Object Detection and Recognition in Digital Images

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.

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.

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 Backgr