Geometric level set methods in imaging, vision, and graphics / Stanley Osher, Nikos Paragios, editors.

Format:

Book

Author/Creator:

Osher, Stanley.

Contributor:

Paragios, Nikos.

Language:

English

Subjects (All):

Image processing--Digital techniques.

Image processing.

Physical Description:

xxix, 513 pages : illustrations ; 25 cm

Place of Publication:

New York : Springer-Verlag, [2003]

Summary:

Level set methods are emerging techniques for representing, deforming, and recovering structures in an arbitrary dimension across different fields (mathematics, fluid dynamics, graphics, imaging, vision, etc.). Advances in numerical analysis have led to computationally efficient tools for computing and analyzing interface motion within level set frameworks in a host of application settings. This authoritative edited survey provides readers with the state-of-the-art in applying level set techniques in the imaging, vision, and graphics domains, presenting thematically grouped chapters contributed by leading experts from both industry and academia. The work bridges the theoretical foundations of level set methods with the latest significant applications. It will assist readers with both the technical aspects of the field as well as its practical ramifications for areas like medical imaging, computer animation, film restoration, video surveillance, visual inspection, and a range of scientific and engineering disciplines.

The edited volume consists of a preface and 24 chapters organized in 9 thematic areas: Level Set Versus Langrangian Methods, Edge Detection & Boundary Extraction, Scale & Vector Image Reconstruction, Grouping, Knowledge-based Segmentation & Registration, Motion Analysis, Computational Stereo & Implicit Surfaces, Medical Image Analysis and Computer Graphics & Simulations. This essential resource carefully integrates the theoretical foundations of level set methods with their actual performance capabilities. Its clarity of organization and approach makes the book accessible for researchers and professionals working in the areas of vision, graphics, image processing, robotics, mathematics, and computational geometry.

Contents:

I Level Set Methods & Lagrangian Approaches 1

1 Level Set Methods / Stanley Osher 3

1.2 Level Set Dictionary and Technology 5

1.3 Numerical Methods 7

1.4 Imaging Science Applications 12

2 Deformable Models: Classic, Topology-Adaptive and Generalized Formulations / Demetri Terzopoulos 21

2.2 Classic Deformable Models 23

2.3 Topology-Adaptive Deformable Models 30

2.4 Generalized Deformable Models 33

II Edge Detection & Boundary Extraction 41

3 Fast Methods for Implicit Active Contour Models / Joachim Weickert, Gerald Kuhne 43

3.2 Implicit Active Contour Models 45

3.3 Numerical Implementation 46

3.4 Experimental Results 51

3.6 Appendix: The Thomas Algorithm 55

4 Fast Edge Integration / Ron Kimmel 59

4.2 Mathematical Notations 60

4.3 Geometric Integral Measures for Active Contours 61

4.4 Calculus of Variations for Geometric Measures 64

4.5 Gradient Descent in Level Set Formulation 69

4.6 Efficient Numerical Schemes 71

5 Variational Snake Theory / Agnes Desolneux, Lionel Moisan, Jean-Michel Morel 79

5.2 Curve flows maximizing the image contrast 83

5.3 Meaningful boundaries 94

5.4 Snakes versus Meaningful Boundaries 97

III Scalar & Vector Image Reconstruction, Restoration 101

6 Multiplicative Denoising and Deblurring: Theory and Algorithms / Leonid Rudin, Pierre-Luis Lions, Stanley Osher 103

6.2 Restoration Algorithms 105

6.3 Constrained Nonlinear Partial Differential Equations 108

6.4 Restoration of Blurry Images Corrupted by Multiplicative Noise 114

7 Total Variation Minimization for Scalar/Vector Regularization / Francoise Dibos, Georges Koepfler, Pascal Monasse 121

7.2 A global approach for Total Variation minimization 123

7.3 A practical algorithm 128

7.4 Experimental results 135

8 Morphological Global Reconstruction and Levelings: Lattice and PDE Approaches / Petros Maragos 141

8.2 Multiscale Levelings and Level Sets 143

8.3 Multiscale Image Operators on Lattices 145

8.4 Multiscale Triphase Operators and Leveling 148

8.5 Partial Differential Equations 150

IV Grouping 157

9 Fast Marching Techniques for Visual Grouping & Segmentation / Eftychis Sifakis, George Tziritas 159

9.2 The Multi-Label Fast Marching algorithm 161

9.3 Colour and texture segmentation 166

9.4 Change detection 170

10 Multiphase Object Detection and Image Segmentation / Luminita Vese 175

10.2 Variational models for image segmentation and image partition 178

10.3 Level set formulations of minimization problems on SBV ([Omega]) 179

10.4 Experimental results 185

11 Adaptive Segmentation of Vector Valued Images / Mikael Rousson, Rachid Deriche 195

11.2 The segmentation problem 196

11.3 On finding the minima 198

11.4 Experiments 200

11.5 Generalization to N regions 204

12 Mumford-Shah for Segmentation and Stereo / Anthony Yezzi, Stefano Soatto, Hailin Jin, Andy Tsai, Alan Willsky 207

12.2 Mumford-Shah based curve evolution 209

12.3 Mumford-Shah on a Moving Manifold: Stereoscopic Segmentation 216

12.4 Implementation 221

12.5 Experiments 223

V Knowledge-based Segmentation & Registration 229

13 Shape Analysis towards Model-based Segmentation / Nikos Paragios, Mikael Rousson 231

13.2 Shape Modeling 232

13.3 Shape Registration 236

13.4 Segmentation & Shape Prior Constraints 242

14 Joint Image Registration and Segmentation / Baba Vemuri, Yunmei Chen 251

14.2 The PDE-based Approach 254

14.3 The Variational Approach 256

14.4 Experimental Results and Applications 260

15 Image Alignment / Francoise Dibos, Georges Koepfler, Pascal Monasse 271

15.2 Correspondences 274

15.3 Votes 277

15.4 Accuracy 278

15.5 Complexity 280

15.6 Projective registration 280

15.7 Experimental results 284

VI Motion Analysis 297

16 Variational Principles in Optical Flow Estimation and Tracking / Nikos Paragios, Rachid Deriche 299

16.2 Geodesic Active Regions 301

16.3 Optical Flow Estimation & Tracking 305

16.4 Complete Recovery of the Apparent Motion 314

17 Region Matching and Tracking under Deformations or Occlusions / Stefano Soatto, Anthony Yezzi, Alessandro Duci 319

17.2 Defining motion and shape average 323

17.3 Shape and deformation of a planar contour 325

17.4 Moving average and tracking 328

17.5 Averaging and registering non-equivalent shapes 329

17.6 Matching with missing parts 330

17.7 Experiments 335

VII Computational Stereo & Implicit Surfaces 341

18 Computational Stereo: A Variational Method / Olivier Faugeras, Jose Gomes, Renaud Keriven 343

18.2 The simplified models 347

18.3 The complete model 351

18.4 Level Set Implementation 355

18.5 Results 359

19 Visualization, Analysis and Shape Reconstruction of Sparse Data / Hongkai Zhao, Stanley Osher 361

19.2 Fast multiscale visualization and analysis of large data sets using distance functions 363

19.3 Construction of implicit surfaces using the level set method 372

20 Variational Problems and Partial Differential Equations on Implicit Surfaces: Bye Bye Triangulated Surfaces? / Marcelo Bertalmio, Facundo Memoli, Li-Tien Cheng, Guillermo Sapiro, Stanley Osher 381

20.2 The framework 384

20.3 Experimental examples 389

VIII Medical Image Analysis 399

21 Knowledge-Based Segmentation of Medical Images / Michael Leventon, Eric Grimson, Olivier Faugeras, Ron Kikinis, William Wells III 401

21.2 Probability distribution on shapes 403

21.3 Shape priors and geodesic active contours 407

21.4 Statistical Image-Surface Relationship 411

21.5 Results 419

22 Topology Preserving Geometric Deformable Models for Brain Reconstruction / Xiao Han, Chenyang Xu, Jerry Prince 421

22.2 Topology Preserving Geometric Deformable Model 426

22.3 Brain Cortical Surface Reconstruction 431

IX Simulations & Graphics 439

23 Editing Geometric Models / Ken Museth, Ross Whitaker, David Breen 441

23.2 Previous Work 445

23.3 Overview of the Editing Pipeline 446

23.4 Level Set Surface Modeling 447

23.5 Definition of Surface Editing Operators 450

23.7 Appendix: Curvature of Level Set Surfaces 459

24 Simulating Natural Phenomena / Ronald Fedkiw 461

24.2 Smoke 463

24.3 Water 468

24.4 Fire 474.

Notes:

"With 195 illustrations."

Includes bibliographical references (pages [481]-513).

ISBN:

0387954880

OCLC:

51969303