Image-Based Geometric Modeling and Mesh Generation

Cover......Page 1
Image-Based Geometric Modeling and Mesh Generation......Page 4
Preface......Page 6
Contents......Page 7
Contributors......Page 9
Challenges and Advances in Image-Based Geometric Modeling and Mesh Generation......Page 12
1 Introduction......Page 13
2.1 Meshing Pipelines Starting from Scanned Images......Page 15
3 Piecewise-Linear Mesh Generation......Page 16
4 High-Order Element Construction......Page 18
Challenges......Page 19
References......Page 20
3D Surface Realignment Tracking for Medical Imaging: A Phantom Study with PET Motion Correction......Page 22
2 Experiments and Methods......Page 23
3 Results and Discussion......Page 26
4 Summary and Conclusions......Page 28
References......Page 29
1 Introduction......Page 31
Problem Description......Page 33
3 B-Spline Reparametrization by L2-Gradient Flow......Page 34
4.1 Spacial Discretization......Page 35
Compute taul......Page 37
4.3 Calculation of Coefficient Matrix of (10) and Its Inverse......Page 39
5.1 Multi-resolution Representations......Page 41
5.2 Gaussian Filter......Page 42
5.3 Least Square Approximations......Page 43
6 Regularity Analysis of Mapping x......Page 44
7 Existence and Uniqueness of x......Page 46
8 Existence and Uniqueness of ODE\'s Solution......Page 48
Gronwall\'s Inequality (See [14])......Page 49
9 Experiments......Page 55
Boundary Conditions......Page 56
Regularization Term Omega (g-1)2......Page 57
The Choice of the N-Sequence......Page 58
Image Sampling......Page 59
References......Page 62
1 Introduction......Page 64
2.1 Conditional Random Fields......Page 66
3 Shape Descriptors......Page 67
3.2.2 Regional Attribute Weighted Geodesic Shape Contexts......Page 68
Visibility from Reference Point......Page 69
Vessel Prior......Page 70
Aneurysm Prior......Page 71
5 Experiments......Page 72
6 Conclusions......Page 74
References......Page 75
Tetrahedral Image-to-Mesh Conversion Approaches for Surgery Simulation and Navigation......Page 77
1 Introduction......Page 78
2.1 Non-rigid Registration......Page 79
2.2 Image-to-Mesh Conversion......Page 81
3.1 Mesh Fitness Criteria......Page 83
3.3 Evaluation Methodology......Page 84
3.4 Results......Page 86
4 Discussion......Page 89
References......Page 90
1 Introduction......Page 93
2.1.1 Computing the Points on the Gaussian Surface......Page 97
2.1.2 Trace Step......Page 98
2.1.3 Polygonization......Page 100
2.2 Volume Tetrahedral Mesh Generation......Page 102
3.1 Performance......Page 103
3.2 Applications......Page 109
4 Conclusion......Page 110
References......Page 112
1 Introduction......Page 115
2.2 Image Segmentation......Page 117
2.3 Mesh Generation......Page 118
3.1 Level Set Methods......Page 119
3.1.1 The Chan and Vese Level Set Method for Curve Evolution......Page 120
3.2.1 The Shontz and Vavasis Finite Element-Based Mesh Warping (FEMWARP) Algorithm......Page 121
4 Ventricular Deformation for Boundaries Obtained from the Level Set Method and FEMWARP in Hydrocephalic Patients......Page 122
4.2 Image Segmentation......Page 123
4.6 Mesh Quality Improvement......Page 124
5 Simulations of the Evolution of the Brain Ventricles in Hydrocephalic Patients......Page 125
5.1 Simulation 1: Small Decrease in the Area of the Ventricles......Page 126
5.2 Simulation 2: Asymmetric Ventricular Shape Change......Page 129
5.3 Simulation 3: Ventricular Deformation with Boundaries Obtained via the Level Set Method......Page 136
6 Conclusions and Future Work......Page 143
References......Page 145
1 Introduction......Page 150
2.1 Tetrahedral Mesh Generation Algorithm......Page 152
2.2 ODT and B-ODT Algorithms......Page 153
2.3 Edge-Based B-ODT Algorithm......Page 155
3 Results......Page 156
References......Page 162
1 Introduction......Page 165
1.1 Previous Work......Page 166
2 Background......Page 167
3 Our Method......Page 168
3.2 Point Rejection Quality Improvement......Page 169
4 Results......Page 171
References......Page 174
1 Introduction......Page 176
2.1 3D Voxel Using XCMT......Page 177
2.2 2D Slices Plus Statistical Processing......Page 180
3.1 Voxel Data Processing......Page 181
3.2 Construction of Non-manifold Model Topology......Page 184
3.3 Non-manifold Models for Periodic Representative Volumes......Page 185
3.4 User Interface Functions to Support Image to Geometry Operations......Page 187
4 Mesh Generation......Page 188
5 Results......Page 191
6 Closing Remarks......Page 196
References......Page 197
1 Introduction......Page 199
Hexahedral Mesh Generation......Page 200
3.1 Problem Description......Page 201
4 Quality Improvement Algorithm and Implementation......Page 203
4.1 The Pillowing Technique......Page 204
4.3 Curve Regularization......Page 206
4.4 Surface Smoothing Using Various Geometric Flows......Page 207
Discretization of Geometric PDEs......Page 210
4.5 Regularization of Boundary Quadrilateral Mesh......Page 211
4.6.2 Global Optimization......Page 213
5.1 Surface Smoothing Using Various Geometric Flows......Page 215
5.2 Quality Improvement for Quadrilateral Meshes......Page 219
5.3 Quality Improvement for Hexahedral Meshes......Page 221
6 Conclusion......Page 222
References......Page 224
Patient-Specific Model Generation and Simulation for Pre-operative Surgical Guidance for Pulmonary Embolism Treatment......Page 226
1 Introduction......Page 227
2.1 Image Segmentation......Page 231
2.3 Volume Mesh Generation......Page 232
3 Patient-Specific Geometric Modeling of an IVC Filter Implanted in the IVC......Page 233
4.2 Image Segmentation......Page 235
4.2.3 Intelligent Scissors......Page 236
4.3.2 Poisson Surface Reconstruction......Page 237
4.4 Generation of a Geometric Model of the IVC Filter......Page 238
4.5.1 Superelasticity-Based Mesh Warping......Page 239
4.5.2 Linear Elasticity-Based Mesh Warping......Page 240
4.7 Computational Fluid Dynamics......Page 241
5.1 Image Segmentation......Page 242
5.2 Surface Mesh Generation......Page 243
5.4 Volume Mesh Generation......Page 245
5.5 Computational Fluid Dynamics......Page 246
6 Conclusions and Future Work......Page 247
References......Page 249
1 Introduction......Page 253
2 Methods......Page 255
2.1 Parameterization......Page 256
2.1.1 Medial Representation......Page 257
2.1.2 Harmonic Mapping......Page 259
2.2 Decomposition......Page 262
2.2.1 Proper Orthogonal Decomposition......Page 263
2.2.2 Independent Component Analysis......Page 264
3 Example......Page 265
4 Future Directions......Page 269
References......Page 270
1 Introduction......Page 272
2 PB Model......Page 274
2.1 Regularization Schemes of the Poisson-Boltzmann Equation......Page 276
2.2 Finite Element Methods......Page 278
3 PNP Model......Page 280
3.1 PNP Equations......Page 283
3.2 Finite Element Algorithms......Page 284
3.2.1 Steady-State Diffusion......Page 285
3.2.2 Unsteady-State Diffusion......Page 286
3.2.3 A Symmetric Transform of the Electro-Diffusion Equations......Page 287
3.3 PB Model as a Special Case of PNP Model......Page 289
5 Numerical Experiments and Biophysical Applications......Page 290
5.1 Steady-State Diffusion: Numerical Accuracy......Page 291
5.2 Accuracy for Solving the Unsteady-State Diffusion......Page 293
5.3 Biophysical Applications: Diffusion-Reaction Study of AChE-ACh System......Page 294
6 Conclusions......Page 297
References......Page 298