CLASSIFICATION METHODS FOR REMOTELY SENSED DATA

Chapter 1 introduces the basic concepts of remote sensing in the optical and microwave region of the electromagnetic spectrum. This chapter is intended to introduce the field of remote sensing to readers with little or no background in this area, and it can be omitted by readers with adequate background knowledge of remote sensing.

Chapter 2 introduces the principles of pattern recognition. Traditional decision rules, including the supervised minimal distance classifier, Gaussian maximum likelihood, and unsupervised clustering techniques are described, together with other methods such as fuzzy-based procedures and decision trees. The chapter also contains brief accounts of dimension reduction methods, including orthogonal transforms, the assessment of classification accuracy, and the principles underlying the choice of training data.

Chapter 3 describes widely used neural network models and architectures including the multilayer perceptron (also called the feed-forward neural network), Kohonen’s self-organized feature map, counterpropagation, the Hopfield network, and networks based upon adaptive resonance theory (ART). 

Chapter 4 deals with pattern recognition techniques based on fuzzy systems. The main topics of this chapter are the construction of fuzzy rules, fuzzy mapping functions, and the corresponding decision processes. 

Chapter 5 presents a survey of methods of quantifying image texture, including fractal- and multifractal-based theory, the multiplicative autoregressive random field model, the grey level co-occurrence matrix, and frequency domain filtering. 

Chapter 6 addresses the theory and the application of Markov random fields. The main application of Markov random fields is to model contextual relationships. Other related topics, including function formulation, image restoration, robust estimation in the presence of noise (outliers), and the derivation of Markov-based texture measures, are also presented. 

Chapter 7 provides several approaches for dealing with multisource data. The methods described include the extension of Bayesian classification theory, evidential reasoning, and Markov random fields.

Contents 
Preface to the Second Edition...................................................................................xi
Preface to the First Edition .................................................................................... xiii Author Biographies .................................................................................................xix


Chapter 1 Remote Sensing in the Optical and Microwave Regions .....................1 


1.1 Introduction to Remote Sensing ................................................4
1.1.1 Atmospheric Interactions .............................................5
1.1.2 Surface Material Reflectance .......................................5
1.1.3 Spatial and Radiometric Resolution.............................8
1.2 Optical Remote Sensing Systems............................................ 10
1.3 Atmospheric Correction .......................................................... 11
1.3.1 Dark Object Subtraction............................................. 12
1.3.2 Modeling Techniques ................................................. 13
1.3.2.1 Modeling the Atmospheric Effect .............. 13

1.3.2.2 Steps in Atmospheric Correction................ 17
1.4 Correction for Topographic Effects......................................... 19
1.5 Remote Sensing in the Microwave Region..............................22
1.6 Radar Fundamentals................................................................23
1.6.1 SLAR Image Resolution ............................................24
1.6.2 Geometric Effects on Radar Images ..........................26
1.6.3 Factors Affecting Radar Backscatter .........................29
1.6.3.1 Surface Roughness .....................................29
1.6.3.2 Surface Conductivity ..................................30
1.6.3.3 Parameters of the Radar Equation..............30
1.7 Imaging Radar Polarimetry..................................................... 31
1.7.1 Radar Polarization State............................................. 32
1.7.2 Polarization Synthesis ................................................34

1.7.3 Polarization Signatures............................................... 35
1.8 Radar Speckle Suppression .....................................................37
1.8.1 Multilook Processing..................................................37
1.8.2 Filters for Speckle Suppression..................................38


Chapter 2 Pattern Recognition Principles........................................................... 41 


2.1 Feature Space Manipulation.................................................... 42
2.1.1 Tasseled Cap Transform............................................. 45
2.1.2 Principal Components Analysis .................................46
2.1.3 Minimum/Maximum Autocorrelation Factors (MAF)............................................................50 2.1.4 Maximum Noise Fraction Transformation................. 51

2.2 Feature Selection ..................................................................... 52
2.3 Fundamental Pattern Recognition Techniques........................54
2.3.1 Unsupervised Methods...............................................54
2.3.1.1 The k-means Algorithm..............................54
2.3.1.2 Fuzzy Clustering.........................................56
2.3.2 Supervised Methods................................................... 57
2.3.2.1 Parallelepiped Method................................ 57
2.3.2.2 Minimum Distance Classifier..................... 57
2.3.2.3 Maximum Likelihood Classifier................. 58
2.4 Combining Classifiers ............................................................. 61
2.5 Incorporation of Ancillary Information .................................. 62
2.5.1 Use of Texture and Context........................................63
2.5.2 Using Ancillary Multisource Data.............................63
2.6 Sampling Scheme and Sample Size ........................................65
2.6.1 Sampling Scheme.......................................................66
2.6.2 Sample Size, Scale, and Spatial Variability ............... 67
2.6.3 Adequacy of Training Data........................................69

2.7 Estimation of Classification Accuracy ....................................69
2.8 Epilogue................................................................................... 74


Chapter 3 Artificial Neural Networks.................................................................77 


3.1 Multilayer Perceptron ..............................................................77
3.1.1 Back-Propagation ....................................................... 78
3.1.2 Parameter Choice, Network Architecture, and Input/Output Coding ..................................................82
3.1.3 Decision Boundaries in Feature Space ......................84
3.1.4 Overtraining and Network Pruning ...........................88
3.2 Kohonen’s Self-Organizing Feature Map................................90
3.2.1 SOM Network Construction and Training.................90
3.2.1.1 Unsupervised Training ............................... 91
3.2.1.2 Supervised Training....................................93

3.2.2 Examples of Self-Organization ..................................94
3.3 Counter-Propagation Networks ...............................................98
3.3.1 Counter-Propagation Network Training.....................99
3.3.2 Training Issues ......................................................... 101
3.4 Hopfield Networks................................................................. 101
3.4.1 Hopfield Network Structure ..................................... 102
3.4.2 Hopfield Network Dynamics.................................... 102
3.4.3 Network Convergence .............................................. 103
3.4.4 Issues Relating to Hopfield Networks ...................... 105
3.4.5 Energy and Weight Coding: An Example................ 106
3.5 Adaptive Resonance Theory (ART)...................................... 108
3.5.1 Fundamentals of the ART Model............................. 109
3.5.2 Choice of Parameters ............................................... 112
3.5.3 Fuzzy ARTMAP ...................................................... 113
3.6 Neural Networks in Remote Sensing Image Classification.... 116

3.6.1 An Overview ............................................................ 116
3.6.2 A Comparative Study ............................................... 119


Chapter 4 Support Vector Machines................................................................. 125 


4.1 Linear Classification.............................................................. 126
4.1.1 The Separable Case.................................................. 126
4.1.2 The Nonseparable Case............................................ 129
4.2 Nonlinear Classification and Kernel Functions..................... 130
4.2.1 Nonlinear SVMs ...................................................... 130
4.2.2 Kernel Functions ...................................................... 132
4.3 Parameter Determination ...................................................... 135
4.3.1 t-Fold Cross-Validations........................................... 137
4.3.2 Bound on Leave-One-Out Error .............................. 138

4.3.3 Grid Search............................................................... 140
4.3.4 Gradient Descent Method ........................................ 142
4.4 Multiclass Classification........................................................ 144
4.4.1 One-against-One, One-against-Others, and DAG.... 144
4.4.2 Multiclass SVMs ...................................................... 146
4.4.2.1 Vapnik’s Approach ................................... 146
4.4.2.2 Methodology of Crammer and Singer ...... 147
4.5 Feature Selection ................................................................... 149
4.6 SVM Classification of Remotely Sensed Data ...................... 150
4.7 Concluding Remarks ............................................................. 153


Chapter 5 Methods Based on Fuzzy Set Theory .............................................. 155 


5.1 Introduction to Fuzzy Set Theory ......................................... 155
5.1.1 Fuzzy Sets: Definition .............................................. 156
5.1.2 Fuzzy Set Operations ............................................... 157
5.2 Fuzzy C-Means Clustering Algorithm.................................. 159
5.3 Fuzzy Maximum Likelihood Classification.......................... 162
5.4 Fuzzy Rule Base.................................................................... 164
5.4.1 Fuzzification............................................................. 165
5.4.2 Inference................................................................... 169
5.4.3 Defuzzification ......................................................... 171
5.5 Image Classification Using Fuzzy Rules............................... 173
5.5.1 Introductory Methodology ....................................... 173
5.5.2 Experimental Results ............................................... 178



Chapter 6 Decision Trees.................................................................................. 183 


6.1 Feature Selection Measures for Tree Induction..................... 184
6.1.1 Information Gain...................................................... 185
6.1.2 Gini Impurity Index ................................................. 188
6.2 ID3, C4.5, and SEE5.0 Decision Trees.................................. 189
6.2.1 ID3............................................................................ 189
6.2.2 C4.5 .......................................................................... 193
6.2.3 SEE5.0...................................................................... 196
6.3 CHAID .................................................................................. 197
6.4 CART..................................................................................... 198
6.5 QUEST .................................................................................. 201
6.5.1 Split Point Selection ................................................. 201

6.5.2 Attribute Selection....................................................203
6.6 Tree Induction from Artificial Neural Networks ..................204
6.7 Pruning Decision Trees .........................................................205
6.7.1 Reduced Error Pruning (REP) .................................207
6.7.2 Pessimistic Error Pruning (PEP)..............................207
6.7.3 Error-Based Pruning (EBP) .....................................208
6.7.4 Cost Complexity Pruning (CCP)..............................209
6.7.5 Minimal Error Pruning (MEP) ................................ 212
6.8 Boosting and Random Forest ................................................ 214
6.8.1 Boosting ................................................................... 214
6.8.2 Random Forest ......................................................... 215
6.9 Decision Trees in Remotely Sensed Data Classification....... 217

6.10 Concluding Remarks .............................................................220


Chapter 7 Texture Quantization........................................................................ 221 


7.1 Fractal Dimensions................................................................222
7.1.1 Introduction to Fractals ............................................223
7.1.2 Estimation of the Fractal Dimension .......................224
7.1.2.1 Fractal Brownian Motion (FBM) .............225
7.1.2.2 Box-Counting Methods and Multifractal Dimension ............................226
7.2 Frequency Domain Filtering ................................................. 231
7.2.1 Fourier Power Spectrum........................................... 231
7.2.2 Wavelet Transform ................................................... 235
7.3 Gray-Level Co-Occurrence Matrix (GLCM)........................ 239
7.3.1 Introduction to the GLCM ....................................... 239
7.3.2 Texture Features Derived from the GLCM.............. 241
7.4 Multiplicative Autoregressive Random Fields.......................243
7.4.1 MAR Model: Definition...........................................243
7.4.2 Estimation of the Parameters of the MAR Model ...245

7.5 The Semivariogram and Window Size Determination .........246
7.6 Experimental Analysis ..........................................................249
7.6.1 Test Image Generation..............................................249
7.6.2 Choice of Texture Features ......................................250
7.6.2.1 Multifractal Dimension ............................250
7.6.2.2 Fourier Power Spectrum...........................250
7.6.2.3 Wavelet Transform....................................250
7.6.2.4 Gray-Level Co-Occurrence Matrix ..........250
7.6.2.5 Multiplicative Autoregressive Random Field .......................................................... 251
7.6.3 Segmentation Results ............................................... 251
7.6.4 Texture Measure of Remote Sensing Patterns.......... 252


Chapter 8 Modeling Context Using Markov Random Fields............................ 255


8.1 Markov Random Fields and Gibbs Random Fields...............256
8.1.1 Markov Random Fields ............................................256
8.1.2 Gibbs Random Fields ............................................... 257
8.1.3 MRF-GRF Equivalence ........................................... 259
8.1.4 Simplified Form of MRF.......................................... 261
8.1.5 Generation of Texture Patterns Using MRF ............263
8.2 Posterior Energy for Image Classification.............................264
8.3 Parameter Estimation ............................................................ 267
8.3.1 Least Squares Fit Method.........................................268
8.3.2 Results of Parameter Estimations ............................ 271
8.4 MAP-MRF Classification Algorithms .................................. 273
8.4.1 Iterated Conditional Modes...................................... 274
8.4.2 Simulated Annealing................................................ 275
8.4.3 Maximizer of Posterior Marginals...........................277
8.5 Experimental Results............................................................. 278



Chapter 9 Multisource  Classification................................................................283


9.1 Image Fusion .........................................................................284
9.1.1 Image Fusion Methods .............................................284
9.1.2 Assessment of Fused Image Quality in the Spectral Domain.......................................................287
9.1.3 Performance Overview of Fusion Methods..............288
9.2 Multisource Classification Using the Stacked-Vector Method...................................................................................288
9.3 The Extension of Bayesian Classification Theory.................290
9.3.1 An Overview ............................................................290
9.3.1.1 Feature Extraction .................................... 291
9.3.1.2 Probability or Evidence Generation..........292
9.3.1.3 Multisource Consensus.............................292
9.3.2 Bayesian Multisource Classification Mechanism.....292
9.3.3 A Refined Multisource Bayesian Model ..................294
9.3.4 Multisource Classification Using the Markov Random Field ...........................................................295


9.3.5 Assumption of Intersource Independence................296
9.4 Evidential Reasoning.............................................................297
9.4.1 Concept Development ..............................................297
9.4.2 Belief Function and Belief Interval..........................299
9.4.3 Evidence Combination .............................................302
9.4.4 Decision Rules for Evidential Reasoning.................304
9.5 Dealing with Source Reliability............................................304
9.5.1 Using Classification Accuracy .................................305
9.5.2 Use of Class Separability .........................................305
9.5.3 Data Information Class Correspondence Matrix .....306

9.5.4 The Genetic Algorithm ............................................307
9.6 Experimental Results.............................................................309
Bibliography ......................................................................................................... 317

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CLASSIFICATION METHODS FOR REMOTELY SENSED DATA