Geometric Level Set Methods in Imaging, Vision, and Graphics / Edition 1

by Stanley Osher, Nikos Paragios

Overview

The topic of level sets is currently very timely and useful for creating realistic 3-D images and animations. They are powerful numerical techniques for analyzing and computing interface motion in a host of application settings. In computer vision, it has been applied to stereo and segmentation, whereas in graphics it has been applied to the postproduction process of in-painting and 3-D model construction.
Osher is co-inventor of the Level Set Methods, a pioneering framework introduced jointly with James Sethian from the University of Berkeley in 1998. This methodology has been used up to now to provide solutions to a wide application range not limited to image processing, computer vision, robotics, fluid mechanics, crystallography, lithography, and computer graphics.
The topic is of great interest to advanced students, professors, and R&D professionals working in the areas of graphics (post-production), video-based surveillance, visual inspection, augmented reality, document image processing, and medical image processing. These techniques are already employed to provide solutions and products in the industry (Cognitech, Siemens, Philips, Focus Imaging). An essential compilation of survey chapters from the leading researchers in the field, emphasizing the applications of the methods. This book can be suitable for a short professional course related with the processing of visual information.

Product Details

ISBN-13:	9781441930231
Publisher:	Springer New York
Publication date:	12/14/2011
Edition description:	Softcover reprint of the original 1st ed. 2003
Pages:	513
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

	Preface	xv
	List of Contributors	xxi
I	Level Set Methods & Lagrangian Approaches	1
1	Level Set Methods	3
1.1	Introduction	3
1.2	Level Set Dictionary and Technology	5
1.3	Numerical Methods	7
1.4	Imaging Science Applications	12
1.5	Conclusion	20
2	Deformable Models: Classic, Topology-Adaptive and Generalized Formulations	21
2.1	Introduction	21
2.2	Classic Deformable Models	23
2.3	Topology-Adaptive Deformable Models	30
2.4	Generalized Deformable Models	33
2.5	Conclusion	40
II	Edge Detection & Boundary Extraction	41
3	Fast Methods for Implicit Active Contour Models	43
3.1	Introduction	43
3.2	Implicit Active Contour Models	45
3.3	Numerical Implementation	46
3.4	Experimental Results	51
3.5	Conclusions	54
3.6	Appendix: The Thomas Algorithm	55
4	Fast Edge Integration	59
4.1	Introduction	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
4.7	Examples	73
4.8	Conclusions	74
5	Variational Snake Theory	79
5.1	Introduction	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	103
6.1	Introduction	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	121
7.1	Introduction	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	141
8.1	Introduction	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
8.6	Discussion	153
IV	Grouping	157
9	Fast Marching Techniques for Visual Grouping & Segmentation	159
9.1	Introduction	159
9.2	The Multi-Label Fast Marching algorithm	161
9.3	Colour and texture segmentation	166
9.4	Change detection	170
9.5	Conclusion	174
10	Multiphase Object Detection and Image Segmentation	175
10.1	Introduction	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
10.5	Conclusion	193
11	Adaptive Segmentation of Vector Valued Images	195
11.1	Introduction	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
11.6	Conclusion and Future Work	205
12	Mumford-Shah for Segmentation and Stereo	207
12.1	Introduction	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	231
13.1	Introduction	231
13.2	Shape Modeling	232
13.3	Shape Registration	236
13.4	Segmentation & Shape Prior Constraints	242
13.5	Discussion	249
14	Joint Image Registration and Segmentation	251
14.1	Introduction	251
14.2	The PDE-based Approach	254
14.3	The Variational Approach	256
14.4	Experimental Results and Applications	260
15	Image Alignment	271
15.1	Introduction	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	299
16.1	Introduction	299
16.2	Geodesic Active Regions	301
16.3	Optical Flow Estimation & Tracking	305
16.4	Complete Recovery of the Apparent Motion	314
16.5	Discussion	314
17	Region Matching and Tracking under Deformations or Occlusions	319
17.1	Introduction	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	343
18.1	Introduction and preliminaries	343
18.2	The simplified models	347
18.3	The complete model	351
18.4	Level Set Implementation	355
18.5	Results	359
18.6	Conclusion	360
19	Visualization, Analysis and Shape Reconstruction of Sparse Data	361
19.1	Introduction	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?	381
20.1	Introduction	381
20.2	The framework	384
20.3	Experimental examples	389
20.4	Concluding remarks	395
VIII	Medical Image Analysis	399
21	Knowledge-Based Segmentation of Medical Images	401
21.1	Introduction	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
21.6	Conclusions	420
22	Topology Preserving Geometric Deformable Models for Brain Reconstruction	421
22.1	Introduction	421
22.2	Topology Preserving Geometric Deformable Model	426
22.3	Brain Cortical Surface Reconstruction	431
22.4	Conclusion	438
IX	Simulations & Graphics	439
23	Editing Geometric Models	441
23.1	Introduction	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
23.6	Conclusion and Future Work	458
23.7	Appendix: Curvature of Level Set Surfaces	459
24	Simulating Natural Phenomena	461
24.1	Introduction	461
24.2	Smoke	463
24.3	Water	468
24.4	Fire	474
	Bibliography	481
	References	481