| Foreword | 6 |
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| Preface | 8 |
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| Contents | 12 |
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| List of Figures | 15 |
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| List of Tables | 20 |
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| Part I: Overview and Foundations | 21 |
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| Chapter 1: Introduction | 22 |
| 1.1 Craniofacial Fractures | 22 |
| 1.2 State-of-the-Art Virtual Craniofacial Surgery | 27 |
| 1.3 The Importance of Computer-Assisted Surgical Planning | 28 |
| 1.4 Organization of the Monograph | 31 |
| Chapter 2: Graph-Theoretic Foundations | 33 |
| 2.1 Some Basic Terminology | 33 |
| 2.2 Matchings in Graphs | 35 |
| 2.3 Isomorphism and Automorphism of Graphs | 37 |
| 2.4 Network Flows | 38 |
| Chapter 3: A Statistical Primer | 42 |
| 3.1 Probability | 42 |
| 3.2 Statistical Inference | 45 |
| 3.3 Bayesian Statistics | 47 |
| 3.4 Random Fields, Bayesian Restoration, and Stochastic Relaxation | 49 |
| Part II: Virtual Craniofacial Reconstruction | 52 |
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| Chapter 4: Virtual Single-Fracture Mandibular Reconstruction | 53 |
| 4.1 Motivation | 53 |
| 4.2 Chapter Organization | 53 |
| 4.3 Related Work and Our Contribution | 54 |
| 4.4 Image Processing | 55 |
| 4.4.1 Thresholding | 57 |
| 4.4.2 Connected Component Labeling | 58 |
| 4.4.3 Contour Data Extraction | 58 |
| 4.5 Surface Matching Using Type-0 Constraints | 59 |
| 4.5.1 Surface Registration Using the ICP Algorithm | 59 |
| 4.5.2 Registration Using the DARCES Algorithm | 61 |
| 4.5.3 Registration Using the Hybrid DARCES-ICP Algorithm | 62 |
| 4.6 Improved Surface Matching with Surface Irregularity Modeling | 63 |
| 4.6.1 Curvature-Based Surface Irregularity Estimation | 63 |
| 4.6.2 Fuzzy Set Theory-Based Surface Irregularity Extraction | 65 |
| 4.6.3 Reward/Penalty Schemes | 66 |
| 4.7 Improved Surface Matching with Type-1 Constraints | 67 |
| 4.7.1 Cycle Graph Automorphs as Initial ICP States | 68 |
| 4.7.2 Selection of the Best Initial State | 68 |
| 4.7.3 Registration Using the Hybrid Geometric-ICP Algorithm | 70 |
| 4.8 Bilateral Symmetry of the Human Mandible | 71 |
| 4.9 Biomechanical Stability of the Human Mandible | 72 |
| 4.10 Composite Reconstruction Using MSE, Symmetry, and Stability | 74 |
| 4.11 Experimental Results | 76 |
| 4.12 Conclusion and Future Work | 81 |
| Chapter 5: Virtual Multiple-Fracture Mandibular Reconstruction | 87 |
| 5.1 Motivation | 87 |
| 5.2 Chapter Organization | 88 |
| 5.3 Related Work and Our Contribution | 88 |
| 5.4 Image Processing | 91 |
| 5.5 Design of a Score Matrix | 92 |
| 5.5.1 Modeling Spatial Proximity | 94 |
| 5.5.2 Modeling Surface Characteristics | 94 |
| 5.5.3 Score Matrix Elements | 95 |
| 5.6 Identification of Opposable Fracture Surfaces | 96 |
| 5.6.1 Combinatorial Nature of the Reconstruction Problem | 96 |
| 5.6.2 Maximum Weight Graph Matching for Restricting the Reconstruction Options | 97 |
| 5.7 Pairwise Registration of the Fracture Surfaces | 98 |
| 5.8 Shape Monitoring of the Reconstructed Mandible | 98 |
| 5.9 Experimental Results | 100 |
| 5.10 Conclusion and Future Work | 103 |
| Part III: Computer-Aided Fracture Detection | 104 |
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| Chapter 6: Fracture Detection Using Bayesian Inference | 105 |
| 6.1 Motivation | 105 |
| 6.2 Chapter Organization | 106 |
| 6.3 Related Work and Our Contribution | 106 |
| 6.4 Image Processing | 108 |
| 6.5 Fracture Point Detection in 2D CT Image Slices | 109 |
| 6.5.1 Initial Pool of Fracture Points | 110 |
| 6.5.2 Final Pool of Fracture Points | 110 |
| 6.6 Stable Fracture Points in a CT Image Sequence | 111 |
| 6.6.1 The Kalman Filter as a Bayesian Inference Process | 111 |
| 6.6.2 Concept of Spatial Consistency | 112 |
| 6.7 Experimental Results | 115 |
| 6.8 Conclusion and Future Work | 121 |
| Chapter 7: Fracture Detection in an MRF-Based Hierarchical Bayesian Framework | 124 |
| 7.1 Motivation | 124 |
| 7.2 Chapter Organization | 125 |
| 7.3 Related Work and Our Contribution | 126 |
| 7.4 Coarse Fracture Localization | 127 |
| 7.4.1 Localization of the Mandible | 128 |
| 7.4.2 Determination of the Fracture-Containing Symmetric Block Pair(s) | 129 |
| 7.4.3 Identification of the Fracture-Containing Image Half | 130 |
| 7.5 Hierarchical Bayesian Restoration Framework | 130 |
| 7.5.1 Statistical Model | 131 |
| 7.5.2 Modeling of the Stochastic Degradation Matrix | 133 |
| 7.6 Experimental Results | 135 |
| 7.7 Conclusion and Future Work | 147 |
| Chapter 8: Fracture Detection Using Max-Flow Min-Cut | 150 |
| 8.1 Motivation | 150 |
| 8.2 Chapter Organization | 150 |
| 8.3 Related Work and Our Contribution | 151 |
| 8.4 Max-Flow Min-Cut in a 2D Flow Network | 152 |
| 8.4.1 Construction of the 2D Flow Network | 152 |
| 8.4.2 Correctness of the 2D Flow Network Model | 154 |
| 8.5 Max-Flow Min-Cut in 3D | 154 |
| 8.5.1 Construction of the 3D Flow Network | 154 |
| 8.5.2 Correctness of the 3D Flow Network Model | 156 |
| 8.6 Experimental Results | 156 |
| 8.7 Conclusion and Future Work | 159 |
| Part IV: Concluding Remarks | 161 |
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| Chapter 9: GUI Design and Research Synopsis | 162 |
| 9.1 Chapter Organization | 162 |
| 9.2 Design of the Graphical User Interface | 162 |
| 9.3 Synopsis | 165 |
| 9.4 Virtual Reconstructive Surgery-An Interdisciplinary Research Perspective | 166 |
| 9.5 Future Research Directions | 167 |
| References | 169 |
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| Index | 176 |
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