Contents	5
	Preface	19
	List of Contributors	23
	Part I Image Reconstruction	35
	Chapter 1Diffusion Filters and Wavelets: What Can They Learn from Each Other?	36
	1.1 Introduction	36
	1.2 Basic Methods	37
	1.3 Relations for Space-Discrete Diffusion	39
	1.4 Relations for Fully Discrete Diffusion	42
	1.5 Wavelets with Higher Vanishing Moments	46
	1.6 Summary	49
	Chapter 2 Total Variation Image Restoration: Overview and Recent Developments	50
	2.1 Introduction	50
	2.2 Properties and Extensions	52
	2.3 Caveats	54
	2.4 Variants	55
	2.5 Further Applications to Image Reconstruction	59
	2.6 Numerical Methods	62
	Chapter 3 PDE-Based Image and Surface Inpainting	66
	3.1 Introduction	66
	3.2 Inpainting by Propagation of Information	69
	3.3 Variational Models for Filling-In	75
	3.4 Surface Reconstruction: The Laplace and the Absolute Minimizing Lipschitz Extension Interpolation	85
	3.5 Dealing with texture	88
	3.6 Other Approaches	91
	3.7 Concluding Remarks	93
	3.9 Acknowledgments	94
	3.8 Appendix	93
	3.9 Acknowledgments	94
	Part II Boundary Extraction, Segmentation and Grouping	96
	Chapter 4 Levelings: Theory and Practice	98
	4.1 Introduction	98
	4.2 Binary connected operators	99
	4.3 Flat grey-tone connected operators	100
	4.4 Extended connected operators	101
	4.5 Levelings for image simplification	104
	4.6 Conclusion	110
	Chapter 5 Graph Cuts in Vision and Graphics: Theories and Applications	112
	5.1 Introduction	112
	5.2 Graph Cuts Basics	113
	5.3 Graph Cuts for Binary Optimization	115
	5.4 Graph Cuts as Hypersurfaces	117
	5.5 Generalizing Graph Cuts for Multi- Label Problems	125
	Chapter 6 Minimal Paths and Fast Marching Methods for Image Analysis	130
	6.1 Introduction	130
	6.2 Minimal Paths	131
	6.3 Minimal paths from a set of endpoints pk	138
	6.4 Multiple minimal paths between regions Rk	140
	6.5 Segmentation by Fast Marching	141
	6.6 Centered Minimal Paths and virtual endoscopy	143
	6.7 Conclusion	144
	Chapter 7 Integrating Shape and Texture in Deformable Models: from Hybrid Methods to Metamorphs	146
	7.1 Introduction	146
	7.2 Hybrid Segmentation Method	149
	7.3 Metamorphs: Deformable Shape and Texture Models	153
	7.4 Conclusions	161
	Chapter 8 Variational Segmentation with Shape Priors	164
	8.1 Introduction	164
	8.2 Shape Representation	166
	8.3 Learning Shape Statistics	169
	8.4 Variational Segmentation and Shape Priors	172
	8.5 Conclusion and Further Work	176
	Chapter 9 Curve Propagation, Level Set Methods and Grouping	178
	9.1 Introduction	178
	9.2 On the Propagation of Curves	179
	9.3 Data-driven Segmentation	184
	9.4 Prior Knowledge	187
	9.5 Discussion	192
	Chapter 10 On a Stochastic Model of Geometric Snakes	194
	10.1 Introduction	194
	10.2 Overview of Geodesic Snake Models	196
	10.3 Birth and Death Zero Range Particle Systems	196
	10.4 Poisson System Simulation	197
	10.5 Choosing a Random Event	199
	10.6 Similarity Invariant Flows	201
	10.7 Stochastic Snakes	204
	10.8 Experimental Results	206
	10.9 Conclusions and Future Research	207
	Part III Shape Modeling & Registration	209
	Chapter 11 Invariant Processing and Occlusion Resistant Recognition of Planar Shapes	210
	11.1 Introduction	210
	11.2 Invariant Point Locations and Displacements	211
	11.3 Invariant Boundary Signatures for Recognition under Partial Occlusions	215
	11.4 Invariant Processing of Planar Shapes	217
	11.5 Concluding Remarks	221
	Chapter 12 Planar Shape Analysis and Its Applications in Image-Based Inferences	222
	12.1 Introduction	222
	12.2 A Framework for Planar Shape Analysis	224
	12.3 Clustering of Shapes	227
	12.4 Interpolation of Shapes in Echocardiographic Image- Sequences	229
	12.5 Study of Human Silhouettes in Infrared Images	233
	12.6 Summary & Discussion	235
	Chapter 13 Diffeomorphic Point Matching	238
	13.1 Introduction	238
	13.2 Diffeomorphic Landmark Matching	239
	13.3 Diffeomorphic Point Shape Matching	247
	13.4 Discussion	252
	Chapter 14 Uncertainty-Driven, Point-Based Image Registration	254
	14.1 Introduction	254
	14.2 Objective Function, ICP and Normal Distances	256
	14.3 Parameter Estimates and Covariance Matrices	259
	14.4 Stable Sampling of ICP Constraints	261
	14.5 Dual-Bootstrap ICP	263
	14.6 Discussion and Conclusion	267
	Part IV Motion Analysis, Optical Flow & Tracking	270
	Chapter 15 Optical Flow Estimation	272
	15.1 Introduction	272
	15.2 Basic Gradient-Based Estimation	273
	15.3 Iterative Optical Flow Estimation	276
	15.4 Robust Motion Estimation	279
	15.5 Motion Models	280
	15.6 Global Smoothing	282
	15.7 Conservation Assumptions	283
	15.8 Probabilistic Formulations	285
	Chapter 16 From Bayes to PDEs in Image Warping	292
	16.1 Motivation and problem statement	292
	16.2 Admissible warps	293
	16.3 Bayesian formulation of warp estimation	295
	16.4 Likelihood: Matching criteria	297
	16.5 Prior: Smoothness criteria	299
	16.6 Warp time and Computing time	302
	16.7 From fluid registration to diffeomorphic minimizers	303
	16.8 Discussion and open problems	304
	Chapter 17 Image Alignment and Stitching	306
	17.1 Introduction	306
	17.2 Motion models	307
	17.3 Direct and feature-based alignment	310
	17.4 Global registration	316
	17.5 Choosing a compositing surface	319
	17.6 Seam selection and pixel blending	320
	17.7 Extensions and open issues	324
	Chapter 18 Visual Tracking: A Short Research Roadmap	326
	18.1 Introduction	326
	18.2 Simple appearance models	327
	18.3 Active contours	329
	18.4 Spatio-temporal filtering	334
	18.5 Further topics	339
	Chapter 19 Shape Gradient for Image and Video Segmentation	342
	19.1 Introduction	342
	19.2 Problem Statement	343
	19.3 From shape derivation tools towards region-based active contours models	345
	19.4 Segmentation using Statistical Region-dependent descriptors	350
	19.5 Discussion	355
	Chapter 20 Model-Based Human Motion Capture	358
	20.1 Introduction	358
	20.2 Methods	360
	20.3 Results	367
	20.4 Discussion	371
	Chapter 21 Modeling Dynamic Scenes: An Overview of Dynamic Textures	374
	21.1 Introduction	374
	21.2 Representation of dynamic textures	377
	21.3 Leaming dynamic textures	377
	21.4 Model Validation	380
	21.5 Recognition	382
	21.6 Segmentation	384
	21.7 Discussion	388
	PartV 3D from Images, Projective Geometry & Stereo Reconstruction	390
	Chapter 22 Differential Geometry from the Frenet Point of View: Boundary Detection, Stereo^ Texture and Color	392
	22.1 Introduction	392
	22.2 Introduction to Frenet-Serret	394
	22.3 Co-Circularity in R^ x S 1	396
	22.4 Stereo: Inferring Frenet 3-Frames from 2-Frames	398
	22.5 Covariant Derivatives, Oriented Textures, and Color	400
	22.6 Discussion	405
	Chapter 23 Shape From Shading	408
	23.1 Introduction	408
	23.2 Mathematical formulation of the SFS problem	410
	23.3 Mathematical study of the SFS problem	412
	23.4 Numerical Solutions by "Propagation and PDEs methods"	415
	23.5 Examples of numerical results	418
	23.6 Conclusion	421
	Chapter 24 3D from Image Sequences: Calibration, Motion and Shape Recovery	422
	24.1 Introduction	422
	24.2 Relating Images	425
	24.3 Structure and motion recovery	426
	24.4 Dense surface estimation	431
	24.5 3D surface reconstruction	433
	24.6 Conclusion	435
	Chapter 25 Multi-view Reconstruction of Static and Dynamic Scenes	438
	25.1 Introduction	438
	25.2 Reconstruction of Static Scenes	439
	25.3 Reconstraction of Dynamic Scenes	449
	25.4 Sensor Planning	452
	25.5 Conclusion	454
	Chapter 26 Graph Cut Algorithms for Binocular Stereo with Occlusions	456
	26.1 Traditional stereo methods	456
	26.2 Stereo with occlusions	459
	26.3 Voxel labeling algorithm	462
	26.4 Pixel labeling algorithm	463
	26.5 Minimizing the energy	464
	26.6 Experimental results	465
	26.7 Conclusions	467
	Chapter 27 Modelling Non-Rigid Dynamic Scenes from Multi-View Image Sequences	472
	27.1 Introduction	472
	27.2 Previous Work	473
	27.3 The Prediction Error as a New Metrie for Stereovision and Scene Flow Estimation	476
	27.4 Experimental Results	481
	27.5 Conclusion and Future Work	484
	Part VI Applications: Medical Image Analysis	487
	Chapter 28 Interactive Graph-Based Segmentation Methods in Cardiovascular Imaging	488
	28.1 Introduction	488
	28.2 Characteristic Behaviors of the Algorithms	489
	28.3 Applications on CT Cardiovascular data	492
	28.4 Conclusions	502
	Chapter 29 3D Active Shape and Appearance Models in Cardiac Image Analysis	504
	29.1 Introduction	504
	29.2 Methods	508
	29.3 Discussion and Conclusion	517
	Chapter 30 Characterization of Diffusion Anisotropy in DWI	520
	30.1 Introduction	520
	30.2 EstimationofPDF	522
	30.3 Estimation of ADC profiles	526
	30.4 Conclusion	532
	Chapter 31 Segmentation of Diffusion Tensor Images	536
	31.1 Introduction	536
	31.2 K-means for DTI segmentation	538
	31.3 Boundary-based active contours for DTI segmentation	538
	31.4 Region- based active contour for DTI segmentation	540
	31.5 Conclusion	547
	Chapter 32 Variational Approaches to the Estimation^ Regularization and Segmentation of Diffusion Tensor Images	550
	32.1 Introduction	550
	32.2 Estimation of Diffusion Tensor Images	551
	32.3 Regularization of Diffusion Tensor Images	553
	32.4 Segmentation of Diffusion Tensor Images	555
	32.5 Conclusion	563
	Chapter 33 An Introduction to Statistical Methods of Medical Image Registration	564
	33.1 Introduction	564
	33.2 The Similarity Measures	565
	33.3 Conclusion	574
	Bibliography	576