2.12.10 Nonnegative
Matrix Factorization 151 2.12.11 Computation of the Nonnegative Matrix
Factorization 155 2.12.12 Image Representation with NMF 160 2.12.13
Implementation of the Nonnegative Matrix Factorization 162 2.12.14
Nonnegative Tensor Factorization 169 2.12.15 Multilinear Methods of Object
Recognition 173 2.13 Closure 179 2.13.1 Chapter Summary 179 2.13.2 Further
Reading 180 2.13.3 Problems and Exercises 181 References 182 3
Classification Methods and Algorithms 189 3.1 Abstract 189 3.2
Classification Framework 190 3.2.1 IMPLEMENTATION Computer Representation
of Features 191 3.3 Subspace Methods for Object Recognition 194 3.3.1
Principal Component Analysis 195 3.3.1.1 Computation of the PCA 199 3.3.1.2
PCA for Multi-Channel Image Processing 210 3.3.1.3 PCA for Background
Subtraction 214 3.3.2 Subspace Pattern Classification 215 3.4 Statistical
Formulation of the Object Recognition 222 3.4.1 Parametric and
Nonparametric Methods 222 3.4.2 Probabilistic Framework 222 3.4.3 Bayes
Decision Rule 223 3.4.4 Maximum a posteriori Classification Scheme 224
3.4.5 Binary Classification Problem 226 3.5 Parametric Methods - Mixture of
Gaussians 227 3.6 The Kalman Filter 233 3.7 Nonparametric Methods 236 3.7.1
Histogram Based Techniques 236 3.7.2 Comparing Histograms 239 3.7.3
IMPLEMENTATION - Multidimensional Histograms 243 3.7.4 Parzen Method 246
3.7.4.1 Kernel Based Methods 248 3.7.4.2 Nearest-Neighbor Method 250 3.8
The Mean Shift Method 251 3.8.1 Introduction to the Mean Shift 251 3.8.2
Continuously Adaptive Mean Shift Method (CamShift) 257 3.8.3 Algorithmic
Aspects of the Mean Shift Tracking 259 3.8.3.1 Tracking of Multiple
Features 259 3.8.3.2 Tracking of Multiple Objects 260 3.8.3.3 Fuzzy
Approach to the CamShift 261 3.8.3.4 Discrimination with Background
Information 262 3.8.3.5 Adaptive Update of the Classifiers 263 3.8.4
IMPLEMENTATION of the CamShift Method 264 3.9 Neural Networks 267 3.9.1
Probabilistic Neural Network 267 3.9.2 IMPLEMENTATION - Probabilistic
Neural Network 270 3.9.3 Hamming Neural Network 274 3.9.4 IMPLEMENTATION of
the Hamming Neural Network 278 3.9.5 Morphological Neural Network 282
3.9.5.1 IMPLEMENTATION of the Morphological Neural Network 285 3.10 Kernels
in Vision Pattern Recognition 291 3.10.1 Kernel Functions 296 3.10.2
IMPLEMENTATION - Kernels 301 3.11 Data Clustering 306 3.11.1 The k-Means
Algorithm 308 3.11.2 Fuzzy c-Means 311 3.11.3 Kernel Fuzzy c-Means 313
3.11.4 Measures of Cluster Quality 315 3.11.5 IMPLEMENTATION Issues 317
3.12 Support Vector Domain Description 327 3.12.1 Implementation of Support
Vector Machines 333 3.12.2 Architecture of the Ensemble of One-Class
Classifiers 334 3.13 Appendix - MATLAB R and other Packages for Pattern
Classification 336 3.14 Closure 336 3.14.1 Chapter Summary 336 3.14.2
Further Reading 337 Problems and Exercises 338 References 339 4 Object
Detection and Tracking 346 4.1 Introduction 346 4.2 Direct Pixel
Classification 346 4.2.1 Ground-Truth Data Collection 347 4.2.2 CASE STUDY
- Human Skin Detection 348 4.2.3 CASE STUDY - Pixel Based Road Signs
Detection 352 4.2.3.1 Fuzzy Approach 353 4.2.3.2 SVM Based Approach 353
4.2.4 Pixel Based Image Segmentation with Ensemble of Classifiers 361 4.3
Detection of Basic Shapes 364 4.3.1 Detection of Line Segments 366 4.3.2
UpWrite Detection of Convex Shapes 367 4.4 Figure Detection 370 4.4.1
Detection of Regular Shapes from Characteristic Points 371 4.4.2 Clustering
of the Salient Points 375 4.4.3 Adaptive Window Growing Method 376 4.4.4
Figure Verification 378 4.4.5 CASE STUDY - Road Signs Detection System 380
4.5 CASE STUDY - Road Signs Tracking and Recognition 385 4.6 CASE STUDY -
Framework for Object Tracking 389 4.7 Pedestrian Detection 395 4.8 Closure
402 4.8.1 Chapter Summary 402 4.8.2 Further Reading 402 Problems and
Exercises 403 References 403 5 Object Recognition 408 5.1 Abstract 408 5.2
Recognition from Tensor Phase Histograms and Morphological Scale Space 409
5.2.1 Computation of the Tensor Phase Histograms in Morphological Scale 411
5.2.2 Matching of the Tensor Phase Histograms 413 5.2.3 CASE STUDY - Object
Recognition with Tensor Phase Histograms in Morphological Scale Space 415
5.3 Invariant Based Recognition 420 5.3.1 CASE STUDY - Pictogram
Recognition with Affine Moment Invariants 421 5.4 Template Based
Recognition 424 5.4.1 Template Matching for Road Signs Recognition 425
5.4.2 Special Distances for Template Matching 428 5.4.3 Recognition with
the Log-Polar and Scale-Spaces 429 5.5 Recognition from Deformable Models
436 5.6 Ensembles of Classifiers 438 5.7 CASE STUDY - Ensemble of
Classifiers for Road Sign Recognition from Deformed Prototypes 440 5.7.1
Architecture of the Road Signs Recognition System 442 5.7.2 Module for
Recognition of Warning Signs 446 5.7.3 The Arbitration Unit 452 5.8
Recognition Based on Tensor Decompositions 453 5.8.1 Pattern Recognition in
SubSpaces Spanned by the HOSVD Decomposition of Pattern Tensors 453 5.8.2
CASE STUDY - Road Sign Recognition System Based on Decomposition of Tensors
with Deformable Pattern Prototypes 455 5.8.3 CASE STUDY - Handwritten Digit
Recognition with Tensor Decomposition Method 462 5.8.4 IMPLEMENTATION of
the Tensor Subspace Classifiers 465 5.9 Eye Recognition for Driver's State
Monitoring 470 5.10 Object Category Recognition 476 5.10.1 Part-Based
Object Recognition 476 5.10.2 Recognition with Bag-of-Visual-Words 477 5.11
Closure 480 5.11.1 Chapter Summary 480 5.11.2 Further Reading 481 Problems
and Exercises 482 Reference 483 A Appendix 487 A.1 Abstract 487 A.2
Morphological Scale-Space 487 A.3 Morphological Tensor Operators 490 A.4
Geometry of Quadratic Forms 491 A.5 Testing Classifiers 492 A.5.1
Implementation of the Confusion Matrix and Testing Object Detection in
Images 496 A.6 Code Acceleration with OpenMP 499 A.6.1 Recipes for
Object-Oriented Code Design with OpenMP 501 A.6.2 Hints on Using and Code
Porting to OpenMP 507 A.6.3 Performance Analysis 511 A.7 Useful MATLAB R
Functions for Matrix and Tensor Processing 512 A.8 Short Guide to the
Attached Software 513 A.9 Closure 516 A.9.1 Chapter Summary 516 A.9.2
Further Reading 519 Problems and Exercises 520 References 520 Index 523
Preface xiii Acknowledgements xv Notations and Abbreviations xvii 1
Introduction 1 1.1 A Sample of Computer Vision 3 1.2 Overview of Book
Contents 6 References 8 2 Tensor Methods in Computer Vision 9 2.1 Abstract
9 2.2 Tensor - A Mathematical Object 10 2.2.1 Main Properties of Linear
Spaces 10 2.2.2 Concept of a Tensor 11 2.3 Tensor - A Data Object 13 2.4
Basic Properties of Tensors 15 2.4.1 Notation of Tensor Indices and
Components 16 2.4.2 Tensor Products 18 2.5 Tensor Distance Measures 20
2.5.1 Overview of Tensor Distances 22 2.5.1.1 Computation of Matrix
Exponent and Logarithm Functions 24 2.5.2 Euclidean Image Distance and
Standardizing Transform 29 2.6 Filtering of Tensor Fields 33 2.6.1 Order
Statistic Filtering of Tensor Data 33 2.6.2 Anisotropic Diffusion Filtering
36 2.6.3 IMPLEMENTATION of Diffusion Processes 40 2.7 Looking into Images
with the Structural Tensor 44 2.7.1 Structural Tensor in Two-Dimensional
Image Space 47 2.7.2 Spatio-Temporal Structural Tensor 50 2.7.3
Multichannel and Scale-Space Structural Tensor 52 2.7.4 Extended Structural
Tensor 54 2.7.4.1 IMPLEMENTATION of the Linear and Nonlinear Structural
Tensor 57 2.8 Object Representation with Tensor of Inertia and Moments 62
2.8.1 IMPLEMENTATION of Moments and their Invariants 65 2.9
Eigendecomposition and Representation of Tensors 68 2.10 Tensor Invariants
72 2.11 Geometry of Multiple Views: The Multifocal Tensor 72 2.12
Multilinear Tensor Methods 75 2.12.1 Basic Concepts of Multilinear Algebra
78 2.12.1.1 Tensor Flattening 78 2.12.1.2 IMPLEMENTATION Tensor
Representation 84 2.12.1.3 The k-mode Product of a Tensor and a Matrix 95
2.12.1.4 Ranks of a Tensor 100 2.12.1.5 IMPLEMENTATION of Basic Operations
on Tensors 101 2.12.2 Higher-Order Singular Value Decomposition (HOSVD) 112
2.12.3 Computation of the HOSVD 114 2.12.3.1 Implementation of the HOSVD
Decomposition 119 2.12.4 HOSVD Induced Bases 121 2.12.5 Tensor Best Rank-1
Approximation 123 2.12.6 Rank-1 Decomposition of Tensors 126 2.12.7 Best
Rank-(R1, R2, . . . , RP) Approximation 131 2.12.8 Computation of the Best
Rank-(R1, R2, . . . , RP) Approximations 134 2.12.8.1 IMPLEMENTATION - Rank
Tensor Decompositions 137 2.12.8.2 CASE STUDY - Data Dimensionality
Reduction 145 2.12.9 Subspace Data Representation 149 2.12.10 Nonnegative
Matrix Factorization 151 2.12.11 Computation of the Nonnegative Matrix
Factorization 155 2.12.12 Image Representation with NMF 160 2.12.13
Implementation of the Nonnegative Matrix Factorization 162 2.12.14
Nonnegative Tensor Factorization 169 2.12.15 Multilinear Methods of Object
Recognition 173 2.13 Closure 179 2.13.1 Chapter Summary 179 2.13.2 Further
Reading 180 2.13.3 Problems and Exercises 181 References 182 3
Classification Methods and Algorithms 189 3.1 Abstract 189 3.2
Classification Framework 190 3.2.1 IMPLEMENTATION Computer Representation
of Features 191 3.3 Subspace Methods for Object Recognition 194 3.3.1
Principal Component Analysis 195 3.3.1.1 Computation of the PCA 199 3.3.1.2
PCA for Multi-Channel Image Processing 210 3.3.1.3 PCA for Background
Subtraction 214 3.3.2 Subspace Pattern Classification 215 3.4 Statistical
Formulation of the Object Recognition 222 3.4.1 Parametric and
Nonparametric Methods 222 3.4.2 Probabilistic Framework 222 3.4.3 Bayes
Decision Rule 223 3.4.4 Maximum a posteriori Classification Scheme 224
3.4.5 Binary Classification Problem 226 3.5 Parametric Methods - Mixture of
Gaussians 227 3.6 The Kalman Filter 233 3.7 Nonparametric Methods 236 3.7.1
Histogram Based Techniques 236 3.7.2 Comparing Histograms 239 3.7.3
IMPLEMENTATION - Multidimensional Histograms 243 3.7.4 Parzen Method 246
3.7.4.1 Kernel Based Methods 248 3.7.4.2 Nearest-Neighbor Method 250 3.8
The Mean Shift Method 251 3.8.1 Introduction to the Mean Shift 251 3.8.2
Continuously Adaptive Mean Shift Method (CamShift) 257 3.8.3 Algorithmic
Aspects of the Mean Shift Tracking 259 3.8.3.1 Tracking of Multiple
Features 259 3.8.3.2 Tracking of Multiple Objects 260 3.8.3.3 Fuzzy
Approach to the CamShift 261 3.8.3.4 Discrimination with Background
Information 262 3.8.3.5 Adaptive Update of the Classifiers 263 3.8.4
IMPLEMENTATION of the CamShift Method 264 3.9 Neural Networks 267 3.9.1
Probabilistic Neural Network 267 3.9.2 IMPLEMENTATION - Probabilistic
Neural Network 270 3.9.3 Hamming Neural Network 274 3.9.4 IMPLEMENTATION of
the Hamming Neural Network 278 3.9.5 Morphological Neural Network 282
3.9.5.1 IMPLEMENTATION of the Morphological Neural Network 285 3.10 Kernels
in Vision Pattern Recognition 291 3.10.1 Kernel Functions 296 3.10.2
IMPLEMENTATION - Kernels 301 3.11 Data Clustering 306 3.11.1 The k-Means
Algorithm 308 3.11.2 Fuzzy c-Means 311 3.11.3 Kernel Fuzzy c-Means 313
3.11.4 Measures of Cluster Quality 315 3.11.5 IMPLEMENTATION Issues 317
3.12 Support Vector Domain Description 327 3.12.1 Implementation of Support
Vector Machines 333 3.12.2 Architecture of the Ensemble of One-Class
Classifiers 334 3.13 Appendix - MATLAB R and other Packages for Pattern
Classification 336 3.14 Closure 336 3.14.1 Chapter Summary 336 3.14.2
Further Reading 337 Problems and Exercises 338 References 339 4 Object
Detection and Tracking 346 4.1 Introduction 346 4.2 Direct Pixel
Classification 346 4.2.1 Ground-Truth Data Collection 347 4.2.2 CASE STUDY
- Human Skin Detection 348 4.2.3 CASE STUDY - Pixel Based Road Signs
Detection 352 4.2.3.1 Fuzzy Approach 353 4.2.3.2 SVM Based Approach 353
4.2.4 Pixel Based Image Segmentation with Ensemble of Classifiers 361 4.3
Detection of Basic Shapes 364 4.3.1 Detection of Line Segments 366 4.3.2
UpWrite Detection of Convex Shapes 367 4.4 Figure Detection 370 4.4.1
Detection of Regular Shapes from Characteristic Points 371 4.4.2 Clustering
of the Salient Points 375 4.4.3 Adaptive Window Growing Method 376 4.4.4
Figure Verification 378 4.4.5 CASE STUDY - Road Signs Detection System 380
4.5 CASE STUDY - Road Signs Tracking and Recognition 385 4.6 CASE STUDY -
Framework for Object Tracking 389 4.7 Pedestrian Detection 395 4.8 Closure
402 4.8.1 Chapter Summary 402 4.8.2 Further Reading 402 Problems and
Exercises 403 References 403 5 Object Recognition 408 5.1 Abstract 408 5.2
Recognition from Tensor Phase Histograms and Morphological Scale Space 409
5.2.1 Computation of the Tensor Phase Histograms in Morphological Scale 411
5.2.2 Matching of the Tensor Phase Histograms 413 5.2.3 CASE STUDY - Object
Recognition with Tensor Phase Histograms in Morphological Scale Space 415
5.3 Invariant Based Recognition 420 5.3.1 CASE STUDY - Pictogram
Recognition with Affine Moment Invariants 421 5.4 Template Based
Recognition 424 5.4.1 Template Matching for Road Signs Recognition 425
5.4.2 Special Distances for Template Matching 428 5.4.3 Recognition with
the Log-Polar and Scale-Spaces 429 5.5 Recognition from Deformable Models
436 5.6 Ensembles of Classifiers 438 5.7 CASE STUDY - Ensemble of
Classifiers for Road Sign Recognition from Deformed Prototypes 440 5.7.1
Architecture of the Road Signs Recognition System 442 5.7.2 Module for
Recognition of Warning Signs 446 5.7.3 The Arbitration Unit 452 5.8
Recognition Based on Tensor Decompositions 453 5.8.1 Pattern Recognition in
SubSpaces Spanned by the HOSVD Decomposition of Pattern Tensors 453 5.8.2
CASE STUDY - Road Sign Recognition System Based on Decomposition of Tensors
with Deformable Pattern Prototypes 455 5.8.3 CASE STUDY - Handwritten Digit
Recognition with Tensor Decomposition Method 462 5.8.4 IMPLEMENTATION of
the Tensor Subspace Classifiers 465 5.9 Eye Recognition for Driver's State
Monitoring 470 5.10 Object Category Recognition 476 5.10.1 Part-Based
Object Recognition 476 5.10.2 Recognition with Bag-of-Visual-Words 477 5.11
Closure 480 5.11.1 Chapter Summary 480 5.11.2 Further Reading 481 Problems
and Exercises 482 Reference 483 A Appendix 487 A.1 Abstract 487 A.2
Morphological Scale-Space 487 A.3 Morphological Tensor Operators 490 A.4
Geometry of Quadratic Forms 491 A.5 Testing Classifiers 492 A.5.1
Implementation of the Confusion Matrix and Testing Object Detection in
Images 496 A.6 Code Acceleration with OpenMP 499 A.6.1 Recipes for
Object-Oriented Code Design with OpenMP 501 A.6.2 Hints on Using and Code
Porting to OpenMP 507 A.6.3 Performance Analysis 511 A.7 Useful MATLAB R
Functions for Matrix and Tensor Processing 512 A.8 Short Guide to the
Attached Software 513 A.9 Closure 516 A.9.1 Chapter Summary 516 A.9.2
Further Reading 519 Problems and Exercises 520 References 520 Index 523
Introduction 1 1.1 A Sample of Computer Vision 3 1.2 Overview of Book
Contents 6 References 8 2 Tensor Methods in Computer Vision 9 2.1 Abstract
9 2.2 Tensor - A Mathematical Object 10 2.2.1 Main Properties of Linear
Spaces 10 2.2.2 Concept of a Tensor 11 2.3 Tensor - A Data Object 13 2.4
Basic Properties of Tensors 15 2.4.1 Notation of Tensor Indices and
Components 16 2.4.2 Tensor Products 18 2.5 Tensor Distance Measures 20
2.5.1 Overview of Tensor Distances 22 2.5.1.1 Computation of Matrix
Exponent and Logarithm Functions 24 2.5.2 Euclidean Image Distance and
Standardizing Transform 29 2.6 Filtering of Tensor Fields 33 2.6.1 Order
Statistic Filtering of Tensor Data 33 2.6.2 Anisotropic Diffusion Filtering
36 2.6.3 IMPLEMENTATION of Diffusion Processes 40 2.7 Looking into Images
with the Structural Tensor 44 2.7.1 Structural Tensor in Two-Dimensional
Image Space 47 2.7.2 Spatio-Temporal Structural Tensor 50 2.7.3
Multichannel and Scale-Space Structural Tensor 52 2.7.4 Extended Structural
Tensor 54 2.7.4.1 IMPLEMENTATION of the Linear and Nonlinear Structural
Tensor 57 2.8 Object Representation with Tensor of Inertia and Moments 62
2.8.1 IMPLEMENTATION of Moments and their Invariants 65 2.9
Eigendecomposition and Representation of Tensors 68 2.10 Tensor Invariants
72 2.11 Geometry of Multiple Views: The Multifocal Tensor 72 2.12
Multilinear Tensor Methods 75 2.12.1 Basic Concepts of Multilinear Algebra
78 2.12.1.1 Tensor Flattening 78 2.12.1.2 IMPLEMENTATION Tensor
Representation 84 2.12.1.3 The k-mode Product of a Tensor and a Matrix 95
2.12.1.4 Ranks of a Tensor 100 2.12.1.5 IMPLEMENTATION of Basic Operations
on Tensors 101 2.12.2 Higher-Order Singular Value Decomposition (HOSVD) 112
2.12.3 Computation of the HOSVD 114 2.12.3.1 Implementation of the HOSVD
Decomposition 119 2.12.4 HOSVD Induced Bases 121 2.12.5 Tensor Best Rank-1
Approximation 123 2.12.6 Rank-1 Decomposition of Tensors 126 2.12.7 Best
Rank-(R1, R2, . . . , RP) Approximation 131 2.12.8 Computation of the Best
Rank-(R1, R2, . . . , RP) Approximations 134 2.12.8.1 IMPLEMENTATION - Rank
Tensor Decompositions 137 2.12.8.2 CASE STUDY - Data Dimensionality
Reduction 145 2.12.9 Subspace Data Representation 149 2.12.10 Nonnegative
Matrix Factorization 151 2.12.11 Computation of the Nonnegative Matrix
Factorization 155 2.12.12 Image Representation with NMF 160 2.12.13
Implementation of the Nonnegative Matrix Factorization 162 2.12.14
Nonnegative Tensor Factorization 169 2.12.15 Multilinear Methods of Object
Recognition 173 2.13 Closure 179 2.13.1 Chapter Summary 179 2.13.2 Further
Reading 180 2.13.3 Problems and Exercises 181 References 182 3
Classification Methods and Algorithms 189 3.1 Abstract 189 3.2
Classification Framework 190 3.2.1 IMPLEMENTATION Computer Representation
of Features 191 3.3 Subspace Methods for Object Recognition 194 3.3.1
Principal Component Analysis 195 3.3.1.1 Computation of the PCA 199 3.3.1.2
PCA for Multi-Channel Image Processing 210 3.3.1.3 PCA for Background
Subtraction 214 3.3.2 Subspace Pattern Classification 215 3.4 Statistical
Formulation of the Object Recognition 222 3.4.1 Parametric and
Nonparametric Methods 222 3.4.2 Probabilistic Framework 222 3.4.3 Bayes
Decision Rule 223 3.4.4 Maximum a posteriori Classification Scheme 224
3.4.5 Binary Classification Problem 226 3.5 Parametric Methods - Mixture of
Gaussians 227 3.6 The Kalman Filter 233 3.7 Nonparametric Methods 236 3.7.1
Histogram Based Techniques 236 3.7.2 Comparing Histograms 239 3.7.3
IMPLEMENTATION - Multidimensional Histograms 243 3.7.4 Parzen Method 246
3.7.4.1 Kernel Based Methods 248 3.7.4.2 Nearest-Neighbor Method 250 3.8
The Mean Shift Method 251 3.8.1 Introduction to the Mean Shift 251 3.8.2
Continuously Adaptive Mean Shift Method (CamShift) 257 3.8.3 Algorithmic
Aspects of the Mean Shift Tracking 259 3.8.3.1 Tracking of Multiple
Features 259 3.8.3.2 Tracking of Multiple Objects 260 3.8.3.3 Fuzzy
Approach to the CamShift 261 3.8.3.4 Discrimination with Background
Information 262 3.8.3.5 Adaptive Update of the Classifiers 263 3.8.4
IMPLEMENTATION of the CamShift Method 264 3.9 Neural Networks 267 3.9.1
Probabilistic Neural Network 267 3.9.2 IMPLEMENTATION - Probabilistic
Neural Network 270 3.9.3 Hamming Neural Network 274 3.9.4 IMPLEMENTATION of
the Hamming Neural Network 278 3.9.5 Morphological Neural Network 282
3.9.5.1 IMPLEMENTATION of the Morphological Neural Network 285 3.10 Kernels
in Vision Pattern Recognition 291 3.10.1 Kernel Functions 296 3.10.2
IMPLEMENTATION - Kernels 301 3.11 Data Clustering 306 3.11.1 The k-Means
Algorithm 308 3.11.2 Fuzzy c-Means 311 3.11.3 Kernel Fuzzy c-Means 313
3.11.4 Measures of Cluster Quality 315 3.11.5 IMPLEMENTATION Issues 317
3.12 Support Vector Domain Description 327 3.12.1 Implementation of Support
Vector Machines 333 3.12.2 Architecture of the Ensemble of One-Class
Classifiers 334 3.13 Appendix - MATLAB R and other Packages for Pattern
Classification 336 3.14 Closure 336 3.14.1 Chapter Summary 336 3.14.2
Further Reading 337 Problems and Exercises 338 References 339 4 Object
Detection and Tracking 346 4.1 Introduction 346 4.2 Direct Pixel
Classification 346 4.2.1 Ground-Truth Data Collection 347 4.2.2 CASE STUDY
- Human Skin Detection 348 4.2.3 CASE STUDY - Pixel Based Road Signs
Detection 352 4.2.3.1 Fuzzy Approach 353 4.2.3.2 SVM Based Approach 353
4.2.4 Pixel Based Image Segmentation with Ensemble of Classifiers 361 4.3
Detection of Basic Shapes 364 4.3.1 Detection of Line Segments 366 4.3.2
UpWrite Detection of Convex Shapes 367 4.4 Figure Detection 370 4.4.1
Detection of Regular Shapes from Characteristic Points 371 4.4.2 Clustering
of the Salient Points 375 4.4.3 Adaptive Window Growing Method 376 4.4.4
Figure Verification 378 4.4.5 CASE STUDY - Road Signs Detection System 380
4.5 CASE STUDY - Road Signs Tracking and Recognition 385 4.6 CASE STUDY -
Framework for Object Tracking 389 4.7 Pedestrian Detection 395 4.8 Closure
402 4.8.1 Chapter Summary 402 4.8.2 Further Reading 402 Problems and
Exercises 403 References 403 5 Object Recognition 408 5.1 Abstract 408 5.2
Recognition from Tensor Phase Histograms and Morphological Scale Space 409
5.2.1 Computation of the Tensor Phase Histograms in Morphological Scale 411
5.2.2 Matching of the Tensor Phase Histograms 413 5.2.3 CASE STUDY - Object
Recognition with Tensor Phase Histograms in Morphological Scale Space 415
5.3 Invariant Based Recognition 420 5.3.1 CASE STUDY - Pictogram
Recognition with Affine Moment Invariants 421 5.4 Template Based
Recognition 424 5.4.1 Template Matching for Road Signs Recognition 425
5.4.2 Special Distances for Template Matching 428 5.4.3 Recognition with
the Log-Polar and Scale-Spaces 429 5.5 Recognition from Deformable Models
436 5.6 Ensembles of Classifiers 438 5.7 CASE STUDY - Ensemble of
Classifiers for Road Sign Recognition from Deformed Prototypes 440 5.7.1
Architecture of the Road Signs Recognition System 442 5.7.2 Module for
Recognition of Warning Signs 446 5.7.3 The Arbitration Unit 452 5.8
Recognition Based on Tensor Decompositions 453 5.8.1 Pattern Recognition in
SubSpaces Spanned by the HOSVD Decomposition of Pattern Tensors 453 5.8.2
CASE STUDY - Road Sign Recognition System Based on Decomposition of Tensors
with Deformable Pattern Prototypes 455 5.8.3 CASE STUDY - Handwritten Digit
Recognition with Tensor Decomposition Method 462 5.8.4 IMPLEMENTATION of
the Tensor Subspace Classifiers 465 5.9 Eye Recognition for Driver's State
Monitoring 470 5.10 Object Category Recognition 476 5.10.1 Part-Based
Object Recognition 476 5.10.2 Recognition with Bag-of-Visual-Words 477 5.11
Closure 480 5.11.1 Chapter Summary 480 5.11.2 Further Reading 481 Problems
and Exercises 482 Reference 483 A Appendix 487 A.1 Abstract 487 A.2
Morphological Scale-Space 487 A.3 Morphological Tensor Operators 490 A.4
Geometry of Quadratic Forms 491 A.5 Testing Classifiers 492 A.5.1
Implementation of the Confusion Matrix and Testing Object Detection in
Images 496 A.6 Code Acceleration with OpenMP 499 A.6.1 Recipes for
Object-Oriented Code Design with OpenMP 501 A.6.2 Hints on Using and Code
Porting to OpenMP 507 A.6.3 Performance Analysis 511 A.7 Useful MATLAB R
Functions for Matrix and Tensor Processing 512 A.8 Short Guide to the
Attached Software 513 A.9 Closure 516 A.9.1 Chapter Summary 516 A.9.2
Further Reading 519 Problems and Exercises 520 References 520 Index 523