peace The basic aim of this research monograph is to develop a unified approach to supervised pattern classification and model-based occluded object recognition. To perform this task we essentially consider soft computing tools, viz., fuzzy relational calculus(FRC), genetic algorithm(GA), and multilayer perceptron(MLP). The supervised approach to pattern classification and model-based approach to occluded object recognition are treated in one framework which is based on either conven- tional interpretation or new interpretation of multidimensional fuzzy implication (MFD) and a novel notion of fuzzy pattern vector(FPV). A completely independent design methodology has been developed on a unified framework which has been thoroughly tested on several synthetic and real life data. In the field of soft com- puting such application-oriented design study is unique in nature. The monograph essentially mimics the cognitive process of human decision making. It carries a message of perceptual integrity in representational diversity The monograph is very much useful to the researchers in the area of pattern classification and computer vision. It is useful for the academics as well as for the professional computer scientists of different research and development centers of industry. The monograph has a combined flavor of theory and practice t The monograph is basically a collection of research contributions of Prof Kumar Ray at Electronics and Communication Sciences Unit of Indian Statistical Institute. Kolkata. Prof. Kumar S. Ray is grateful to Mandrita Mondal for her constant encour agement and support to complete the monograph. Kumar S Ray
Preface The basic aim of this research monograph is to develop a unified approach to supervised pattern classification and model-based occluded object recognition. To perform this task we essentially consider soft computing tools, viz., fuzzy relational calculus (FRC), genetic algorithm (GA), and multilayer perceptron (MLP). The supervised approach to pattern classification and model-based approach to occluded object recognition are treated in one framework which is based on either conventional interpretation or new interpretation of multidimensional fuzzy implication (MFI) and a novel notion of fuzzy pattern vector (FPV). A completely independent design methodology has been developed on a unified framework which has been thoroughly tested on several synthetic and real life data. In the field of soft computing such application-oriented design study is unique in nature. The monograph essentially mimics the cognitive process of human decision making. It carries a message of perceptual integrity in representational diversity. The monograph is very much useful to the researchers in the area of pattern classification and computer vision. It is useful for the academics as well as for the professional computer scientists of different research and development centers of industry. The monograph has a combined flavor of theory and practice. The monograph is basically a collection of research contributions of Prof. Kumar S. Ray at Electronics and Communication Sciences Unit of Indian Statistical Institute, Kolkata. Prof. Kumar S. Ray is grateful to Mandrita Mondal for her constant encouragement and support to complete the monograph. Kumar S. Ray vii
Contents 1 Soft Computing Approach to Pattern Classification and Object Recognition 1.1 Introduction 2 1. 2 Passage Between Conventional Approach to Pattern Classification(Object Recognition) and Soft Computing Approach to Pattern Classification(Object Recognition) References 2 Pattern Classification Based on Conventional Interpretation of mFI 2.1 Introduction 2.2 Statement of the problem 557 2.3 Existing Method to Solve Fuzzy Relation Equation 2.4 Modified Approach to Solve Fuzzy Relational Equation 2.4.1 Derivative of max-Function 2. 4.2 Derivative of Min-Function 2.4.3 Modified Approach to the Computation of Derivative of Fuzzy-Max and Fuzzy-Min Functions 2.4.4 Algorithm for the Estimation of R 2.4.5 Illustration of the Modified Approach to the estimation of究 2.5 Design of the Classifier Based on Fuzzy Relational Calculus 27 2.6. 1 Classification of First Synthetic Data 2.6.2 Classification of Second Synthetic Data 2.7 Applications 2.7.1 Experimental Results 9 Conclusion
Contents 1 Soft Computing Approach to Pattern Classification and Object Recognition ................................ 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Passage Between Conventional Approach to Pattern Classification (Object Recognition) and Soft Computing Approach to Pattern Classification (Object Recognition) . . . . . . 5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2 Pattern Classification Based on Conventional Interpretation of MFI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2 Statement of the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.3 Existing Method to Solve Fuzzy Relation Equation . . . . . . . . . . 18 2.4 Modified Approach to Solve Fuzzy Relational Equation . . . . . . 22 2.4.1 Derivative of Max-Function . . . . . . . . . . . . . . . . . . . . . 22 2.4.2 Derivative of Min-Function . . . . . . . . . . . . . . . . . . . . . 23 2.4.3 Modified Approach to the Computation of Derivative of Fuzzy-Max and Fuzzy-Min Functions . . . . . . . . . . . . 24 2.4.4 Algorithm for the Estimation of < . . . . . . . . . . . . . . . . 26 2.4.5 Illustration of the Modified Approach to the Estimation of <. . . . . . . . . . . . . . . . . . . . . . . . . 27 2.5 Design of the Classifier Based on Fuzzy Relational Calculus . . . 27 2.6 Effectiveness of the Proposed Method . . . . . . . . . . . . . . . . . . . 32 2.6.1 Classification of First Synthetic Data. . . . . . . . . . . . . . . 33 2.6.2 Classification of Second Synthetic Data. . . . . . . . . . . . . 35 2.7 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.7.1 Experimental Results. . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.8 Comparative Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 ix
3 Pattern Classification Based on New Interpretation of MFI 43 3.1 Introduction 3.2 Statement of the problem 3.3 Design of the Multidimensional Classifier Based on Fuzzy Relational Calculus(FRC) 46 3.4 Effectiveness of the Proposed Method 3.4.1 Classification of First Synthetic Data 3.4.2 Classification of Second Synthetic Data 3.5 Applications 3.5.1 Experiment on the Classification of the Telugu Vowels 3.5.2 Experiment on the Classification of Bengali Vowels 3.6 Conclusion References 4 Pattern Classification Based on New Interpretation of MFT and Floating Point Genetic algorithm 61 4.1 Introduction 4.2 Solution of Fuzzy Relational Equation by GA 63 4.2.1 Computational Details to Solve Eq(4. 4) Using Floating Point ga 4.2.2 Algorithm for the Estimation of 4.3 Designing of the Classifier Based on the Fuzzy Relational Calculus and genetic algorithms 4.4 Effectiveness of the Proposed Method 4.4.1 Classification of First Synthetic Data 68 4. 4.2 Classification of Second Synthetic Data 4.5 Application of the Proposed Method for Vowel Classification problem 4.5.1 Experiment on the Classification of the Telugu Vowels 7 .6 Comparative Study 4.7 Benchmark stud 73 5 Neuro-Genetic Approach to Pattern Classification Based on the New Interpretation of MFI 5.1 Introduction 77 5.2 Implementation of the New Interpretation of MFI on MLP Type Neural Network 5.3 Genetic-Algorithm-Based Learning Environment 5.3.1 Genetic Algorithm for Global Optimizatio 5.3.2 Backpropagation Versus GA
3 Pattern Classification Based on New Interpretation of MFI. . . . . . 43 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.2 Statement of the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.3 Design of the Multidimensional Classifier Based on Fuzzy Relational Calculus (FRC) . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.4 Effectiveness of the Proposed Method . . . . . . . . . . . . . . . . . . . 48 3.4.1 Classification of First Synthetic Data. . . . . . . . . . . . . . . 49 3.4.2 Classification of Second Synthetic Data. . . . . . . . . . . . . 49 3.5 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.5.1 Experiment on the Classification of the Telugu Vowels . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.5.2 Experiment on the Classification of Bengali Vowels . . . . 57 3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4 Pattern Classification Based on New Interpretation of MFI and Floating Point Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . 61 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4.2 Solution of Fuzzy Relational Equation by GA . . . . . . . . . . . . . 63 4.2.1 Computational Details to Solve Eq. (4.4) Using Floating Point GA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.2.2 Algorithm for the Estimation of < . . . . . . . . . . . . . . . . 66 4.3 Designing of the Classifier Based on the Fuzzy Relational Calculus and Genetic Algorithms . . . . . . . . . . . . . . . . . . . . . . 67 4.4 Effectiveness of the Proposed Method . . . . . . . . . . . . . . . . . . . 68 4.4.1 Classification of First Synthetic Data. . . . . . . . . . . . . . . 68 4.4.2 Classification of Second Synthetic Data. . . . . . . . . . . . . 68 4.5 Application of the Proposed Method for Vowel Classification Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.5.1 Experiment on the Classification of the Telugu Vowels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.6 Comparative Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.7 Benchmark Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 5 Neuro-Genetic Approach to Pattern Classification Based on the New Interpretation of MFI . . . . . . . . . . . . . . . . . . . . . . . . 77 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5.2 Implementation of the New Interpretation of MFI on MLP Type Neural Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 5.3 Genetic-Algorithm-Based Learning Environment. . . . . . . . . . . . 79 5.3.1 Genetic Algorithm for Global Optimization . . . . . . . . . . 79 5.3.2 Backpropagation Versus GA . . . . . . . . . . . . . . . . . . . . 80 x Contents
5.3.3 Four Basic Features of ga 5.4 Improvement of the Network Performance Using Regularization 5.5 Formulation of the problem 5.6 Numerical Examples 5.6.1 Classification of Synthetic Data 5.6.2 Classification of Vowels 28887%9 5.6.3 Classification with Regularization 5.7 Conclusion References 6 Knowledge-Based Occluded Object Recognition Based on New Interpretation of MFI and Floating Point Genetic 6.1 Introduction 6.2 Statement of the problem 6.3 Design of Knowledge-Based Occluded Object Recognizer 6.3.1 Local Feature Extraction 3.2 Training phase 108 6.3.3 Testing Phase l11 63 4 Condition of recognition l11 6.4 Control scheme of the vision process 6.5 Effectiveness of the Proposed Classifier 116 6.5.1 Recognition of the scene Consist of model Objects Mi and M2 116 6.5.2 Recognition of the Scene Consist of Model Objects M, M. and m 118 ro-Fuzzy Approach to Occluded Object Recognition Based on New Interpretation of MFI .2 Implementation of the New Interpretation of MFI on Back Propagation-Type Neural Network 122 7.3 Formulation of the problem 7.3.1 Local Feature Extraction 7.3.2 Process of fuzzification 7.3.3 Assignment of the Membership Function to the Consequent Part of the If-Then Rules 7. 3. 4 Process of Defuzzification 7.3.5 Generation of the Model-Based Object Recognition
5.3.3 Four Basic Features of GA. . . . . . . . . . . . . . . . . . . . . . 80 5.3.4 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 5.4 Improvement of the Network Performance Using Regularization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.5 Formulation of the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.6 Numerical Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.6.1 Classification of Synthetic Data . . . . . . . . . . . . . . . . . . 87 5.6.2 Classification of Vowels . . . . . . . . . . . . . . . . . . . . . . . 98 5.6.3 Classification with Regularization . . . . . . . . . . . . . . . . . 99 5.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 6 Knowledge-Based Occluded Object Recognition Based on New Interpretation of MFI and Floating Point Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 6.2 Statement of the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 6.3 Design of Knowledge-Based Occluded Object Recognizer . . . . . 105 6.3.1 Local Feature Extraction . . . . . . . . . . . . . . . . . . . . . . . 106 6.3.2 Training Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 6.3.3 Testing Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 6.3.4 Condition of Recognition . . . . . . . . . . . . . . . . . . . . . . . 111 6.4 Control Scheme of the Vision Process . . . . . . . . . . . . . . . . . . . 113 6.5 Effectiveness of the Proposed Classifier . . . . . . . . . . . . . . . . . . 116 6.5.1 Recognition of the Scene Consist of Model Objects M1 and M2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 6.5.2 Recognition of the Scene Consist of Model Objects M1, M2, and M3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 6.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 7 Neuro-Fuzzy Approach to Occluded Object Recognition Based on New Interpretation of MFI . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 7.2 Implementation of the New Interpretation of MFI on Back Propagation-Type Neural Network. . . . . . . . . . . . . . . . . . . . . . 122 7.3 Formulation of the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . 123 7.3.1 Local Feature Extraction . . . . . . . . . . . . . . . . . . . . . . . 123 7.3.2 Process of Fuzzification. . . . . . . . . . . . . . . . . . . . . . . . 125 7.3.3 Assignment of the Membership Function to the Consequent Part of the If–Then Rules . . . . . . . . . . . . . . 125 7.3.4 Process of Defuzzification . . . . . . . . . . . . . . . . . . . . . . 126 7.3.5 Generation of the Model-Based Object Recognition Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Contents xi
7.4 Experimental Results 7.4.1 Case Study 1 7.4.2 Case Study 2 7.5 Conclusion 142 References Appendix A: on and F Pattern vecto 147 ppendix B: Good Function Appendix C: Operators of Fuzzy Equation 163 Appendix D: Genetic Operators on the Floating Point Chromosomes
7.4 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 7.4.1 Case Study 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 7.4.2 Case Study 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 7.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 Appendix A: Multidimensional Fuzzy Implication and Fuzzy Pattern Vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 Appendix B: Good Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Appendix C: Operators of Fuzzy Equation . . . . . . . . . . . . . . . . . . . 163 Appendix D: Genetic Operators on the Floating Point Chromosomes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 xii Contents