Mathematical problems in image processing: partial differential equations and the calculus of variations
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2006
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Applied mathematical sciences
147 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXXI, 377 S. Ill. graph. Darst. |
| ISBN: | 0387322000 9780387322001 9781441921826 |
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| 100 | 1 | |a Aubert, Gilles |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Mathematical problems in image processing |b partial differential equations and the calculus of variations |c Gilles Aubert ; Pierre Kornprobst |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 2006 | |
| 300 | |a XXXI, 377 S. |b Ill. graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Applied mathematical sciences |v 147 | |
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| 650 | 4 | |a Image processing |x Mathematics | |
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Datensatz im Suchindex
| _version_ | 1804135584593084416 |
|---|---|
| adam_text | Contents
Foreword
Preface to the Second Edition
Preface to the First Edition
Guide to the Main Mathematical Concepts and
Their Application
Notation and Symbols
1
1.1
1.2
1.3
1.4
2
How to Read This Chapter
2.1
2.1.1
2.1.2
2.1.3
2.1.4
2.2
xx Contents
2.2.1 Basic
2.2.2
2.2.3
2.2.4
2.3
2.3.1
2.3.2
2.3.3
2.3.4
2.4
2.4.1
2.4.2
2.4.3
2.5
2.5.1
2.5.2
2.5.3
2.5.4
2.5.5
2.5.6
3
How to Read This Chapter
3.1
3.2
3.2.1
3.2.2
3.2.3
the Minimization Problem
3.2.4
The Projection Approach
The Half-Quadratic Minimization Approach
3.2.5
3.2.6
3.3
3.3.1
The Heat Equation
Nonlinear Diffusion
The Alvarez-Guichard-Lions-Morel
Scale Space Theory
Weickert s Approach
Surface Based Approaches
3.3.2
The
Contents xxi
Regularization
Catte et al
3.3.3
The Osher and Rudin Shock Filters
A Case Study: Construction of a Solution by
the Method of Characteristics
Comments on the Shock-Filter Equation
3.3.4
and PDEs
Neighborhood Filters
How to Suppress the Staircase Effect?
Nonlocal Means Filter (NL-Means)
4
How to Read This Chapter
4.1
4.2
4.2.1
4.2.2
Existence of a Solution
4.2.3
4.2.4
Functional
4.2.5
4.3
4.3.1
4.3.2
4.3.3
4.3.4
Characterization of the Distance Function
Existence and Uniqueness
4.3.5
4.3.6
Global Stopping Criterion
Toward More General Shape Representation
5
How to Read This Chapter
5.1
5.1.1
5.1.2
The
The
The Chan and Shen Total Variation Minimization
Approach
xxii Contents
5.1.3 PDE-Based
The Bertalmio et
The Chan and Shen Curvature-Driven Diffusion
Approach
5.1.4
5.2
5.2.1
5.2.2
5.2.3
5.2.4
Prior Numerical Contribution
The Aujol
Study of the Asymptotic Case
Back to Meyer s Model
5.2.5
Denoising Capabilities
Dealing With Texture
5.2.6
5.3
5.3.1
5.3.2
The Optical Flow Constraint (OFC)
Solving the Aperture Problem
Overview of a Discontinuity-Preserving
Variational Approach
Alternatives to the OFC
5.3.3
Introduction
A Variational Formulation
Mathematical Study of the
Time-Sampled Energy
Experiments
5.3.4
Principles of Video Inpainting
Total Variation (TV) Minimization Approach
Motion Compensated
5.4
5.4.1
5.4.2
Image Classification
5.4.3
Restoration
5.5
5.5.1
5.5.2
Contents xxiii
5.5.3 The Energy
5.5.4 PDE-Based
A Introduction to Finite Difference Methods
How to Read This Chapter
A.I Definitions and Theoretical Considerations Illustrated
by the 1-D Parabolic Heat Equation
A.I.I Getting Started
A.I.
A.1.3 The Lax Theorem
A.
A.I.
A.
A.3 Difference Schemes in Image Analysis
A.3.1 Getting Started
A.
A.
Shock Filters
A.3.4 Curve Evolution with the Level-Set Method
Mean Curvature Motion
Constant Speed Evolution
The Pure Advection Equation
Image Segmentation by the Geodesic
Active Contour Model
В
How to Read This Chapter
B.I The CImg Library
B.2 What Is Available Online?
References
Index
|
| adam_txt |
Contents
Foreword
Preface to the Second Edition
Preface to the First Edition
Guide to the Main Mathematical Concepts and
Their Application
Notation and Symbols
1
1.1
1.2
1.3
1.4
2
How to Read This Chapter
2.1
2.1.1
2.1.2
2.1.3
2.1.4
2.2
xx Contents
2.2.1 Basic
2.2.2
2.2.3
2.2.4
2.3
2.3.1
2.3.2
2.3.3
2.3.4
2.4
2.4.1
2.4.2
2.4.3
2.5
2.5.1
2.5.2
2.5.3
2.5.4
2.5.5
2.5.6
3
How to Read This Chapter
3.1
3.2
3.2.1
3.2.2
3.2.3
the Minimization Problem
3.2.4
The Projection Approach
The Half-Quadratic Minimization Approach
3.2.5
3.2.6
3.3
3.3.1
The Heat Equation
Nonlinear Diffusion
The Alvarez-Guichard-Lions-Morel
Scale Space Theory
Weickert's Approach
Surface Based Approaches
3.3.2
The
Contents xxi
Regularization
Catte et al
3.3.3
The Osher and Rudin Shock Filters
A Case Study: Construction of a Solution by
the Method of Characteristics
Comments on the Shock-Filter Equation
3.3.4
and PDEs
Neighborhood Filters
How to Suppress the Staircase Effect?
Nonlocal Means Filter (NL-Means)
4
How to Read This Chapter
4.1
4.2
4.2.1
4.2.2
Existence of a Solution
4.2.3
4.2.4
Functional
4.2.5
4.3
4.3.1
4.3.2
4.3.3
4.3.4
Characterization of the Distance Function
Existence and Uniqueness
4.3.5
4.3.6
Global Stopping Criterion
Toward More General Shape Representation
5
How to Read This Chapter
5.1
5.1.1
5.1.2
The
The
The Chan and Shen Total Variation Minimization
Approach
xxii Contents
5.1.3 PDE-Based
The Bertalmio et
The Chan and Shen Curvature-Driven Diffusion
Approach
5.1.4
5.2
5.2.1
5.2.2
5.2.3
5.2.4
Prior Numerical Contribution
The Aujol
Study of the Asymptotic Case
Back to Meyer's Model
5.2.5
Denoising Capabilities
Dealing With Texture
5.2.6
5.3
5.3.1
5.3.2
The Optical Flow Constraint (OFC)
Solving the Aperture Problem
Overview of a Discontinuity-Preserving
Variational Approach
Alternatives to the OFC
5.3.3
Introduction
A Variational Formulation
Mathematical Study of the
Time-Sampled Energy
Experiments
5.3.4
Principles of Video Inpainting
Total Variation (TV) Minimization Approach
Motion Compensated
5.4
5.4.1
5.4.2
Image Classification
5.4.3
Restoration
5.5
5.5.1
5.5.2
Contents xxiii
5.5.3 The Energy
5.5.4 PDE-Based
A Introduction to Finite Difference Methods
How to Read This Chapter
A.I Definitions and Theoretical Considerations Illustrated
by the 1-D Parabolic Heat Equation
A.I.I Getting Started
A.I.
A.1.3 The Lax Theorem
A.
A.I.
A.
A.3 Difference Schemes in Image Analysis
A.3.1 Getting Started
A.
A.
Shock Filters
A.3.4 Curve Evolution with the Level-Set Method
Mean Curvature Motion
Constant Speed Evolution
The Pure Advection Equation
Image Segmentation by the Geodesic
Active Contour Model
В
How to Read This Chapter
B.I The CImg Library
B.2 What Is Available Online?
References
Index |
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| callnumber-sort | QA 11 |
| callnumber-subject | QA - Mathematics |
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| ctrlnum | (OCoLC)254684975 (DE-599)BVBBV021735602 |
| dewey-full | 621.36/70151 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 621 - Applied physics |
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| dewey-search | 621.36/70151 |
| dewey-sort | 3621.36 570151 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Informatik Mathematik Elektrotechnik / Elektronik / Nachrichtentechnik |
| discipline_str_mv | Informatik Mathematik Elektrotechnik / Elektronik / Nachrichtentechnik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV021735602 |
| illustrated | Illustrated |
| index_date | 2024-07-02T15:27:46Z |
| indexdate | 2024-07-09T20:42:50Z |
| institution | BVB |
| isbn | 0387322000 9780387322001 9781441921826 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014949050 |
| oclc_num | 254684975 |
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| owner_facet | DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-824 DE-29T DE-91 DE-BY-TUM DE-M347 DE-11 DE-20 DE-188 |
| physical | XXXI, 377 S. Ill. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Springer |
| record_format | marc |
| series | Applied mathematical sciences |
| series2 | Applied mathematical sciences |
| spelling | Aubert, Gilles Verfasser aut Mathematical problems in image processing partial differential equations and the calculus of variations Gilles Aubert ; Pierre Kornprobst 2. ed. New York [u.a.] Springer 2006 XXXI, 377 S. Ill. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences 147 Computação gráfica larpcal Mathematik Image processing Mathematics Bildverarbeitung (DE-588)4006684-8 gnd rswk-swf Variationsrechnung (DE-588)4062355-5 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Bildverarbeitung (DE-588)4006684-8 s Partielle Differentialgleichung (DE-588)4044779-0 s Variationsrechnung (DE-588)4062355-5 s DE-604 Kornprobst, Pierre Verfasser aut Applied mathematical sciences 147 (DE-604)BV000005274 147 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014949050&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Aubert, Gilles Kornprobst, Pierre Mathematical problems in image processing partial differential equations and the calculus of variations Applied mathematical sciences Computação gráfica larpcal Mathematik Image processing Mathematics Bildverarbeitung (DE-588)4006684-8 gnd Variationsrechnung (DE-588)4062355-5 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4006684-8 (DE-588)4062355-5 (DE-588)4044779-0 |
| title | Mathematical problems in image processing partial differential equations and the calculus of variations |
| title_auth | Mathematical problems in image processing partial differential equations and the calculus of variations |
| title_exact_search | Mathematical problems in image processing partial differential equations and the calculus of variations |
| title_exact_search_txtP | Mathematical problems in image processing partial differential equations and the calculus of variations |
| title_full | Mathematical problems in image processing partial differential equations and the calculus of variations Gilles Aubert ; Pierre Kornprobst |
| title_fullStr | Mathematical problems in image processing partial differential equations and the calculus of variations Gilles Aubert ; Pierre Kornprobst |
| title_full_unstemmed | Mathematical problems in image processing partial differential equations and the calculus of variations Gilles Aubert ; Pierre Kornprobst |
| title_short | Mathematical problems in image processing |
| title_sort | mathematical problems in image processing partial differential equations and the calculus of variations |
| title_sub | partial differential equations and the calculus of variations |
| topic | Computação gráfica larpcal Mathematik Image processing Mathematics Bildverarbeitung (DE-588)4006684-8 gnd Variationsrechnung (DE-588)4062355-5 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Computação gráfica Mathematik Image processing Mathematics Bildverarbeitung Variationsrechnung Partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014949050&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005274 |
| work_keys_str_mv | AT aubertgilles mathematicalproblemsinimageprocessingpartialdifferentialequationsandthecalculusofvariations AT kornprobstpierre mathematicalproblemsinimageprocessingpartialdifferentialequationsandthecalculusofvariations |