Object detection and recognition in digital images: theory and practice

Preface

Acknowledgements

Notations and Abbreviations

1. Introduction

1.1. A Sample of Computer Vision

1.2. Overview of Book Contents

References

2. Tensor Methods in Computer Vision

2.1. Abstract

2.2. Tensor - A Mathematical Object

2.2.1. Main Properties of Linear Spaces

2.2.2. Concept of a Tensor

2.3. Tensor - A Data Object

2.4. Basic Properties of Tensors

2.4.1. Notation of Tensor Indices and Components

2.4.2. Tensor Products

2.5. Tensor Distance Measures

2.5.1. Overview of Tensor Distances

2.5.1.1. Computation of Matrix Exponent and Logarithm Functions

2.5.2. Euclidean Image Distance and Standardizing Transform

2.6. Filtering of Tensor Fields

2.6.1. Order Statistic Filtering of Tensor Data

2.6.2. Anisotropic Diffusion Filtering

2.6.3. IMPLEMENTATION of Diffusion Processes

2.7. Looking into Images with the Structural Tensor

2.7.1. Structural Tensor in Two-Dimensional Image Space

2.7.2. Spatio-Temporal Structural Tensor

2.7.3. Multichannel and Scale-Space Structural Tensor

2.7.4. Extended Structural Tensor

2.7.4.1. IMPLEMENTATION of the Linear and Nonlinear Structural Tensor

2.8. Object Representation with Tensor of Inertia and Moments

2.8.1. IMPLEMENTATION of Moments and their Invariants

2.9. Eigendecomposition and Representation of Tensors

2.10. Tensor Invariants

2.11. Geometry of Multiple Views: The Multifocal Tensor

2.12. Multilinear Tensor Methods

2.12.1. Basic Concepts of Multilinear Algebra

2.12.1.1. Tensor Flattening

2.12.1.2. IMPLEMENTATION Tensor Representation

2.12.1.3. The k-mode Product of a Tensor and a Matrix

2.12.1.4. Ranks of a Tensor

2.12.1.5. IMPLEMENTATION of Basic Operations on Tensors

2.12.2. Higher-Order Singular Value Decomposition (HOSVD)

2.12.3. Computation of the HOSVD

2.12.3.1. Implementation of the HOSVD Decomposition

2.12.4. HOSVD Induced Bases

2.12.5. Tensor Best Rank-1 Approximation

2.12.6. Rank-1 Decomposition of Tensors

2.12.7. Best Rank-(R 1 , R 2 , …, R P ) Approximation

2.12.8. Computation of the Best Rank-(R 1 , R 2 , … R P ) Approximations

2.12.8.1. IMPLEMENTATION-Rank Tensor Decompositions

2.12.8.2. CASE STUDY - Data Dimensionality Reduction

2.12.9. Subspace Data Representation

2.12.10. Nonnegative Matrix Factorization

2.12.11. Computation of the Nonnegative Matrix Factorization

2.12.12. Image Representation with NMF

2.12.13. Implementation of the Nonnegative Matrix Factorization

2.12.14. Nonnegative Tensor Factorization

2.12.15. Multilinear Methods of Object Recognition

2.13. Closure

2.13.1. Chapter Summary

2.13.2. Further Reading

2.13.3. Problems and Exercises

References

3. Classification Methods and Algorithms

3.1. Abstract

3.2. Classification Framework

3.2.1. IMPLEMENTATION Computer Representation of Features

3.3. Subspace Methods for Object Recognition

3.3.1. Principal Component Analysis

3.3.1.1. Computation of the PCA

3.3.1.2. PCA for Multi-Channel Image Processing

3.3.1.3. PCA for Background Subtraction

3.3.2. Subspace Pattern Classification

3.4. Statistical Formulation of the Object Recognition

3.4.1. Parametric and Nonparametric Methods

3.4.2. Probabilistic Framework

3.4.3. Bayes Decision Rule

3.4.4. Maximum a posteriori Classification Scheme

3.4.5. Binary Classification Problem

3.5. Parametric Methods - Mixture of Gaussians

3.6. The Kalman Filter

3.7. Nonparametric Methods

3.7.1. Histogram Based Techniques

3.7.2. Comparing Histograms

3.7.3. IMPLEMENTATION - Multidimensional Histograms

3.7.4. Parzen Method

3.7.4.1. Kernel Based Methods

3.7.4.2. Nearest-Neighbor Method

3.8. The Mean Shift Method

3.8.1. Introduction to the Mean Shift

3.8.2. Continuously Adaptive Mean Shift Method (CamShift)

3.8.3. Algorithmic Aspects of the Mean Shift Tracking

3.8.3.1. Tracking of Multiple Features

3.8.3.2. Tracking of Multiple Objects

3.8.3.3. Fuzzy Approach to the CamShift

3.8.3.4. Discrimination with Background Information

3.8.3.5. Adaptive Update of the Classifiers

3.8.4. IMPLEMENTATION of the CamShift Method

3.9. Neural Networks

3.9.1. Probabilistic Neural Network

3.9.2. IMPLEMENTATION-Probabilistic Neural Network

3.9.3. Hamming Neural Network

3.9.4. IMPLEMENTATION of the Hamming Neural Network

3.9.5. Morphological Neural Network

3.9.5.1. IMPLEMENTATION of the Morphological Neural Network

3.10. Kernels in Vision Pattern Recognition

3.10.1. Kernel Functions

3.10.2. IMPLEMENTATION-Kernels

3.11. Data Clustering

3.11.1. The k-Means Algorithm

3.11.2. Fuzzy c-Means

3.11.3. Kernel Fuzzy c-Means

3.11.4. Measures of Cluster Quality

3.11.5. IMPLEMENTATION Issues

3.12. Support Vector Domain Description

3.12.1. Implementation of Support Vector Machines

3.12.2. Architecture of the Ensemble of One-Class Classifiers

3.13. Appendix MATLAB® and other Packages for Pattern Classification

3.14. Closure

3.14.1. Chapter Summary

3.14.2. Further Reading

Problems and Exercises

References

4. Object Detection and Tracking

4.1. Introduction

4.2. Direct Pixel Classification

4.2.1. Ground-Truth Data Collection

4.2.2. CASE STUDY - Human Skin Detection

4.2.3. CASE STUDY - Pixel Based Road Signs Detection

4.2.3.1. Fuzzy Approach

4.2.3.2. SVM Based Approach

4.2.4. Pixel Based Image Segmentation with Ensemble of Classifiers

4.3. Detection of Basic Shapes

4.3.1. Detection of Line Segments

4.3.2. Up Write Detection of Convex Shapes

4.4. Figure Detection

4.4.1. Detection of Regular Shapes from Characteristic Points

4.4.2. Clustering of the Salient Points

4.4.3. Adaptive Window Growing Method

4.4.4. Figure Verification

4.4.5. CASE STUDY-Road Signs Detection System

4.5. CASE STUDY - Road Signs Tracking and Recognition

4.6. CASE STUDY - Framework for Object Tracking

4.7. Pedestrian Detection

4.8. Closure

4.8.1. Chapter Summary

4.8.2. Further Reading

Problems and Exercises

References

5. Object Recognition

5.1. Abstract

5.2. Recognition from Tensor Phase Histograms and Morphological Scale Space

5.2.1. Computation of the Tensor Phase Histograms in Morphological Scale

5.2.2. Matching of the Tensor Phase Histograms

5.2.3. CASE STUDY - Object Recognition with Tensor Phase Histograms in Morphological Scale Space

5.3. Invariant Based Recognition

5.3.1. CASE STUDY - Pictogram Recognition with Affine Moment Invariants

5.4. Template Based Recognition

5.4.1. Template Matching for Road Signs Recognition

5.4.2. Special Distances for Template Matching

5.4.3. Recognition with the Log-Polar and Scale-Spaces

5.5. Recognition from Deformable Models

5.6. Ensembles of Classifiers

5.7. CASE STUDY - Ensemble of Classifiers for Road Sign Recognition from Deformed Prototypes

5.17.1. Architecture of the Road Signs Recognition System

5.7.2. Module for Recognition of Warning Signs

5.7.3. The Arbitration Unit

5.8. Recognition Based on Tensor Decompositions

5.8.1. Pattern Recognition in SubSpaces Spanned by the HOSVD Decomposition of Pattern Tensors

5.8.2. CASE STUDY - Road Sign Recognition System Based on Decomposition of Tensors with Deformable Pattern Prototypes

5.8.3. CASE STUDY - Handwritten Digit Recognition with Tensor Decomposition Method

5.8.4. IMPLEMENTATION of the Tensor Subspace Classifiers

5.9. Eye Recognition for Driver's State Monitoring

5.10. Object Category Recognition

5.10.1. Part-Based Object Recognition

5.10.2. Recognition with Bag-of-Visual-Words

5.11. Closure

5.11.1. Chapter Summary

5.11.2. Further Reading

Problems and Exercises

Reference

A. Appendix

A.1. Abstract

A.2. Morphological Scale-Space

A.3. Morphological Tensor Operators

A.4. Geometry of Quadratic Forms

A.5. Testing Classifiers

A.5.1. Implementation of the Confusion Matrix and Testing Object Detection in Images

A.6. Code Acceleration with OpenMP

A.6.1. Recipes for Object-Oriented Code Design with OpenMP

A.6.2. Hints on Using and Code Porting to OpenMP

A.6.3. Performance Analysis

A.7. Useful MATLAB® Functions for Matrix and Tensor Processing

A.8. Short Guide to the Attached Software

A.9. Closure

A.9.1. Chapter Summary

A.9.2. Further Reading

Problems and Exercises

References

Index