Level set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2008
|
| Ausgabe: | 2. ed., repr. |
| Schriftenreihe: | Cambridge monographs on applied and computational mathematics
3 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 1. Aufl. u.d.T.: Sethian, James A.: Level set methods |
| Beschreibung: | XX, 378 S. zahlr. Ill., graph. Darst |
| ISBN: | 9780521642040 0521642043 9780521645577 0521645573 |
Internformat
MARC
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| 100 | 1 | |a Sethian, James Albert |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Level set methods and fast marching methods |b evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science |c J. A. Sethian |
| 250 | |a 2. ed., repr. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2008 | |
| 300 | |a XX, 378 S. |b zahlr. Ill., graph. Darst | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Cambridge monographs on applied and computational mathematics |v 3 | |
| 500 | |a 1. Aufl. u.d.T.: Sethian, James A.: Level set methods | ||
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Datensatz im Suchindex
| _version_ | 1804138330052362240 |
|---|---|
| adam_text | Contents
Preface
to the Second Edition page
xi
Introduction
xv
Part I: Equations of Motion for Moving Interfaces
1
1
Formulation of Interface Propagation
3
1.1
A boundary value formulation
4
1.2
An initial value formulation
6
1.3
Advantages of these perspectives
8
1.4
A general framework
10
1.5
A look ahead/A look back
11
1.6
A larger perspective
12
Part II: Theory and Algorithms
15
2
Theory of Curve and Surface Evolution
17
2.1
Fundamental formulation
17
2.2
Total variation: stability and the growth of oscillations
18
2.3
The role of entropy conditions and weak solutions
20
2.4
Effects of curvature
24
3
Viscosity Solutions and Hamilton-Jacobi Equations
29
3.1
Viscosity solutions of Hamilton-Jacobi equations
30
3.2
Some additional comments and references
32
4
Traditional Techniques for Tracking Interfaces
34
4.1
Marker /string methods
34
4.2
Volume-of-fluid techniques
38
4.3
Constructing an approximation to the gradient
41
5
Hyperbolic Conservation Laws
44
5.1
The linear wave equation
44
5.2
The non-linear wave equation
48
vii
viii Contents
6
Basic
Algorithms for Interface Evolution
60
6.1
Convergence of schemes for Hamilton-Jacobi equations
60
6.2
Hyperbolic schemes and Hamilton-Jacobi equations
61
6.3
The example of a propagating one-dimensional graph
63
6.4
The initial value problem: the Level Set Method
65
6.5
The boundary value problem: the stationary method
68
6.6
Schemes for non-convex speed functions
69
6.7
Approximations to geometric variables
69
6.8
Calculating additional quantities
71
6.9
Initialization
72
6.10
Computational domain boundary conditions
72
6.11
Putting it all together
73
Part III: Efficiency, Adaptivity, and Extensions
75
7
Efficient Schemes: the Narrow Band Level Set Method
77
7.1
Parallel algorithms
77
7.2
Adaptive mesh refinement
78
7.3
Narrow banding and fast methods
80
7.4
Details of the Narrow Band implementation
84
8
Efficient Schemes: Fast Marching Methods
86
8.1
Iteration
87
8.2
Causality
87
8.3
The update procedure for the Fast Marching Method
90
8.4
Heap sorts and computational efficiency
90
8.5
Initial conditions
92
8.6
Network path algorithms
93
8.7
Optimal orderings
96
8.8
Higher accuracy Fast Marching Methods
96
8.9
Non-uniform orthogonal grids
98
8.10
General static Hamilton-Jacobi equations
99
8.11
Some clarifying comments
99
9
Triangulated Versions of Level Set Methods
101
9.1
Fundamentals and notation
102
9.2
A monotone scheme for H{Vu)
105
9.3
A positive scheme for homogeneous H(Vu)
109
9.4
A Petrov-Galerkin formulation
112
9.5
Time integration schemes
113
9.6
Algorithms
114
9.7
Schemes for curvature flow
116
9.8
Mesh adaptivity
118
Contents ix
10
Triangulated Fast Marching Methods
120
10.1
The update procedure
120
10.2
A scheme for a particular triangulated domain
121
10.3
Fast Marching Methods on triangulated domains
123
11
Constructing Extension Velocities
127
11.1
The need for extension velocities
127
11.2
Various approaches to extension velocities
129
11.3
Equations for extension velocities
131
11.4
Building extension velocities
133
11.5
A quick demonstration
137
11.6
Re-initialization
138
12
Tests of Basic Methods
141
12.1
The basic Cartesian Level Set Method
141
12.2
Triangulated Level Set Methods for
Н
-J
equations.
146
12.3
Accuracy of Fast Marching Methods
150
12.4
Tests of extension velocity methodology
153
13
Building Level Set and Fast Marching Applications
161
Part IV: Applications
165
14
Geometry
167
14.1
Statement of problem
167
14.2
Equations of motion
169
14.3
Results
. 169
14.4
Flows under more general metrics
175
14.5
Volume-preserving flows
175
14.6
Motion under the second derivative of curvature
177
14.7
Triple points: variational and diffusion methods
183
15
Grid Generation
191
15.1
Statement of problem
191
15.2
Equations of motion
193
15.3
Results, complications, and future work
196
16
Image Enhancement and Noise Removal
200
16.1
Statement of problem
200
16.2
Equations of motion
202
16.3
Results
208
16.4
Related work
211
17
Computer Vision: Shape Detection and Recognition
214
17.1
Shape-from-shading
215
17.2
Shape detection/recovery
218
x
Contents
17.3
Surface
evolution and the stereo problem
227
17.4
Reconstruction of obstacles in inverse problems
229
17.5
Shape recognition
231
18
Combustion, Solidification, Fluids, and Electromigration
240
18.1
Combustion
241
18.2
Crystal growth and dendritic solidification
249
18.3
Fluid mechanics
255
18.4
Additional applications
258
18.5
Void evolution and electromigration
261
19
Computational Geometry and Computer-aided Design
267
19.1
Shape-Offsetting
267
19.2
Voronoi diagrams
268
19.3
Curve flows with constraints
269
19.4
Minimal surfaces and surfaces of prescribed curvature
270
19.5
Extensions to surfaces of prescribed curvature
274
19.6
Boolean operations on shapes
277
19.7
Extracting and combining two-dimensional shapes
281
19.8
Shape smoothing
282
20
Optimality and First Arrivals
284
20.1
Optimal path planning
284
20.2
Constructing shortest paths on weighted domains
289
20.3
Constructing shortest paths on manifolds
292
20.4
Seismic traveltimes
298
20.5
Aircraft collision avoidance using Level Set Methods
305
20.6
Visibility evaluations
307
21
Etching and Deposition in Microchip Fabrication
313
21.1
Physical effects and background
313
21.2
Equations of motion for etching/deposition
317
21.3
Additional numerical issues
324
21.4
Two-dimensional results
325
21.5
Three-dimensional simulations
342
21.6
Timings
348
21.7
Validation with experimental results
349
22
Summary/New Areas/Future Work
357
Bibliography
360
Index
376
|
| adam_txt |
Contents
Preface
to the Second Edition page
xi
Introduction
xv
Part I: Equations of Motion for Moving Interfaces
1
1
Formulation of Interface Propagation
3
1.1
A boundary value formulation
4
1.2
An initial value formulation
6
1.3
Advantages of these perspectives
8
1.4
A general framework
10
1.5
A look ahead/A look back
11
1.6
A larger perspective
12
Part II: Theory and Algorithms
15
2
Theory of Curve and Surface Evolution
17
2.1
Fundamental formulation
17
2.2
Total variation: stability and the growth of oscillations
18
2.3
The role of entropy conditions and weak solutions
20
2.4
Effects of curvature
24
3
Viscosity Solutions and Hamilton-Jacobi Equations
29
3.1
Viscosity solutions of Hamilton-Jacobi equations
30
3.2
Some additional comments and references
32
4
Traditional Techniques for Tracking Interfaces
34
4.1
Marker /string methods
34
4.2
Volume-of-fluid techniques
38
4.3
Constructing an approximation to the gradient
41
5
Hyperbolic Conservation Laws
44
5.1
The linear wave equation
44
5.2
The non-linear wave equation
48
vii
viii Contents
6
Basic
Algorithms for Interface Evolution
60
6.1
Convergence of schemes for Hamilton-Jacobi equations
60
6.2
Hyperbolic schemes and Hamilton-Jacobi equations
61
6.3
The example of a propagating one-dimensional graph
63
6.4
The initial value problem: the Level Set Method
65
6.5
The boundary value problem: the stationary method
68
6.6
Schemes for non-convex speed functions
69
6.7
Approximations to geometric variables
69
6.8
Calculating additional quantities
71
6.9
Initialization
72
6.10
Computational domain boundary conditions
72
6.11
Putting it all together
73
Part III: Efficiency, Adaptivity, and Extensions
75
7
Efficient Schemes: the Narrow Band Level Set Method
77
7.1
Parallel algorithms
77
7.2
Adaptive mesh refinement
78
7.3
Narrow banding and fast methods
80
7.4
Details of the Narrow Band implementation
84
8
Efficient Schemes: Fast Marching Methods
86
8.1
Iteration
87
8.2
Causality
87
8.3
The update procedure for the Fast Marching Method
90
8.4
Heap sorts and computational efficiency
90
8.5
Initial conditions
92
8.6
Network path algorithms
93
8.7
Optimal orderings
96
8.8
Higher accuracy Fast Marching Methods
96
8.9
Non-uniform orthogonal grids
98
8.10
General static Hamilton-Jacobi equations
99
8.11
Some clarifying comments
99
9
Triangulated Versions of Level Set Methods
101
9.1
Fundamentals and notation
102
9.2
A monotone scheme for H{Vu)
105
9.3
A positive scheme for homogeneous H(Vu)
109
9.4
A Petrov-Galerkin formulation
112
9.5
Time integration schemes
113
9.6
Algorithms
114
9.7
Schemes for curvature flow
116
9.8
Mesh adaptivity
118
Contents ix
10
Triangulated Fast Marching Methods
120
10.1
The update procedure
120
10.2
A scheme for a particular triangulated domain
121
10.3
Fast Marching Methods on triangulated domains
123
11
Constructing Extension Velocities
127
11.1
The need for extension velocities
127
11.2
Various approaches to extension velocities
129
11.3
Equations for extension velocities
131
11.4
Building extension velocities
133
11.5
A quick demonstration
137
11.6
Re-initialization
138
12
Tests of Basic Methods
141
12.1
The basic Cartesian Level Set Method
141
12.2
Triangulated Level Set Methods for
Н
-J
equations.
146
12.3
Accuracy of Fast Marching Methods
150
12.4
Tests of extension velocity methodology
153
13
Building Level Set and Fast Marching Applications
161
Part IV: Applications
165
14
Geometry
167
14.1
Statement of problem
167
14.2
Equations of motion
169
14.3
Results
. 169
14.4
Flows under more general metrics
175
14.5
Volume-preserving flows
175
14.6
Motion under the second derivative of curvature
177
14.7
Triple points: variational and diffusion methods
183
15
Grid Generation
191
15.1
Statement of problem
191
15.2
Equations of motion
193
15.3
Results, complications, and future work
196
16
Image Enhancement and Noise Removal
200
16.1
Statement of problem
200
16.2
Equations of motion
202
16.3
Results
208
16.4
Related work
211
17
Computer Vision: Shape Detection and Recognition
214
17.1
Shape-from-shading
215
17.2
Shape detection/recovery
218
x
Contents
17.3
Surface
evolution and the stereo problem
227
17.4
Reconstruction of obstacles in inverse problems
229
17.5
Shape recognition
231
18
Combustion, Solidification, Fluids, and Electromigration
240
18.1
Combustion
241
18.2
Crystal growth and dendritic solidification
249
18.3
Fluid mechanics
255
18.4
Additional applications
258
18.5
Void evolution and electromigration
261
19
Computational Geometry and Computer-aided Design
267
19.1
Shape-Offsetting
267
19.2
Voronoi diagrams
268
19.3
Curve flows with constraints
269
19.4
Minimal surfaces and surfaces of prescribed curvature
270
19.5
Extensions to surfaces of prescribed curvature
274
19.6
Boolean operations on shapes
277
19.7
Extracting and combining two-dimensional shapes
281
19.8
Shape smoothing
282
20
Optimality and First Arrivals
284
20.1
Optimal path planning
284
20.2
Constructing shortest paths on weighted domains
289
20.3
Constructing shortest paths on manifolds
292
20.4
Seismic traveltimes
298
20.5
Aircraft collision avoidance using Level Set Methods
305
20.6
Visibility evaluations
307
21
Etching and Deposition in Microchip Fabrication
313
21.1
Physical effects and background
313
21.2
Equations of motion for etching/deposition
317
21.3
Additional numerical issues
324
21.4
Two-dimensional results
325
21.5
Three-dimensional simulations
342
21.6
Timings
348
21.7
Validation with experimental results
349
22
Summary/New Areas/Future Work
357
Bibliography
360
Index
376 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Sethian, James Albert |
| author_facet | Sethian, James Albert |
| author_role | aut |
| author_sort | Sethian, James Albert |
| author_variant | j a s ja jas |
| building | Verbundindex |
| bvnumber | BV035164859 |
| classification_rvk | SK 920 |
| classification_tum | MAT 671f |
| ctrlnum | (OCoLC)316142500 (DE-599)BVBBV035164859 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. ed., repr. |
| format | Book |
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| id | DE-604.BV035164859 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:52:08Z |
| indexdate | 2024-07-09T21:26:28Z |
| institution | BVB |
| isbn | 9780521642040 0521642043 9780521645577 0521645573 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016971905 |
| oclc_num | 316142500 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-M347 DE-29T DE-11 |
| owner_facet | DE-355 DE-BY-UBR DE-M347 DE-29T DE-11 |
| physical | XX, 378 S. zahlr. Ill., graph. Darst |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge monographs on applied and computational mathematics |
| series2 | Cambridge monographs on applied and computational mathematics |
| spelling | Sethian, James Albert Verfasser aut Level set methods and fast marching methods evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science J. A. Sethian 2. ed., repr. Cambridge [u.a.] Cambridge Univ. Press 2008 XX, 378 S. zahlr. Ill., graph. Darst txt rdacontent n rdamedia nc rdacarrier Cambridge monographs on applied and computational mathematics 3 1. Aufl. u.d.T.: Sethian, James A.: Level set methods Maschinelles Sehen (DE-588)4129594-8 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Randeffekt (DE-588)4484760-9 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Randeffekt (DE-588)4484760-9 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Strömungsmechanik (DE-588)4077970-1 s Maschinelles Sehen (DE-588)4129594-8 s Cambridge monographs on applied and computational mathematics 3 (DE-604)BV011073737 3 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016971905&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sethian, James Albert Level set methods and fast marching methods evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science Cambridge monographs on applied and computational mathematics Maschinelles Sehen (DE-588)4129594-8 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Randeffekt (DE-588)4484760-9 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| subject_GND | (DE-588)4129594-8 (DE-588)4128130-5 (DE-588)4484760-9 (DE-588)4077970-1 |
| title | Level set methods and fast marching methods evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science |
| title_auth | Level set methods and fast marching methods evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science |
| title_exact_search | Level set methods and fast marching methods evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science |
| title_exact_search_txtP | Level set methods and fast marching methods evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science |
| title_full | Level set methods and fast marching methods evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science J. A. Sethian |
| title_fullStr | Level set methods and fast marching methods evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science J. A. Sethian |
| title_full_unstemmed | Level set methods and fast marching methods evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science J. A. Sethian |
| title_short | Level set methods and fast marching methods |
| title_sort | level set methods and fast marching methods evolving interfaces in computational geometry fluid mechanics computer vision and materials science |
| title_sub | evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science |
| topic | Maschinelles Sehen (DE-588)4129594-8 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Randeffekt (DE-588)4484760-9 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| topic_facet | Maschinelles Sehen Numerisches Verfahren Randeffekt Strömungsmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016971905&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011073737 |
| work_keys_str_mv | AT sethianjamesalbert levelsetmethodsandfastmarchingmethodsevolvinginterfacesincomputationalgeometryfluidmechanicscomputervisionandmaterialsscience |