5.3.3 Non-Linear Support Vector Machines ........................... 146
5.4 SVMs for Multiclass Classification ......................................... 148
5.4.1 One Against the Rest Classification .............................. 149
5.4.2 Pairwise Classification ................................................ 149
5.4.3 Classification based on Decision Directed Acyclic Graph
and Decision Tree Structure ........................................ 150
5.4.4 Multiclass Objective Function ..................................... 152
5.5 Optimization Methods ......................................................... 152
5.6 Summary ........................................................................... 154
6 Markov Random Field Models
159
6.1 Introduction ....................................................................... 159
6.2 MRF and Gibbs Distribution ................................................. 161
6.2.1 Random Field and Neighborhood ................................ 161
6.2.2 Cliques, Potential and Gibbs Distributions .................... 162
6.3 MRF Modeling in Remote Sensing Applications ....................... 165
6.4 Optimization Algorithms ..................................................... 167
6.4.1 Simulated Annealing .................................................. 168
6.4.2 Metropolis Algorithm ................................................ 173
6.4.3 Iterated Conditional Modes Algorithm ......................... 175
6.5 Summary ........................................................................... 177
Part III Applications
7 MI Based Registration of Multi-Sensor and Multi-Temporal Images 181
7.1 Introduction ....................................................................... 181
7.2 Registration Consistency ...................................................... 183
7.3 Multi-Sensor Registration ..................................................... 184
7.3.1 Registration of Images
Having a Large Difference in Spatial Resolution ............. 184
7.3.2 Registration ofImages
Having Similar Spatial Resolutions ............................... 188
7.4 Multi-Temporal Registration ................................................ 190
7.5 Summary ........................................................................... 197
8 Feature Extraction from Hyperspectral Data Using ICA
199
8.1 Introduction ....................................................................... 199
8.2 PCA vs ICA for Feature Extraction ......................................... 200
8.3 Independent Component Analysis Based
Feature Extraction Algorithm (ICA-FE) .................................. 202
8.4 Undercomplete Independent Component Analysis Based
Feature Extraction Algorithm (UlCA-FE) ............................... 203
8.5 Experimental Results ........................................................... 210
8.6 Summary ........................................................................... 215
5.4 SVMs for Multiclass Classification ......................................... 148
5.4.1 One Against the Rest Classification .............................. 149
5.4.2 Pairwise Classification ................................................ 149
5.4.3 Classification based on Decision Directed Acyclic Graph
and Decision Tree Structure ........................................ 150
5.4.4 Multiclass Objective Function ..................................... 152
5.5 Optimization Methods ......................................................... 152
5.6 Summary ........................................................................... 154
6 Markov Random Field Models
159
6.1 Introduction ....................................................................... 159
6.2 MRF and Gibbs Distribution ................................................. 161
6.2.1 Random Field and Neighborhood ................................ 161
6.2.2 Cliques, Potential and Gibbs Distributions .................... 162
6.3 MRF Modeling in Remote Sensing Applications ....................... 165
6.4 Optimization Algorithms ..................................................... 167
6.4.1 Simulated Annealing .................................................. 168
6.4.2 Metropolis Algorithm ................................................ 173
6.4.3 Iterated Conditional Modes Algorithm ......................... 175
6.5 Summary ........................................................................... 177
Part III Applications
7 MI Based Registration of Multi-Sensor and Multi-Temporal Images 181
7.1 Introduction ....................................................................... 181
7.2 Registration Consistency ...................................................... 183
7.3 Multi-Sensor Registration ..................................................... 184
7.3.1 Registration of Images
Having a Large Difference in Spatial Resolution ............. 184
7.3.2 Registration ofImages
Having Similar Spatial Resolutions ............................... 188
7.4 Multi-Temporal Registration ................................................ 190
7.5 Summary ........................................................................... 197
8 Feature Extraction from Hyperspectral Data Using ICA
199
8.1 Introduction ....................................................................... 199
8.2 PCA vs ICA for Feature Extraction ......................................... 200
8.3 Independent Component Analysis Based
Feature Extraction Algorithm (ICA-FE) .................................. 202
8.4 Undercomplete Independent Component Analysis Based
Feature Extraction Algorithm (UlCA-FE) ............................... 203
8.5 Experimental Results ........................................................... 210
8.6 Summary ........................................................................... 215