Contributors .................................................. xv
Chapter 1
SIMULATING BACTERIAL BIOFILMS .................................. 1
David L. Chopp
1. Introduction ............................................... 1
2. General Mathematical Model ................................. 3
3. Example: Quorum-Sensing in P. aeruginosa Biofilms .......... 6
4. Numerical Implementation ................................... 8
5. Examples .................................................. 24
6. Conclusion ................................................ 28
7. Acknowledgments ........................................... 28
8. References ................................................ 28
Chapter 2
DISTANCE TRANSFORM ALGORITHMS AND THEIR
IMPLEMENTATION AND EVALUATION ................................. 33
George J. Grevera
1. Introduction .............................................. 33
2. Distance Transform Algorithms ............................. 36
3. Evaluating Distance Transform Algorithms .................. 47
4. Results of Evaluation ..................................... 49
5. Concluding Remarks ........................................ 50
6. Acknowledgments ........................................... 50
7. Appendix .................................................. 58
8. References ................................................ 59
Chapter 3
LEVEL SET TECHNIQUES FOR STRUCTURAL INVERSION
IN MEDICAL IMAGING ............................................ 61
Oliver Dorn and Dominique Lesselier
1. Introduction .............................................. 62
2. Level Set Techniques for Linear Inverse Problems .......... 63
3. Level Set Techniques for Nonlinear Inverse Problems ....... 76
4. Acknowledgments ........................................... 87
5. References ................................................ 88
Chapter 4
SHAPE AND TEXTURE-BASED DEFORMABLE MODELS
FOR FACIAL IMAGE ANALYSIS ...................................... 91
Stan Z. Li, Zhen Lei, Ying Zheng, and Zeng-Fu Wang
1. Introduction ............................................... 91
2. Classical Deformable Models ................................ 93
3. Motivations for Improvements ............................... 97
4. Direct Appearance Models ................................... 99
5. Texture-Constrained Active Shape Model .................... 104
6. Evaluation for Face Alignment ............................. 110
7. Experimental Results ...................................... 117
8. Conclusion ................................................ 129
9. Acknowledgments ........................................... 129
10. Notes ..................................................... 130
11. References ................................................ 130
Chapter 5
DETECTION OF THE BREAST CONTOUR IN MAMMOGRAMS
BY USING ACTIVE CONTOUR MODELS ................................ 133
Ricardo J. Ferrari, Rangaraj M. Rangayyan, J.E. Leo
Desautels, Annie F. Frére and Rejane A. Borges
1. Introduction .............................................. 134
2. Method 1: Identification of the breast boundary using a
traditional active deformable contour model ............... 135
3. Method 2: Identification of the breast boundary using an
adaptive active deformable contour model (AADCM) .......... 142
4. Results and Discussion .................................... 154
5. Conclusions ............................................... 160
6. Acknowledgments ........................................... 160
7. References ................................................ 162
Chapter 6
STATISTICAL DEFORMABLE MODELS FOR CARDIAC
SEGMENTATIONAND FUNCTIONAL ANALYSIS IN
GATED-SPECT STUDIES ........................................... 163
C. Tobon-Gomez, S. Ordas, A.F. Frangi, S. Aguade and
J. Castell
1. Introduction .............................................. 164
2. Three-Dimensional Active Shape Models (3D-ASM) ............ 172
3. Materials and Methods ..................................... 179
4. Results ................................................... 183
5. Discussion ................................................ 189
6. Conclusions ............................................... 190
7. Acknowledgments ........................................... 190
8. References ................................................ 191
Chapter 7
LEVEL SET FORMULATION
FOR DUAL SNAKE MODELS ......................................... 195
Gilson A. Giraldi, Paulo S.S. Rodrigues, Rodrigo L.S.
Silva, Antonio L. Apolinário Jr. and Jasjit S. Suri
1. Introduction .............................................. 195
2. Background Review ......................................... 197
3. T-Snakes Model ............................................ 199
4. Dual-T-Snakes Algorithm ................................... 200
5. Level Set ................................................. 201
6. Dual-Level-Set Approach ................................... 203
7. Segmentation Framework .................................... 213
8. Dual-Level-Set Results .................................... 215
9. Discussion ................................................ 223
10. Conclusions and Future Works .............................. 225
11. Acknowledgments ........................................... 225
12. Appendix: Theoretical Perspectives ........................ 226
13. References ................................................ 231
Chapter 8
ACCURATE TRACKING OF MONOTONICALLY
ADVANCING FRONTS .............................................. 235
M. Sabry Hassouna and A.A. Farag
1. Introduction .............................................. 235
2. The Fast Marching Method .................................. 237
3. Methods ................................................... 239
4. Numerical Experiments ..................................... 245
5. Discussion ................................................ 251
6. Conclusion ................................................ 253
7. Appendix .................................................. 253
8. References ................................................ 258
Chapter 9
TOWARD CONSISTENTLY BEHAVING DEFORMABLE MODELS
FOR IMPROVED AUTOMATION IN IMAGE SEGMENTATION ................. 259
Rongxin Li and Sébastien Ourselin
1. Introduction .............................................. 259
2. Background ................................................ 261
3. Skeleton by Influence Zones Based on Topographic
Distance .................................................. 264
4. Computing the GTD Transform and Swamping Transform ........ 266
5. Image Partitioning Based on GTD transforms ................ 268
6. Integration into Deformable Models ........................ 270
7. Qualitative Evaluations ................................... 273
8. Quantitative Validation ................................... 277
9. Application: Determination of Tissue Density .............. 285
10. Discussion and Conclusion ................................. 288
11. Acknowledgments ........................................... 289
12. Notes ..................................................... 290
13. References ................................................ 290
Chapter 10
APPLICATION OF DEFORMABLE MODELS FOR THE DETECTION
OF ACUTE RENAL REJECTION ...................................... 293
Ayman El-Baz, Aly A. Farag, Seniha E. Yuksel, Mohamed
E.A. El-Ghar, Torek A. Eldiasty, and Mohamed A. Ghoneim
1. Introduction .............................................. 294
2. Related Work in Renal Image Analysis Using DCE-MRI ........ 296
3. Related Work in Shape-Based Segmentation .................. 298
4. Methods and Data Acquisition .............................. 301
5. Kidney Segmentation ....................................... 301
6. Model for the local deformation ........................... 317
7. Cortex Segmentation ....................................... 327
8. Results ................................................... 327
9. Conclusion ................................................ 329
10. References ................................................ 330
Chapter 11
PHYSICALLY AND STATISTICALLY BASED DEFORMABLE
MODELS FOR MEDICAL IMAGE ANALYSIS ............................. 335
Ghassan Hamarneh and Chris McIntosh
1. Energy-Minimizing Deformable Models ....................... 335
2. Smart Snakes: Incorporating Knowledge about Shape ......... 351
3. Statistically Constrained Snakes: Combining ACMs and
ASMs ...................................................... 363
4. Deformable Spatiotemporal Shape Models: Extending
Active Shape Models to 2D+Time ............................ 372
5. References ................................................ 383
Chapter 12
DEFORMABLE ORGANISMS FOR MEDICAL IMAGE ANALYSIS ............... 387
Ghassan Hamarneh and Chris McIntosh
1. Introduction and Motivation ............................... 387
2. Deformable Organisms: An Artificial Life Modeling
Paradigm for Medical Image Analysis ....................... 391
3. The Layered Architecture of Deformable Organisms .......... 395
4. Results and Applications .................................. 428
5. Summary ................................................... 436
6. Notes ..................................................... 439
7. References ................................................ 439
Chapter 13
PDE-BASED THREE DIMENSIONAL PATH PLANNING
FOR VIRTUAL ENDOSCOPY ......................................... 445
M. Sabry Hassouna, Aly A. Farag, and Robert Falk
1. Introduction .............................................. 446
2. Previous Work ............................................. 446
3. Limitation of Existing Methods ............................ 449
4. The Proposed Medial Curve Extraction Framework ............ 449
5. Validation and Sensitivity Analysis ....................... 462
6. Results ................................................... 469
7. Conclusion and Future work ................................ 473
8. References ................................................ 473
Chapter 14
OBJECT TRACKING IN IMAGE SEQUENCE COMBINING
HAUSDORFF DISTANCE, NON-EXTENSIVE ENTROPY IN
LEVEL SET FORMULATION ......................................... 477
Paulo S. Rodrigues, Gilson A. Giraldi, Ruey-Feng Chang
and Jasjit S. Suri
1. Introduction .............................................. 478
2. Related Work .............................................. 481
3. Background ................................................ 484
4. Proposed Hausdorff-Tsallis Level Set Algorithm ............ 494
5. Experimental Results ...................................... 495
6. Discussion ................................................ 511
7. Conclusions and Future Work ............................... 512
8. Acknowledgments ........................................... 512
9. References ................................................ 512
Chapter 15
DEFORMABLE MODEL-BASED IMAGE REGISTRATION ..................... 517
Jundong Liu
1. Introduction .............................................. 517
2. Mutual Information Metric and Artifact Effects ............ 522
3. Segmentation-Guided Deformable Image Registration
Frameworks ................................................ 531
4. Discussion and Conclusions ................................ 538
5. References ............................................... 539
Index ......................................................... 543
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