Shape and shape theory:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Chichester u.a.
Wiley
1999
|
| Schriftenreihe: | Wiley series in probability and statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 306 S. graph. Darst. |
| ISBN: | 0471968234 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804127832488542208 |
|---|---|
| adam_text | IMAGE 1
SHAPE AND SHAPE THEORY
D. G. KENDALL CHURCHILL COLLEGE, UNIVERSITY OF CAMBRIDGE, UK D. BARDEN
GIRTON COLLEGE, UNIVERSITY OF CAMBRIDGE, UK
T. K. CARNE KING S COLLEGE, UNIVERSITY OF CAMBRIDGE, UK
H. LE UNIVERSITY OF NOTTINGHAM, UK
JOHN WILEY & SONS, LTD CHICHESTER * NEW YORK * WEINHEIM * BRISBANE *
SINGAPORE * TORONTO
IMAGE 2
CONTENTS
PREFACE IX
CHAPTER 1 SHAPES AND SHAPE SPACES 1
1.1 ORIGINS 1
1.2 SOME PRELIMINARY OBSERVATIONS 2
1.3 A MATIIX REPRESENTATION FOR THE SHAPE OF A K-AD 1
1.4 ELEMENTARY SHAPE SPACES * AND E* 10
1.5 THE FUBINI- STUDY METRIC ON T, 17
1.6 THE PROOF OF CASSON S THEOREM 20
CHAPTER 2 THE GLOBAL STNICTURE OF SHAPE SPACES 23
2.1 THE PROBLEM 23
2.2 WHEN IS A SPACE FAMILIAER 24
2.3 CW COMPLEXES 25
2.4 A CELLULAR DECOMPOSITION OF THE UNIT SPHERE 25
2.5 THE CELLULAR DECOMPOSITION OF SHAPE SPACES 27
2.6 INCLUSIONS AND ISOMETRIES 29
2.7 SIMPLE CONNECTIVITY AND HIGHER HOMOTOPY GROUPS 30
2.8 THE MAPPING CONE DECOMPOSITION 33
2.9 HOMOTOPY TYPE AND CASSON S THEOREM 36
CHAPTER 3 COMPUTING THE HOMOLOGY OF CELL COMPLEXES 41
3.1 THE ORIENTATION OF CERTAIN SPACES X 41
3.2 THE ORIENTATION OF SPHERICAL CELLS 42
3.3 THE BOUNDARY OF AN ORIENTED CELL 43
3.4 THE CHAIN COMPLEX, HOMOLOGY AND COHOMOLOGY GROUPS 45
3.5 REDUCED HOMOLOGY 47
3.6 THE HOMOLOGY EXACT SEQUENCE FOR SHAPE SPACES 47
IMAGE 3
VI
CONTENTS
3.7 APPLICATIONS OF THE EXACT SEQUENCE 50
3.8 TOPOLOGICAL INVARIANTS THAT DISTINGUISH BETWEEN SHAPE SPACES 52
C H A P T ER 4 A CHAIN COMPLEX FOR SHAPE SPACES 55
4.1 THE CHAIN COMPLEX 55
4.2 THE SPACE OF UNORIENTED SHAPES 57
4.3 THE BOUNDARY MAP IN THE CHAIN COMPLEX 57
4.4 DECOMPOSING THE CHAIN COMPLEX 59
4.5 HOMOLOGY AND COHOMOLOGY OF THE SPACES 62
4.6 CONNECTIVITY OF SHAPE SPACES 65
4.7 LIMITS OF SHAPE SPACES 68
CHAPTER 5 THE HOMOLOGY G R O U PS OF SHAPE SPACES 69
5.1 SPACES OF SHAPES IN 2-SPACE 70
5.2 SPACES OF SHAPES IN 3-SPACE 71
5.3 SPACES OF SHAPES IN 4-SPACE 72
5.4 SPACES OF UNORIENTED SHAPES IN 2-SPACE 78
5.5 SPACES OF UNORIENTED SHAPES IN 3-SPACE 80
5.6 SPACES OF UNORIENTED SHAPES IN 4-SPACE 82
5.7 DECOMPOSING THE ESSENTIAL COMPLEXES 84
5.8 CLOSED FORMULAE FOR THE HOMOLOGY GROUPS 91
5.9 DUALITY IN SHAPE SPACES 100
CHAPTER 6 GEODESICS IN SHAPE SPACES 105
6.1 THE ACTION OF SO(M) ON THE PRE-SHAPE SPHERE 106
6.2 VIEWING THE INDUCED RIEMANNIAN METRIC THROUGH HORIZONTAL GEODESICS
107
6.3 THE SINGULAR POINTS AND THE NESTING PRINCIPLE 111
6.4 THE DISTANCE BETWEEN SHAPES 114
6.5 THE SET OF GEODESICS BETWEEN TWO SHAPES 116
6.6 THE NON-UNIQUENESS OF MINIMAL GEODESICS 120
6.7 THE CUT LOCUS IN SHAPE SPACES 124
6.8 THE DISTANCES AND PROJECTIONS TO LOWER STRATA 127
CHAPTER 7 THE RIEMANNIAN STRUCTURE OF SHAPE SPACES 135
7.1 THE RIEMANNIAN METRIC 135
7.2 THE METRIC RE-EXPRESSED THROUGH NATURAL LOCAL VECTOR FIELDS 138
7.3 THE RIEMANNIAN CURVATURE TENSOR 149
IMAGE 4
CONTENTS VUE
C H A P T ER 8 INDUCED SHAPE-MEASURES 157
8.1 GEOMETRIE PRELIMINARIES 158
8.2 THE SHAPE-MEASURE ON EJJ, INDUCED BY K LABELLED IID ISOTROPIC
GAUSSIAN DISTRIBUTIONS ON W 160
8.3 SHAPE-MEASURES ON E* +1 OF POISSON-DELAUNAY TILES 164
8.4 SHAPE-MEASURES ON E* INDUCED BY K LABELLED IID NON-ISOTROPIC
GAUSSIAN DISTRIBUTIONS ON R 2 168
8.5 SHAPE-MEASURES ON E^ INDUCED BY COMPLEX NORMAL DISTRIBUTIONS 172
8.6 THE SHAPE-MEASURE ON E| INDUCED BY THREE LABELLED IID UNIFORM
DISTRIBUTIONS IN A COMPACT CONVEX SET 176
8.7 THE SHAPE-MEASURE ON EJ INDUCED BY THREE LABELLED IID UNIFORM
DISTRIBUTIONS IN A CONVEX POLYGON. I: THE SINGULAR TESSELLATION 181
8.8 THE SHAPE-MEASURE ON Y? 2 INDUCED BY THREE LABELLED IID UNIFORM
DISTRIBUTIONS IN A CONVEX POLYGON. II: THE EXPLICIT FORMULA 190
C H A P T ER 9 M E AN SHAPES A ND THE SHAPE OF THE MEANS 201
9.1 CONCEPT OF MEANS IN NON-LINEAR SPACES 201
9.2 METRICS ON SHAPE SPACE 204
9.3 UNIQUENESS OF FRECHET MEANS OF SHAPE-MEASURES 206
9.4 FRECHET MEANS AND THE SHAPE OF THE MEANS 213
9.5 UNIQUENESS OF FRECHET MEANS OF N GIVEN SHAPES 217
9.6 PROCRUSTEAN MEAN SHAPES 226
CHAPTER 10 VISUALISING THE HIGHER DIMENSIONAL 231
SHAPE SPACES 10.1 THE TWO-DIMENSIONAL REPRESENTATION OF E* 231
10.2 THE CELL-DECOMPOSITION OF SO(3) 233
10.3 THE ACTION OF THE GROUP D 237
10.4 THE GEODESICS OF Y, 239
10.5 SOME DISTRIBUTIONS ON EJ 243
10.6 A DIFFUSUM ON E* 244
C H A P T ER 11 GENERAL SHAPE SPACES 249
11.1 SHAPE SPACES FOR GENERAL MANIFOLDS 249
11.2 SIZE-AND-SHAPE SPACES 254
11.3 SIZE-AND-SHAPE SPACES FOR THE PLANE 262
11.4 SPHERES AND HYPERBOLIC SPACES 264
IMAGE 5
VLLL
CONTENTS
11.5 RELATIVE METRICS 11.6 ELLIPTIC FUNCTIONS 11.7 SHAPE SPACES FOR
TRIANGLES IN THE SPHERE AND THE HYPERBOLIC PLANE
267 273
276
APPENDIX A.L A.2 A.3
A.4 A.5
BIBLIOGRAPHY
INDEX
UNARY OPERATORS ON GROUPS BINARY OPERATORS ON GROUPS THE UNIVERSAL
COEFFICIENT THEOREMS DUALITY IN MANIFOLDS
THE SPLITTING OF EXACT SEQUENCES
283 283 284 286 287
290
293
299
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:39:37Z |
| institution | BVB |
| isbn | 0471968234 |
| language | English |
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| physical | XI, 306 S. graph. Darst. |
| publishDate | 1999 |
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| publisher | Wiley |
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| series2 | Wiley series in probability and statistics |
| spelling | Shape and shape theory D. G. Kendall ... Chichester u.a. Wiley 1999 XI, 306 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Forme, Théorie de la (topologie) ram Théorie de la forme (Topologie) Shape-Theorie (DE-588)4193842-2 gnd rswk-swf Shape-Theorie (DE-588)4193842-2 s DE-604 Kendall, David G. Sonstige oth GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008947545&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Shape and shape theory Forme, Théorie de la (topologie) ram Théorie de la forme (Topologie) Shape-Theorie (DE-588)4193842-2 gnd |
| subject_GND | (DE-588)4193842-2 |
| title | Shape and shape theory |
| title_auth | Shape and shape theory |
| title_exact_search | Shape and shape theory |
| title_full | Shape and shape theory D. G. Kendall ... |
| title_fullStr | Shape and shape theory D. G. Kendall ... |
| title_full_unstemmed | Shape and shape theory D. G. Kendall ... |
| title_short | Shape and shape theory |
| title_sort | shape and shape theory |
| topic | Forme, Théorie de la (topologie) ram Théorie de la forme (Topologie) Shape-Theorie (DE-588)4193842-2 gnd |
| topic_facet | Forme, Théorie de la (topologie) Théorie de la forme (Topologie) Shape-Theorie |
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