Variational methods in image segmentation: with seven image processing experiments
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston u.a.
Birkhäuser
1995
|
| Schriftenreihe: | Progress in nonlinear differential equations and their applications
14 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 215 - 237 |
| Beschreibung: | XVI, 245 S. Ill., graph. Darst. |
| ISBN: | 3764337206 0817637206 |
Internformat
MARC
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| 100 | 1 | |a Morel, Jean-Michel |d 1953- |e Verfasser |0 (DE-588)136525229 |4 aut | |
| 245 | 1 | 0 | |a Variational methods in image segmentation |b with seven image processing experiments |c Jean-Michel Morel ; Sergio Solimini |
| 264 | 1 | |a Boston u.a. |b Birkhäuser |c 1995 | |
| 300 | |a XVI, 245 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in nonlinear differential equations and their applications |v 14 | |
| 500 | |a Literaturverz. S. 215 - 237 | ||
| 650 | 7 | |a Images, traitement des - Techniques numériques - Mathématiques |2 ram | |
| 650 | 7 | |a Mesure géométrique, théorie de la |2 ram | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Geometric measure theory | |
| 650 | 4 | |a Image processing |x Digital techniques |x Mathematics | |
| 650 | 0 | 7 | |a Geometrische Maßtheorie |0 (DE-588)4125258-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Bildsegmentierung |0 (DE-588)4145448-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Variationsrechnung |0 (DE-588)4062355-5 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Variationsrechnung |0 (DE-588)4062355-5 |D s |
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| 830 | 0 | |a Progress in nonlinear differential equations and their applications |v 14 |w (DE-604)BV007934389 |9 14 | |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006658940&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-006658940 | |
Datensatz im Suchindex
| _version_ | 1807682363545616384 |
|---|---|
| adam_text |
CONTENTS
PREFACE
.
IX
INTRODUCTION
.
XI
PART
I.
MODELIZATION
1.
EDGE
DETECTION
AND
SEGMENTATION
.
3
1.
IS
THERE
A
GENERAL
THEORY
FOR
SEGMENTATION?
.
3
2.
PRINCIPLES
OF
MULTISCALE
ANALYSIS
.
7
2.
LINEAR
AND
NONLINEAR
MULTISCALE
FILTERING
.
8
1.
THE
LINEAR
MODEL
(HILDRETH,
MARR,
WITKIN,
KOENDERINK,.)
.
8
2.
THE
PERONA
AND
MALIK
THEORY
.
11
3.
ANISOTROPIC
DIFFUSION
AND
"
MEAN
CURVATURE
MOTION
"
.
15
4.
IMAGE
RESTORATION
BY
MEAN
CURVATURE
MOTION
.
16
3.
REGION
AND
EDGE
GROWING
METHODS
.
21*
1.
FORMALIZATION
OF
REGION
GROWING
METHODS.
(BRICE
AND
FENNEMA,
PAVLIDIS,
.)
.
21
2.
EDGE
GROWING
METHODS
.
25
3.
HYBRID
METHODS
.
28
4.
HOW
TO
TRANSLATE
A
HEURISTIC
ALGORITHM
INTO
A
VARIATIONAL
THEORY
.
29
4.
VARIATIONAL
THEORIES
OF
SEGMENTATION
.
35
1.
THE
NITZBERG
AND
MUMFORD
2.1-D
SKETCH
.
35
2.
THE
"
STRUCTURAL
SALIENCY
"
OF
SHA
'
ASHUA
AND
ULLMAN
.
37
3.
THE
"
MINIMUM
DESCRIPTION
LENGTH
"
METHOD
OF
YVON
LECLERC
.
.
39
4.
ALGORITHMS
FOR
MINIMIZING
THE
GENERAL
MUMFORD
AND
SHAH
ENERGY
.
40
5.
AFFINE
INVARIANT
SEGMENTATION
.
42
5.
THE
PIECEWISE
CONSTANT
MUMFORD-SHAH
MODEL:
MATHEMATICAL
ANALYSIS
.
46
1.
MAIN
THEOREM
.
47
2.
DEFINITION
AND
ELEMENTARY
PROPERTIES
OF
SEGMENTATIONS
.
47
3.
PROPERTIES
OF
SEGMENTATIONS
OBTAINED
BY
MERGING.
PROOF
OF
THE
MAIN
THEOREM
.
52
VI
CONTENTS
4.
A
PYRAMIDAL
ALGORITHM
COMPUTING
2-NORMAL
SEGMENTATIONS
.
58
5.
EXAMPLES
.
60
PART
II.
ELEMENTS
OF
GEOMETRIC
MEASURE
THEORY
6.
HAUSDORFF
MEASURE
.
63
1.
HAUSDORFF
OUTER
MEASURE
.
63
2.
OUTER
MEASURES
IN
TOPOLOGICAL
SPACES
.
70
3.
CONNECTED
SETS
OF
FINITE
1-DIMENSIONAL
HAUSDORFF
MEASURE
.
75
4.
A
SUGGESTING
EXAMPLE
OF
HAUSDORFF
MEASURABLE
SET
WITH
FINITE
LENGTH
.
76
7.
COVERING
LEMMAS
IN
A
METRIC
SPACE
.
79
1.
ELEMENTARY
PROPERTIES
OF
GENERIC
COVERINGS
.
79
2.
VITALI
COVERINGS
.
82
3.
HAUSDORFF
AND
LEBESGUE
MEASURE
.
84
8.
DENSITY
PROPERTIES
.
86
1.
UPPER
AND
LOWER
DENSITY
.
87
2.
REGULAR
SETS
.
90
9.
TANGENCY
PROPERTIES
OF
REGULAR
SUBSETS
OF
.
94
1.
REFLECTION
LEMMAS
.
94
2.
APPROXIMATE
TANGENT
SPACE
.
99
3.
EXISTENCE
OF
A
TANGENT
SPACE
.
108
10.
SEMICONTINUITY
PROPERTIES
OF
HAUSDORFF
MEASURE
118
1.
HAUSDORFF
DISTANCE
.
118
2.
COUNTEREXAMPLES
TO
THE
SEMICONTINUITY
OF
THE
HAUSDORFF
MEASURE
FOR
THE
HAUSDORFF
METRIC
.
120
3.
UPPER
SEMICONTINUITY
IN
[0,1]
.
121
4.
LOWER
SEMICONTINUITY
OF
THE
HAUSDORFF
MEASURE
ON
UNIFORMLY
CONCENTRATED
SETS
.
122
5.
SEQUENCES
OF
COMPACT
CONNECTED
1-SETS
.
125
11.
RECTIFIABLE
SETS
.
127
1.
RECTIFIABLE
SURFACES
AND
RECTIFIABLE
SETS
.
127
2.
REGULARITY
OF
RECTIFIABLE
SETS
.
128
3.
RECTIFIABLE
CURVES
.
133
12.
PROPERTIES
OF
REGULAR
AND
RECTIFIABLE
SETS
.
136
1.
GEOMETRIC
LEMMAS
.
136
2.
EQUIVALENCE
OF
THE
NOTIONS
OF
REGULARITY
AND
RECTIFIABILITY
.
.
.
138
CONTENTS
VII
3.
PROJECTION
PROPERTIES
OF
IRREGULAR
SETS
.
142
PART
III.
EXISTENCE
AND
STRUCTURAL
PROPERTIES
OF
THE
MINIMAL
SEGMENTATIONS
FOR
THE
MUMFORD-SHAH
MODEL
13.
PROPERTIES
OF
THE
APPROXIMATING
IMAGE
IN
THE
MUMFORD-SHAH
MODEL
.
151
1.
NOTATION
AND
PRELIMINARY
LEMMAS
.
151
2.
GREEN
FORMULAS
.
155
3.
INTERIOR
REGULARITY
ESTIMATES
.
161
14.
SMALL
OSCILLATION
COVERINGS
AND
THE
EXCISION
METHOD
.
165
1.
THE
EXCISION
METHOD
.
165
2.
SMALL
OSCILLATION
COVERINGS
.
167
3.
THE
EXCISION
LEMMAS
.
169
4.
THE
INTERPOLATION
LEMMA
.
170
5.
ENERGY
JUMP
ESTIMATES
.
174
6.
PROOF
OF
THE
EXCISION
LEMMAS
.
176
15.
DENSITY
PROPERTIES
AND
EXISTENCE
THEORY
FOR
THE
MUMFORD-SHAH
MINIMIZERS
.
1&2
1.
THE
ESSENTIALITY
PROPERTY
.
183
2.
THE
UNIFORM
DENSITY
PROPERTY
.
184
3.
THE
CONCENTRATION
PROPERTY
.
188
4.
THE
PROJECTION
PROPERTIES
.
189
5.
EXISTENCE
THEORY
FOR
THE
MUMFORD-SHAH
MINIMIZERS
.
192
6.
NONUNIQUENESS
OF
THE
MUMFORD-SHAH
MINIMIZERS
.
197
16.
FURTHER
PROPERTIES
OF
THE
MINIMIZERS:
COVERING
THE
EDGE
SET
WITH
A
SINGLE
CURVE
.
199
1.
THE
DAVID-SEMMES
CONCENTRATED
RECTIFIABILITY
PROPERTY
.
.
.
199
2.
DUAL
CURVE
LEMMAS
.
202
3.
EXISTENCE
OF
A
RECTIFIABLE
CURVE
CONTAINING
THE
EDGE
SET
.
205
4.
EXISTENCE
OF
A
REGULAR
CURVE
CONTAINING
THE
EDGE
SET
.
206
BIBLIOGRAPHICAL
NOTES
.
209
REFERENCES
REFERENCES
OF
PART
I
.
215
I-A)
IMAGE
SEGMENTATION
AND
EDGE
DETECTION,
SURVEYS
AND
MONOGRAPHS.
I-B)
ARTICLES
PROPOSING
ALGORITHMS
FOR
EDGE
DETECTION
AND
IMAGE
SEGMENTATION.
VIII
CONTENTS
I-C)
SCALE
SPACE
THEORY.
I-D)
MATHEMATICAL
ANALYSIS
RELATED
TO
SCALE
SPACE
THEORY.
I-E)
MONOGRAPHS
IN
IMAGE
PROCESSING.
I-F)
ARTICLES
ON
TEXTURE
ANALYSIS
AND
SEGMENTATION.
I-G)
WAVELETS,
THEORY
AND
RELATION
TO
IMAGE
PROCESSING
AND
SCALE
SPACE.
I-H)
RELATED
TOPICS
IN
PSYCHOPHYSICS,
NEUROBIOLOGY
AND
GESTALT
THEORY.
REFERENCES
OF
PART
II
.
232
II-A)
REFERENCES
ON
GEOMETRIC
MEASURE
THEORY
AND
RECTIFIABILITY
II-B)
MONOGRAPHS
ON
MATHEMATICS
AND
GEOMETRIC
MEASURE
THEORY.
REFERENCES
OF
PART
IILMATHEMATICAL
ANALYSIS
OF
THE
MUMFORD-SHAH
MODEL
.
234
INDEX
.
239
INDEX
OF
SEGMENTATION
ALGORITHMS
.
243
NOTATION
.
244 |
| any_adam_object | 1 |
| author | Morel, Jean-Michel 1953- Solimini, Sergio |
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| dewey-search | 621.3/67 |
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| dewey-tens | 620 - Engineering and allied operations |
| discipline | Informatik Mathematik Elektrotechnik / Elektronik / Nachrichtentechnik |
| format | Book |
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| id | DE-604.BV010040380 |
| illustrated | Illustrated |
| indexdate | 2024-08-18T00:17:20Z |
| institution | BVB |
| isbn | 3764337206 0817637206 |
| language | English |
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| physical | XVI, 245 S. Ill., graph. Darst. |
| publishDate | 1995 |
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| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in nonlinear differential equations and their applications |
| series2 | Progress in nonlinear differential equations and their applications |
| spelling | Morel, Jean-Michel 1953- Verfasser (DE-588)136525229 aut Variational methods in image segmentation with seven image processing experiments Jean-Michel Morel ; Sergio Solimini Boston u.a. Birkhäuser 1995 XVI, 245 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Progress in nonlinear differential equations and their applications 14 Literaturverz. S. 215 - 237 Images, traitement des - Techniques numériques - Mathématiques ram Mesure géométrique, théorie de la ram Mathematik Geometric measure theory Image processing Digital techniques Mathematics Geometrische Maßtheorie (DE-588)4125258-5 gnd rswk-swf Bildsegmentierung (DE-588)4145448-0 gnd rswk-swf Variationsrechnung (DE-588)4062355-5 gnd rswk-swf Bildsegmentierung (DE-588)4145448-0 s Variationsrechnung (DE-588)4062355-5 s DE-604 Geometrische Maßtheorie (DE-588)4125258-5 s Solimini, Sergio Verfasser aut Progress in nonlinear differential equations and their applications 14 (DE-604)BV007934389 14 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006658940&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Morel, Jean-Michel 1953- Solimini, Sergio Variational methods in image segmentation with seven image processing experiments Progress in nonlinear differential equations and their applications Images, traitement des - Techniques numériques - Mathématiques ram Mesure géométrique, théorie de la ram Mathematik Geometric measure theory Image processing Digital techniques Mathematics Geometrische Maßtheorie (DE-588)4125258-5 gnd Bildsegmentierung (DE-588)4145448-0 gnd Variationsrechnung (DE-588)4062355-5 gnd |
| subject_GND | (DE-588)4125258-5 (DE-588)4145448-0 (DE-588)4062355-5 |
| title | Variational methods in image segmentation with seven image processing experiments |
| title_auth | Variational methods in image segmentation with seven image processing experiments |
| title_exact_search | Variational methods in image segmentation with seven image processing experiments |
| title_full | Variational methods in image segmentation with seven image processing experiments Jean-Michel Morel ; Sergio Solimini |
| title_fullStr | Variational methods in image segmentation with seven image processing experiments Jean-Michel Morel ; Sergio Solimini |
| title_full_unstemmed | Variational methods in image segmentation with seven image processing experiments Jean-Michel Morel ; Sergio Solimini |
| title_short | Variational methods in image segmentation |
| title_sort | variational methods in image segmentation with seven image processing experiments |
| title_sub | with seven image processing experiments |
| topic | Images, traitement des - Techniques numériques - Mathématiques ram Mesure géométrique, théorie de la ram Mathematik Geometric measure theory Image processing Digital techniques Mathematics Geometrische Maßtheorie (DE-588)4125258-5 gnd Bildsegmentierung (DE-588)4145448-0 gnd Variationsrechnung (DE-588)4062355-5 gnd |
| topic_facet | Images, traitement des - Techniques numériques - Mathématiques Mesure géométrique, théorie de la Mathematik Geometric measure theory Image processing Digital techniques Mathematics Geometrische Maßtheorie Bildsegmentierung Variationsrechnung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006658940&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV007934389 |
| work_keys_str_mv | AT moreljeanmichel variationalmethodsinimagesegmentationwithsevenimageprocessingexperiments AT soliminisergio variationalmethodsinimagesegmentationwithsevenimageprocessingexperiments |