OBJECT DETECTION AND RECOGNITION IN DIGITAL IMAGES
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1 OBJECT DETECTION AND RECOGNITION IN DIGITAL IMAGES THEORY AND PRACTICE Bogustaw Cyganek AGH University of Science and Technology, Poland WILEY A John Wiley &. Sons, Ltd., Publication
2 Contents Preface Acknowledgements Notations and Abbreviations xiii xv xvii 1 Introduction A Sample of Computer Vision Overview of Book Contents 6 References 8 2 Tensor Methods in Computer Vision Abstract Tensor - A Mathematical Object Main Properties of Linear Spaces Concept of a Tensor Tensor - A Data Object Basic Properties of Tensors Notation of Tensor Indices and Components Tensor Products Tensor Distance Measures Overview of Tensor Distances Computation of Matrix Exponent and Logarithm Functions Euclidean Image Distance and Standardizing Transform Filtering of Tensor Fields Order Statistic Filtering of Tensor Data Anisotropic Diffusion Filtering IMPLEMENTATION of Diffusion Processes Looking into Images with the Structural Tensor / Structural Tensor in Two-Dimensional Image Space Spatio-Temporal Structural Tensor Multichannel and Scale-Space Structural Tensor Extended Structural Tensor IMPLEMENTATION of the Linear and Nonlinear Structural Tensor 57
3 Vlll Contents 2.8 Object Representation with Tensor of Inertia and Moments IMPLEMENTATION of Moments and their Invariants Eigendecomposition and Representation of Tensors Tensor Invariants Geometry of Multiple Views: The Multifocal Tensor Multilinear Tensor Methods Basic Concepts of Multilinear Algebra Tensor Flattening IMPLEMENTATION Tensor Representation The k-mode Product of a Tensor and a Matrix Ranks of a Tensor IMPLEMENTATION of Basic Operations on Tensors Higher-Order Singular Value Decomposition (HOSVD) Computation of the HOSVD Implementation of the HOSVD Decomposition HOSVD Induced Bases Tensor Best Rank-1 Approximation Rank-1 Decomposition of Tensors Best Rank-(Rj, R2,..., Rp) Approximation Computation of the Best Rank-(R], R2,..., Rp) Approximations IMPLEMENTATION - Rank Tensor Decompositions CASE STUDY - Data Dimensionality Reduction Subspace Data Representation Nonnegative Matrix Factorization Computation of the Nonnegative Matrix Factorization Image Representation with NMF Implementation of the Nonnegative Matrix Factorization Nonnegative Tensor Factorization Multilinear Methods of Object Recognition Closure Chapter Summary Further Reading Problems and Exercises 181 References Classification Methods and Algorithms Abstract Classification Framework IMPLEMENTATION Computer Representation of Features Subspace Methods for Object Recognition Principal Component Analysis Computation ofthe PC A PCA for Multi-Channel Image Processing PCA for Background Subtraction Subspace Pattern Classification 215
4 Contents ix 3.4 Statistical Formulation of the Object Recognition Parametric and Nonparametric Methods Probabilistic Framework Bay es Decision Rule Maximum a posteriori Classification Scheme Binary Classification Problem Parametric Methods - Mixture of Gaussians The Kaiman Filter Nonparametric Methods Histogram Based Techniques Comparing Histograms IMPLEMENTATION - Multidimensional Histograms Parzen Method Kernel Based Methods Nearest-Neighbor Method The Mean Shift Method Introduction to the Mean Shift Continuously Adaptive Mean Shift Method (CamShiff) Algorithmic Aspects ofthe Mean Shift Tracking Tracking of Multiple Features Tracking of Multiple Objects Fuzzy Approach to the CamShift Discrimination with Background Information Adaptive Update ofthe Classifiers IMPLEMENTATION of the CamShift Method Neural Networks Probabilistic Neural Network IMPLEMENTATION - Probabilistic Neural Network Hamming Neural Network IIA IMPLEMENTATION of the Hamming Neural Network Morphological Neural Network IMPLEMENTATION of the Morphological Neural Network Kernels in Vision Pattern Recognition Kernel Functions IMPLEMENTATION-Kernels Data Clustering The k-means Algorithm Fuzzy c-means Kernel Fuzzy c-means Measures of Cluster Quality IMPLEMENTATION Issues Support Vector Domain Description Implementation of Support Vector Machines Architecture of the Ensemble of One-Class Classifiers Appendix - MATLAB and other Packages for Pattern Classification Closure 336
5 X Contents Chapter Summary Further Reading 337 Problems and Exercises 338 References Object Detection and Tracking Introduction Direct Pixel Classification Ground-Truth Data Collection CASE STUDY - Human Skin Detection CASE STUDY - Pixel Based Road Signs Detection Fuzzy Approach SVM Based Approach Pixel Based Image Segmentation with Ensemble of Classifiers Detection of Basic Shapes Detection of Line Segments Up Write Detection ofconvex Shapes Figure Detection Detection of Regular Shapes from Characteristic Points Clustering of the Salient Points Adaptive Window Growing Method Figure Verification, CASE STUDY - Road Signs Detection System CASE STUDY - Road Signs Tracking and Recognition CASE STUDY - Framework for Object Tracking Pedestrian Detection Closure Chapter Summary Further Reading 402 Problems and Exercises 403 References Object Recognition Abstract Recognition from Tensor Phase Histograms and Morphological Scale Space Computation of the Tensor Phase Histograms in Morphological Scale Matching of the Tensor Phase Histograms CASE STUDY- Object Recognition with Tensor Phase Histograms in Morphological Scale Space Invariant Based Recognition CASE STUDY - Pictogram Recognition with Affine Moment Invariants Template Based Recognition Template Matching for Road Signs Recognition Special Distances for Template Matching Recognition with the Log-Polar and Scale-Spaces 429
6 Contents XI 5.5 Recognition from Deformable Models Ensembles of Classifiers CASE STUDY - Ensemble of Classifiers for Road Sign Recognition from Deformed Prototypes / Architecture of the Road Signs Recognition System Module for Recognition of Warning Signs The Arbitration Unit Recognition Based on Tensor Decompositions Pattern Recognition in SubSpaces Spanned by the HOSVD Decomposition of Pattern Tensors CASE STUDY- Road Sign Recognition System Based on Decomposition of Tensors with Deformable Pattern Prototypes CASE STUDY - Handwritten Digit Recognition with Tensor Decomposition Method IMPLEMENTATION of the Tensor Subspace Classifiers Eye Recognition for Driver's State Monitoring Object Category Recognition Part-Based Object Recognition Al Recognition with Bag-of-Visual-Words All 5.11 Closure Chapter Summary /.2 Further Reading 481 Problems and Exercises 482 Reference 483 A Appendix 487 A.l 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 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
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