Fuzzy Algorithms. With Applications to Image Processing and Pattern Recognition

Title Page......Page 4
Series Info\r......Page 2
Copyright\r......Page 5
Preface......Page 6
Acknowledgements......Page 8
Contents......Page 10
1.1.1 Probability and Fuzziness......Page 14
1.1.2 Fuzzy Sets......Page 16
1.1.3 Properties of Fuzzy Sets......Page 18
1.1.4 Operations on Fuzzy Sets......Page 21
1.2 Fuzzy Relations......Page 24
1.3 Fuzzy Models for Image Processing and Pattern Recognition......Page 27
2.1 Introduction......Page 30
2.2 Heuristic Selections......Page 31
2.3 Clustering Approaches......Page 36
2.3.1 C-means Clustering Approach......Page 37
2.3.2 Learning with Adaptive Vector Quantization......Page 39
2.3.3 Self-organizing Map Approach......Page 41
2.3.4 Merging Neighboring Membership Functions......Page 46
2.4.1 Gradient Descent Algorithm......Page 48
2.4.2 Neural Network Approach......Page 51
2.5 Concluding Remarks......Page 57
3.1 Introduction......Page 58
3.2.1 Statistical Decision Rule......Page 60
3.2.2 Gaussian Distributions......Page 63
3.3.1 Model Fitting Method......Page 65
3.3.2 Otsu\'s Thresholding Method......Page 67
3.3.3 Minimum Error Thresholding Met hod......Page 69
3.4.1 Fuzzy Membership Functions......Page 70
3.4.2 Threshold Selection Based on Fuzzy Measure......Page 71
3.4.3 Fast Computation......Page 73
3.5.1 Analytical Formulation......Page 74
3.5.2 Analysis of Cost Functions......Page 75
3.6 Multilevel Thresholding......Page 76
3.6.1 Generalization of Model Fitting Method......Page 79
3.6.2 Generalization of Non-iterative Methods......Page 81
3.7.1 Segment at ion of Document Images......Page 82
3.7.2 Segment at ion of Building Images......Page 83
3.7.3 Segmentat ion of Human Images......Page 84
3.8 Concluding Remarks......Page 97
4.1 Introduction......Page 98
4.2 C-means Algorithm......Page 99
4.3 Fuzzy C-means Algorithm......Page 100
4.4 Comparison between Hard and Fuzzy Clustering Algorithms......Page 102
4.5 Cluster Validity......Page 104
4.6.1 Characterization of Tissues in MR Images......Page 106
4.6.2 Segmentation of Natural Color Images......Page 108
4.6.3 Fuzzy Parameter Identification......Page 113
4.7 Concluding Remarks......Page 119
5.1 Introduction......Page 122
5.2.1 Location Similarity......Page 125
5.2.2 Orientation Similarity......Page 126
5.2.3 Relation Similarity......Page 127
5.3.1 Entropy Measure......Page 130
5.3.2 Matching Costs......Page 132
5.3.3 Examples......Page 134
5.4.1 Detecting and Removing Extra Lines......Page 138
5.4.2 Detecting and Recovering Missing Lines......Page 140
5.5.1 Basic Algorithm......Page 142
5.5.2 Fast Algorithm......Page 144
5.6.2 Point Pattern Matching......Page 147
5.7 Concluding Remarks......Page 148
6.1 Introduction......Page 152
6.2 Learning from Examples......Page 154
6.3.1 Decision Trees and Rules......Page 158
6.3.3 Fuzzified Decision Rules......Page 163
6.4 Fuzzy Aggregation Network Approach......Page 165
6.5 Minimization of Fuzzy Rules......Page 166
6.5.2 Minimization Based on Karnaugh Maps......Page 169
6.6 Defuzzification and Optimization......Page 172
6.6.2 Maximum Accumulated Matching......Page 173
6.6.4 Two-layer Perceptron Approach......Page 174
6.7.1 Segmentation of Map Images......Page 176
6.7.2 Printed Upper-case English Letter Recognition......Page 187
6.7.3 Handwritten Numeral Recognition......Page 191
6.8 Concluding Remarks......Page 199
7.1 Introduction......Page 202
7.2 Voting Schemes......Page 203
7.3 Maximum Posteriori Probability......Page 204
7.5 Fuzzy Measures and Fuzzy Integrals......Page 205
7.5.1 Fuzzy Measures......Page 207
7.5.3 A Fuzzy Integral Model for Classifier Fusion......Page 208
7.6 Applications......Page 210
7.6.1 Optimized Nearest Neighbor Classifier......Page 211
7.6.2 Markov Chain- based Classifier......Page 214
7.6.3 Combined Classifiers......Page 217
7.7 Concluding Remarks......Page 224
Bibliography......Page 226
Index......Page 234