Statistical shape analysis:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester [u.a.]
Wiley
1998
|
| Schriftenreihe: | Wiley series in probability and statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. [321] - 336 |
| Beschreibung: | XVII, 347 S. Ill., graph. Darst. |
| ISBN: | 0471958166 |
Internformat
MARC
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| 264 | 1 | |a Chichester [u.a.] |b Wiley |c 1998 | |
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| 490 | 0 | |a Wiley series in probability and statistics | |
| 500 | |a Literaturverz. S. [321] - 336 | ||
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Datensatz im Suchindex
| _version_ | 1804140742869778432 |
|---|---|
| adam_text | IMAGE 1
STATISTICAL SHAPE ANALYSIS
I. L. DRYDEN AND K. V. MARDIA UNIVERSITY OFLEEDS, UK
JOHN WILEY& SONS CHICHESTER * NEW YORK * WEINHEIM * BRISBANE * SINGAPORE
* TORONTO
IMAGE 2
CONTENTS
PREFACE XV
ACKNOWLEDGEMENTS XIX
1 INTRODUCTION 1
1.1 DEFINITION AND MOTIVATION 1
1.1.1 LANDMARKS 3
1.1.2 TRADITIONAL METHODS 6
1.1.3 GEOMETRICAL METHODS 7
1.2 PRACTICAL APPLICATIONS 9
1.2.1 BIOLOGY: MOUSE VERTEBRAE 9
1.2.2 BIOLOGY: GORILLA SKULLS 10
1.2.3 MEDICINE: BRAIN MR SCANS OF SCHIZOPHRENIE PATIENTS 11
1.2.4 IMAGE ANALYSIS: POSTCODE RECOGNITION 11
1.2.5 ARCHAEOLOGY: ALIGNMENTS OF STANDING STONES 13
1.2.6 GEOGRAPHY: CENTRAL PLACE THEORY 14
1.2.7 GEOLOGY: MICROFOSSILS 15
1.2.8 BIOLOGY: MACAQUE SKULLS 16
1.2.9 BIOLOGY: SOOTY MANGABEYS 17
1.2.10 AGRICULTURE: FISH RECOGNITION 17
1.2.11 AGRICULTURE: ROBOTIC HARVESTING OF MUSHROOMS 17
1.2.12 GENETICS: ELECTROPHORETIC GELS 17
2 PRELIMINARIES: SIZE MEASURES AND SHAPE COORDINATES 23
2.1 CONFIGURATION SPACE 23
2.2 SIZE 23
2.3 SOME SHAPE COORDINATE SYSTEMS 26
2.3.1 ANGLES AND RATIOS OF LENGTHS 26
2.3.2 BOOKSTEIN COORDINATES: PLANAR CASE 27
2.3.3 TRIANGLECASE 32
2.3.4 KENDALI COORDINATES: PLANAR CASE . . 34
2.3.5 KENDALL S SPHERICAL COORDINATES FOR TRIANGLES 36
2.3.6 WATSON S TRIANGLE COORDINATES 38
IMAGE 3
X CONTENTS
3 PRELIMINARIES: PLANAR PROCRUSTES ANALYSIS 39
3.1 INTRODUCTION 39
3.2 SHAPE DISTANCE AND PROCRUSTES MATCHING 39
3.3 ESTIMATION OF MEAN SHAPE 44
3.4 SHAPE VARIABILITY 47
4 SHAPE SPACE AND DISTANCES 53
4.1 SHAPE SPACE 53
4.1.1 INTRODUCTION 53
4.1.2 FILTERING TRANSLATION 54
4.1.3 PRE-SHAPE 55
4.1.4 SHAPE 56
4.1.5 SIZE-AND-SHAPE: REMOVING LOCATION AND ROTATION 57
4.1.6 REFLECTION SHAPE 57
4.1.7 ALTERNATIVE STANDARDIZATIONS 58
4.1.8 OVER-DIMENSIONED CASE 58
4.1.9 PLANAR CASE 59
4.2 DISTANCES 61
4.2.1 PROCRUSTES DISTANCES 61
4.2.2 ALTERNATIVE DISTANCES 62
4.2.3 PLANAR CASE 68
4.2.4 TRIANGLECASE 69
4.3 ADVANCED SHAPE COORDINATE SYSTEMS 70
4.3.1 TANGENT SPACE COORDINATES 71
4.3.2 KENT S POLAR COORDINATES 77
4.3.3 BOOKSTEIN COORDINATES FOR THREE DIMENSIONAL DATA 78
4.3.4 GOODALL-MARDIA QR SHAPE COORDINATES 81
4.3.5 GOODALL-MARDIA POLAR SHAPE COORDINATES 82
5 GENERAL PROCRUSTES METHODS 83
5.1 INTRODUCTION 83
5.2 ORDINARY PROCRUSTES ANALYSIS 84
5.2.1 FUELL ORDINARY PROCRUSTES ANALYSIS 84
5.3 GENERALIZED PROCRUSTES ANALYSIS 87
5.3.1 INTRODUCTION 87
5.3.2 ALGORITHM FOR HIGHER DIMENSIONS 90
5.4 VARIANTS OF PROCRUSTES ANALYSIS 92
5.4.1 ORDINARY PARTIAL PROCRUSTES 92
5.4.2 GENERALIZED PARTIAL PROCRUSTES 95
5.4.3 REFLECTION PROCRUSTES 95
5.5 SHAPE VARIABILITY: PRINCIPAL COMPONENTS ANALYSIS 96
5.5.1 TWO DIMENSIONAL DATA 96
5.5.2 POINT DISTRIBUTION MODEIS 106
5.5.3 PCA IN SHAPE ANALYSIS AND MULTIVARIATE ANALYSIS 107
IMAGE 4
CONTENTS XI
6 SHAPE MODELS FOR TWO DIMENSIONAL DATA 109
6.1 UNIFORM DISTRIBUTION 109
6.2 COMPLEX BINGHAM DISTRIBUTION . 1 11
6.2.1 THE DENSITY 111
6.2.2 THE NORMALIZING CONSTANT 113
6.2.3 PROPERTIES 114
6.2.4 INFERENCE 115
6.2.5 RELATIONSHIP WITH THE FISHER DISTRIBUTION 117
6.3 COMPLEX WATSON DISTRIBUTION 118
6.3.1 THE DENSITY 118
6.3.2 CALCULATION OF THE INTEGRATING CONSTANT 119
6.3.3 INFERENCE 120
6.3.4 LARGE CONCENTRATIONS 122
6.4 COMPLEX ANGULAR CENTRAL GAUSSIAN DISTRIBUTION 123
6.5 A ROTATIONALLY SYMMETRIE SHAPE FAMILY 123
6.6 OFFSET NORMAL SHAPE DISTRIBUTIONS 124
6.6.1 EQUAL MEAN CASE IN TWO DIMENSIONS 125
6.6.2 THE ISOTROPIC CASE IN TWO DIMENSIONS 129
6.6.3 THE TRIANGLE CASE 133
6.6.4 APPROXIMATIONS: LARGE AND SMALL VARIATIONS 133
6.6.5 MOMENTS 135
6.6.6 ISOTROPY 137
6.7 OFFSET NORMAL SHAPE DISTRIBUTIONS WITH GENERAL COVARIANCES . . ..
138 6.7.1 THE COMPLEX NORMAL CASE 139
6.7.2 THE EQUAL MEANS CASE 141
6.7.3 PROPERTIES 143
6.7.4 INFERENCE FOR OFFSET NORMAL DISTRIBUTIONS 144
6.8 A BAYESIAN APPROACH 149
6.9 PRACTICAL INFERENCE 150
7 TANGENT SPACE INFERENCE 151
7.1 TANGENT SPACE INFERENCE 151
7.1.1 ONE SAMPLE HOTELLING S T 2 TEST 151
7.1.2 TWO INDEPENDENT SAMPLE HOTELLING S T 2 TEST 153
7.1.3 PERMUTATION TEST 159
7.1.4 EXTENSIONS 159
7.1.5 DIMENSION REDUETION IN INFERENCE 160
7.2 INFERENCE USING PROCRUSTES STATISTICS UNDER ISOTROPY 160
7.2.1 ONE SAMPLE GOODALL S F TEST 160
7.2.2 TWO INDEPENDENT SAMPLE GOODALL S F TEST 162
7.2.3 ONE WAY ANALYSIS OF VARIANCE 166
7.2.4 FURTHER INFERENCE FOR PROCRUSTES STATISTICS 166
7.3 EDGE SUPERIMPOSITION SHAPE COORDINATES 168
7.3.1 BOOKSTEIN COORDINATES 168
IMAGE 5
XII CONTENTS
7.3.2 HOTELLING S T 2 TWO SAMPLE TEST USING BOOKSTEIN COORDINATES . 170
7.3.3 ADVANTAGES AND DISADVANTAGES 173
7.3.4 EXTENSIONS 173
8 SIZE-AND-SHAPE 175
8.1 INTRODUCTION 175
8.2 ALLOMETRY 175
8.3 GEOMETRY 176
8.4 OFFSET NORMAL SIZE-AND-SHAPE DISTRIBUTIONS 180
8.4.1 THE SIZE-AND-SHAPE DENSITY 181
8.5 PARTICULAR CASES 183
8.5.1 THE COMPLEX NORMAL CASE 183
8.5.2 THE EQUAL MEANS CASE 184
8.5.3 THE ISOTROPIC CASE 184
8.6 INFERENCE USING THE OFF SET NORMAL MODEL 187
8.7 ALTERNATIVE DISTRIBUTIONS 188
8.8 SIZE-AND-SHAPE VERSUS SHAPE 189
9 DISTRIBUTIONS FOR HIGHER DIMENSIONS 191
9.1 INTRODUCTION 191
9.2 QR DECOMPOSITION 191
9.3 SIZE-AND-SHAPE DISTRIBUTIONS 192
9.3.1 COINCIDENT MEANS 192
9.3.2 COLLINEAR MEANS 193
9.3.3 PLANAR MEANS 193
9.3.4 HIGHER RANK CASE 194
9.4 SHAPE DENSITIES AND BARTLETT S DECOMPOSITION 194
9.4.1 COINCIDENT MEANS 195
9.4.2 COLLINEAR MEANS 196
9.5 MULTIVARIATE APPROACH 197
9.6 APPROXIMATIONS . 197
9.7 A ROTATIONALLY SYMMETRIE SHAPE FAMILY 198
10 DEFORMATIONS AND DESCRIBING SHAPE CHANGE 199
10.1 DEFORMATIONS 199
10.1.1 INTRODUCTION 199
10.1.2 DEFINITION AND DESIRABLE PROPERTIES 200
10.1.3 D ARCY THOMPSON S TRANSFORMATION GRIDS 200
10.2 THE AFFINE DEFORMATION 201
10.2.1 THE TRIANGLE CASE: BOOKSTEIN S HYPERBOLIC SHAPE SPACE . . .. 203
10.3 PAIRSOFTHIN-PLATESPLINES 205
10.3.1 THIN-PLATE SPLINES 205
10.3.2 TRANSFORMATION GRIDS 207
10.3.3 PRINCIPAL AND PARTIAL WARP DECOMPOSITIONS 214
IMAGE 6
CONTENTS XIUE
10.3.4 PRINCIPAL COMPONENT ANALYSIS WITH NON-EUCLIDEAN METRICS . . 220
10.3.5 RELATIVE WARPS 223
10.4 ALTERNATIVE APPROACHES AND HISTORY 229
10.4.1 EARLY TRANSFORMATION GRIDS 229
10.4.2 FINITE DEMENT ANALYSIS 232
10.4.3 BIORTHOGONAL GRIDS 234
10.4.4 OTHER DEFORMATIONS 236
10.5 KRIGING 236
10.5.1 UNIVERSAL KRIGING 236
10.5.2 DEFORMATIONS 237
10.5.3 INTRINSIC KRIGING 238
10.5.4 KRIGING WITH DERIVATIVE CONSTRAINTS 239
10.6 STATISTICAL SHAPE CHANGE 242
10.6.1 TANGENT SPACE METHODS 244
10.6.2 GROWTH CURVE MODEIS FOR TRIANGLE SHAPES 245
10.6.3 GEOMETRIE COMPONENTS OF SHAPE CHANGE 246
10.6.4 PAIRED SHAPE DISTRIBUTIONS 249
11 SHAPE IN IMAGES 251
11.1 INTRODUCTION 251
11.2 HIGH-LEVEL BAYESIAN IMAGE ANALYSIS 253
11.3 PRIOR MODELS FOR OBJECTS 254
11.3.1 GEOMETRIE PARAMETER APPROACH 254
11.3.2 LANDMARKS: SHAPE DISTRIBUTIONS AND POINT DISTRIBUTION MODEIS 257
11.3.3 GRAPHICAL TEMPLATES 258
11.3.4 THIN-PLATE SPLINES 259
11.3.5 OUTLINES 259
11.4 INFERENCE 263
11.5 MULTIPLE OBJECTS AND OCCLUSIONS 265
11.5.1 CLASSICAL HOUGH TRANSFORM 267
11.5.2 MORPHOLOGICAL OPERATIONS 267
11.5.3 A MARKOVIAN OBJEET PROCESS 268
11.6 WARPING AND IMAGE AVERAGING 269
11.6.1 WARPING 269
11.6.2 IMAGE AVERAGING 271
11.6.3 MERGING IMAGES 271
11.7 DISCUSSION 278
12 ADDITIONAL TOPICS 279
12.1 CONSISTENCY 279
12.2 DISTANCE-BASED METHODS 280
12.2.1 MULTIDIMENSIONAL SCALING 281
12.2.2 EDMA 282
12.2.3 TESTS FOR SHAPE DIFFERENCE 283
IMAGE 7
XIV CONTENTS
12.2.4 LOG-DISTANCES AND MULTIVARIATE ANALYSIS 284
12.2.5 DISTANCE METHODS VERSUS GEOMETRICAL METHODS 286
12.2.6 EUCLIDEAN SHAPE TENSOR ANALYSIS 287
12.2.7 ANGULAR SHAPE ANALYSIS 287
12.3 INCOMPLETE DATA 288
12.4 GENERAL SHAPE SPACES 288
12.4.1 DEFINITIONS 288
12.4.2 TWO OBJECT MATCHING 289
12.4.3 GENERALIZED MATCHING 290
12.5 AFFINE SHAPE 290
12.5.1 LEAST SQUARES MATCHING: TWO OBJECTS 290
12.5.2 LEAST SQUARES MATCHING: MULTIPLE OBJECTS 292
12.6 ROBUST SUPERIMPOSITION METHODS 295
12.6.1 RESISTANCE TO LANDMARK OUTLIERS 295
12.6.2 OBJECT OUTLIERS 298
12.7 SMOOTHING 299
12.7.1 SMOOTHED MATCHING 299
12.7.2 SMOOTHED PRINCIPAL COMPONENT ANALYSIS 300
12.8 DISTRIBUTION-FREE METHODS 302
12.9 UNLABELLED POINTS 303
12.9.1 FIAT TRIANGLES AND ALIGNMENTS 303
12.9.2 UNLABELLED SHAPE DENSITIES 304
12.9.3 FURTHER PROBABILISTIC ISSUES 304
12.9.4 DELAUNAY TRIANGLES 305
12.10 LANDMARK-FREE APPROACHES 305
12.10.1 CURVATURE 307
12.11 POSTSCRIPT 309
APPENDIX A: NOTATION 311
APPENDIX B: SOFTWARE AND DATA 313
MOUSE VERTEBRAE 313
GORILLA SKULLS 317
HANDWRITTEN DIGIT 3 DATA 318
OTHERSOURCES 320
REFERENCES AND AUTHOR INDEX 321
INDEX 337
|
| any_adam_object | 1 |
| author | Dryden, Ian L. Mardia, Kantilal V. 1935- |
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| dewey-ones | 514 - Topology |
| dewey-raw | 514/.24 |
| dewey-search | 514/.24 |
| dewey-sort | 3514 224 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV035798303 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:04:49Z |
| institution | BVB |
| isbn | 0471958166 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018657489 |
| oclc_num | 245663286 |
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| owner | DE-83 |
| owner_facet | DE-83 |
| physical | XVII, 347 S. Ill., graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley series in probability and statistics |
| spelling | Dryden, Ian L. Verfasser aut Statistical shape analysis I. L. Dryden and K. V. Mardia Chichester [u.a.] Wiley 1998 XVII, 347 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Literaturverz. S. [321] - 336 Forme, Théorie de la (Topologie) - Méthodes statistiques Statistische methoden gtt Topologie gtt Shape theory (Topology) Statistical methods Geometrische Topologie (DE-588)4156724-9 gnd rswk-swf Geometrische Topologie (DE-588)4156724-9 s 1\p DE-604 Mardia, Kantilal V. 1935- Verfasser (DE-588)122951913 aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018657489&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Dryden, Ian L. Mardia, Kantilal V. 1935- Statistical shape analysis Forme, Théorie de la (Topologie) - Méthodes statistiques Statistische methoden gtt Topologie gtt Shape theory (Topology) Statistical methods Geometrische Topologie (DE-588)4156724-9 gnd |
| subject_GND | (DE-588)4156724-9 |
| title | Statistical shape analysis |
| title_auth | Statistical shape analysis |
| title_exact_search | Statistical shape analysis |
| title_full | Statistical shape analysis I. L. Dryden and K. V. Mardia |
| title_fullStr | Statistical shape analysis I. L. Dryden and K. V. Mardia |
| title_full_unstemmed | Statistical shape analysis I. L. Dryden and K. V. Mardia |
| title_short | Statistical shape analysis |
| title_sort | statistical shape analysis |
| topic | Forme, Théorie de la (Topologie) - Méthodes statistiques Statistische methoden gtt Topologie gtt Shape theory (Topology) Statistical methods Geometrische Topologie (DE-588)4156724-9 gnd |
| topic_facet | Forme, Théorie de la (Topologie) - Méthodes statistiques Statistische methoden Topologie Shape theory (Topology) Statistical methods Geometrische Topologie |
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