| Preface | p. xv |
| List of Contributors | p. xxi |
| Level Set Methods & Lagrangian Approaches | p. 1 |
| Level Set Methods | p. 3 |
| Introduction | p. 3 |
| Level Set Dictionary and Technology | p. 5 |
| Numerical Methods | p. 7 |
| Imaging Science Applications | p. 12 |
| Conclusion | p. 20 |
| Deformable Models: Classic, Topology-Adaptive and Generalized Formulations | p. 21 |
| Introduction | p. 21 |
| Classic Deformable Models | p. 23 |
| Topology-Adaptive Deformable Models | p. 30 |
| Generalized Deformable Models | p. 33 |
| Conclusion | p. 40 |
| Edge Detection & Boundary Extraction | p. 41 |
| Fast Methods for Implicit Active Contour Models | p. 43 |
| Introduction | p. 43 |
| Implicit Active Contour Models | p. 45 |
| Numerical Implementation | p. 46 |
| Experimental Results | p. 51 |
| Conclusions | p. 54 |
| Appendix: The Thomas Algorithm | p. 55 |
| Fast Edge Integration | p. 59 |
| Introduction | p. 59 |
| Mathematical Notations | p. 60 |
| Geometric Integral Measures for Active Contours | p. 61 |
| Calculus of Variations for Geometric Measures | p. 64 |
| Gradient Descent in Level Set Formulation | p. 69 |
| Efficient Numerical Schemes | p. 71 |
| Examples | p. 73 |
| Conclusions | p. 74 |
| Variational Snake Theory | p. 79 |
| Introduction | p. 79 |
| Curve flows maximizing the image contrast | p. 83 |
| Meaningful boundaries | p. 94 |
| Snakes versus Meaningful Boundaries | p. 97 |
| Scalar & Vector Image Reconstruction, Restoration | p. 101 |
| Multiplicative Denoising and Deblurring: Theory and Algorithms | p. 103 |
| Introduction | p. 103 |
| Restoration Algorithms | p. 105 |
| Constrained Nonlinear Partial Differential Equations | p. 108 |
| Restoration of Blurry Images Corrupted by Multiplicative Noise | p. 114 |
| Total Variation Minimization for Scalar/Vector Regularization | p. 121 |
| Introduction | p. 121 |
| A global approach for Total Variation minimization | p. 123 |
| A practical algorithm | p. 128 |
| Experimental results | p. 135 |
| Morphological Global Reconstruction and Levelings: Lattice and PDE Approaches | p. 141 |
| Introduction | p. 141 |
| Multiscale Levelings and Level Sets | p. 143 |
| Multiscale Image Operators on Lattices | p. 145 |
| Multiscale Triphase Operators and Leveling | p. 148 |
| Partial Differential Equations | p. 150 |
| Discussion | p. 153 |
| Grouping | p. 157 |
| Fast Marching Techniques for Visual Grouping & Segmentation | p. 159 |
| Introduction | p. 159 |
| The Multi-Label Fast Marching algorithm | p. 161 |
| Colour and texture segmentation | p. 166 |
| Change detection | p. 170 |
| Conclusion | p. 174 |
| Multiphase Object Detection and Image Segmentation | p. 175 |
| Introduction | p. 175 |
| Variational models for image segmentation and image partition | p. 178 |
| Level set formulations of minimization problems on SBV ([Omega]) | p. 179 |
| Experimental results | p. 185 |
| Conclusion | p. 193 |
| Adaptive Segmentation of Vector Valued Images | p. 195 |
| Introduction | p. 195 |
| The segmentation problem | p. 196 |
| On finding the minima | p. 198 |
| Experiments | p. 200 |
| Generalization to N regions | p. 204 |
| Conclusion and Future Work | p. 205 |
| Mumford-Shah for Segmentation and Stereo | p. 207 |
| Introduction | p. 207 |
| Mumford-Shah based curve evolution | p. 209 |
| Mumford-Shah on a Moving Manifold: Stereoscopic Segmentation | p. 216 |
| Implementation | p. 221 |
| Experiments | p. 223 |
| Knowledge-based Segmentation & Registration | p. 229 |
| Shape Analysis towards Model-based Segmentation | p. 231 |
| Introduction | p. 231 |
| Shape Modeling | p. 232 |
| Shape Registration | p. 236 |
| Segmentation & Shape Prior Constraints | p. 242 |
| Discussion | p. 249 |
| Joint Image Registration and Segmentation | p. 251 |
| Introduction | p. 251 |
| The PDE-based Approach | p. 254 |
| The Variational Approach | p. 256 |
| Experimental Results and Applications | p. 260 |
| Image Alignment | p. 271 |
| Introduction | p. 271 |
| Correspondences | p. 274 |
| Votes | p. 277 |
| Accuracy | p. 278 |
| Complexity | p. 280 |
| Projective registration | p. 280 |
| Experimental results | p. 284 |
| Motion Analysis | p. 297 |
| Variational Principles in Optical Flow Estimation and Tracking | p. 299 |
| Introduction | p. 299 |
| Geodesic Active Regions | p. 301 |
| Optical Flow Estimation & Tracking | p. 305 |
| Complete Recovery of the Apparent Motion | p. 314 |
| Discussion | p. 314 |
| Region Matching and Tracking under Deformations or Occlusions | p. 319 |
| Introduction | p. 319 |
| Defining motion and shape average | p. 323 |
| Shape and deformation of a planar contour | p. 325 |
| Moving average and tracking | p. 328 |
| Averaging and registering non-equivalent shapes | p. 329 |
| Matching with missing parts | p. 330 |
| Experiments | p. 335 |
| Computational Stereo & Implicit Surfaces | p. 341 |
| Computational Stereo: A Variational Method | p. 343 |
| Introduction and preliminaries | p. 343 |
| The simplified models | p. 347 |
| The complete model | p. 351 |
| Level Set Implementation | p. 355 |
| Results | p. 359 |
| Conclusion | p. 360 |
| Visualization, Analysis and Shape Reconstruction of Sparse Data | p. 361 |
| Introduction | p. 361 |
| Fast multiscale visualization and analysis of large data sets using distance functions | p. 363 |
| Construction of implicit surfaces using the level set method | p. 372 |
| Variational Problems and Partial Differential Equations on Implicit Surfaces: Bye Bye Triangulated Surfaces? | p. 381 |
| Introduction | p. 381 |
| The framework | p. 384 |
| Experimental examples | p. 389 |
| Concluding remarks | p. 395 |
| Medical Image Analysis | p. 399 |
| Knowledge-Based Segmentation of Medical Images | p. 401 |
| Introduction | p. 401 |
| Probability distribution on shapes | p. 403 |
| Shape priors and geodesic active contours | p. 407 |
| Statistical Image-Surface Relationship | p. 411 |
| Results | p. 419 |
| Conclusions | p. 420 |
| Topology Preserving Geometric Deformable Models for Brain Reconstruction | p. 421 |
| Introduction | p. 421 |
| Topology Preserving Geometric Deformable Model | p. 426 |
| Brain Cortical Surface Reconstruction | p. 431 |
| Conclusion | p. 438 |
| Simulations & Graphics | p. 439 |
| Editing Geometric Models | p. 441 |
| Introduction | p. 441 |
| Previous Work | p. 445 |
| Overview of the Editing Pipeline | p. 446 |
| Level Set Surface Modeling | p. 447 |
| Definition of Surface Editing Operators | p. 450 |
| Conclusion and Future Work | p. 458 |
| Appendix: Curvature of Level Set Surfaces | p. 459 |
| Simulating Natural Phenomena | p. 461 |
| Introduction | p. 461 |
| Smoke | p. 463 |
| Water | p. 468 |
| Fire | p. 474 |
| Bibliography | p. 481 |
| References | p. 481 |
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