Computer Vision-Guided Virtual Craniofacial Surgery (eBook)

Foreword 6
Preface 8
Contents 12
List of Figures 15
List of Tables 20
Part I: Overview and Foundations 21
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
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
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
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
Index 176