VIII
Contents
2.6.1 Supervised Classification ............................................ 67
2.6.2 Unsupervised Classification........................................ 69
2.6.3 Crisp Classification Algorithms ................................... 71
2.6.4 Fuzzy Classification Algorithms ................................... 74
2.6.5 Classification Accuracy Assessment.............................. 76
2.7 Image Change Detection ...................................................... 79
2.8 Image Fusion...................................................................... 80
2.9 Automatic Target Recognition ............................................... 81
2.10 Summary ........................................................................... 82
Part II Theory
3 Mutual Information:
A Similarity Measure for Intensity Based Image Registration
89
3.1 Introduction....................................................................... 89
3.2 Mutual Information Similarity Measure.................................. 90
3.3 Joint Histogram Estimation Methods..................................... 93
3.3.1 Two-Step Joint Histogram Estimation ........................... 93
3.3.2 One-Step Joint Histogram Estimation........................... 94
3.4 Interpolation Induced Artifacts ............................................ 95
3.5 Generalized Partial Volume Estimation ofJoint Histograms...... 99
3.6 Optimization Issues in the Maximization of MI ....................... 103
3.7 Summary ........................................................................... 107
4 Independent Component Analysis
109
4.1 Introduction ....................................................................... 109
4.2 Concept ofICA ................................................................... 109
4.3 ICA Algorithms .................................................................. 113
4.3.1 Preprocessing using PCA ............................................ 113
4.3.2 Information Minimization Solution for ICA .................. 115
4.3.3 ICA Solution through Non-Gaussianity Maximization .... 121
4.4 Application ofICA to Hyperspectral Imagery .......................... 123
4.4.1 Feature Extraction Based Model .................................. 124
4.4.2 Linear Mixture Model Based ModeL ............................ 125
4.4.3 An ICA algorithm for Hyperspectral Image Processing ... 126
4.5 Summary ........................................................................... 129
5 Support Vector Machines
133
5.1 Introduction ....................................................................... 133
5.2 Statistical Learning Theory ................................................... 135
5.2.1 Empirical Risk Minimization ....................................... 136
5.2.2 Structural Risk Minimization ...................................... 137
5.3 Design of Support Vector Machines ....................................... 138
5.3.1 Linearly Separable Case .............................................. 139
5.3.2 Linearly Non-Separable Case ....................................... 143