The Statistical Theory of Shape:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1996
|
| Schriftenreihe: | Springer Series in Statistics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In general terms, the shape of an object, data set, or image can be defined as the total of all information that is invariant under translations, rotations, and isotropic rescalings. Thus two objects can be said to have the same shape if they are similar in the sense of Euclidean geometry. For example, all equilateral triangles have the same shape, and so do all cubes. In applications, bodies rarely have exactly the same shape within measurement error. In such cases the variation in shape can often be the subject of statistical analysis. The last decade has seen a considerable growth in interest in the statistical theory of shape. This has been the result of a synthesis of a number of different areas and a recognition that there is considerable common ground among these areas in their study of shape variation. Despite this synthesis of disciplines, there are several different schools of statistical shape analysis. One of these, the Kendall school of shape analysis, uses a variety of mathematical tools from differential geometry and probability, and is the subject of this book. The book does not assume a particularly strong background by the reader in these subjects, and so a brief introduction is provided to each of these topics. Anyone who is unfamiliar with this material is advised to consult a more complete reference. As the literature on these subjects is vast, the introductory sections can be used as a brief guide to the literature |
| Beschreibung: | 1 Online-Ressource (X, 230 p) |
| ISBN: | 9781461240327 9781461284734 |
| ISSN: | 0172-7397 |
| DOI: | 10.1007/978-1-4612-4032-7 |
Internformat
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| 500 | |a In general terms, the shape of an object, data set, or image can be defined as the total of all information that is invariant under translations, rotations, and isotropic rescalings. Thus two objects can be said to have the same shape if they are similar in the sense of Euclidean geometry. For example, all equilateral triangles have the same shape, and so do all cubes. In applications, bodies rarely have exactly the same shape within measurement error. In such cases the variation in shape can often be the subject of statistical analysis. The last decade has seen a considerable growth in interest in the statistical theory of shape. This has been the result of a synthesis of a number of different areas and a recognition that there is considerable common ground among these areas in their study of shape variation. Despite this synthesis of disciplines, there are several different schools of statistical shape analysis. One of these, the Kendall school of shape analysis, uses a variety of mathematical tools from differential geometry and probability, and is the subject of this book. The book does not assume a particularly strong background by the reader in these subjects, and so a brief introduction is provided to each of these topics. Anyone who is unfamiliar with this material is advised to consult a more complete reference. As the literature on these subjects is vast, the introductory sections can be used as a brief guide to the literature | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Small, Christopher G. 1956- |
| author_GND | (DE-588)112053807 |
| author_facet | Small, Christopher G. 1956- |
| author_role | aut |
| author_sort | Small, Christopher G. 1956- |
| author_variant | c g s cg cgs |
| building | Verbundindex |
| bvnumber | BV042420193 |
| classification_tum | MAT 000 |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-4032-7 |
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| id | DE-604.BV042420193 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:06Z |
| institution | BVB |
| isbn | 9781461240327 9781461284734 |
| issn | 0172-7397 |
| language | English |
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| publishDate | 1996 |
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| spelling | Small, Christopher G. 1956- Verfasser (DE-588)112053807 aut The Statistical Theory of Shape by Christopher G. Small New York, NY Springer New York 1996 1 Online-Ressource (X, 230 p) txt rdacontent c rdamedia cr rdacarrier Springer Series in Statistics 0172-7397 In general terms, the shape of an object, data set, or image can be defined as the total of all information that is invariant under translations, rotations, and isotropic rescalings. Thus two objects can be said to have the same shape if they are similar in the sense of Euclidean geometry. For example, all equilateral triangles have the same shape, and so do all cubes. In applications, bodies rarely have exactly the same shape within measurement error. In such cases the variation in shape can often be the subject of statistical analysis. The last decade has seen a considerable growth in interest in the statistical theory of shape. This has been the result of a synthesis of a number of different areas and a recognition that there is considerable common ground among these areas in their study of shape variation. Despite this synthesis of disciplines, there are several different schools of statistical shape analysis. One of these, the Kendall school of shape analysis, uses a variety of mathematical tools from differential geometry and probability, and is the subject of this book. The book does not assume a particularly strong background by the reader in these subjects, and so a brief introduction is provided to each of these topics. Anyone who is unfamiliar with this material is advised to consult a more complete reference. As the literature on these subjects is vast, the introductory sections can be used as a brief guide to the literature Statistics Electronic data processing Statistics, general Computing Methodologies Datenverarbeitung Statistik Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Shape-Theorie (DE-588)4193842-2 gnd rswk-swf Statistische Analyse (DE-588)4116599-8 gnd rswk-swf Stochastische Geometrie (DE-588)4133202-7 gnd rswk-swf Shape-Theorie (DE-588)4193842-2 s Stochastische Geometrie (DE-588)4133202-7 s 1\p DE-604 Differentialgeometrie (DE-588)4012248-7 s 2\p DE-604 Statistische Analyse (DE-588)4116599-8 s 3\p DE-604 https://doi.org/10.1007/978-1-4612-4032-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Small, Christopher G. 1956- The Statistical Theory of Shape Statistics Electronic data processing Statistics, general Computing Methodologies Datenverarbeitung Statistik Differentialgeometrie (DE-588)4012248-7 gnd Shape-Theorie (DE-588)4193842-2 gnd Statistische Analyse (DE-588)4116599-8 gnd Stochastische Geometrie (DE-588)4133202-7 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4193842-2 (DE-588)4116599-8 (DE-588)4133202-7 |
| title | The Statistical Theory of Shape |
| title_auth | The Statistical Theory of Shape |
| title_exact_search | The Statistical Theory of Shape |
| title_full | The Statistical Theory of Shape by Christopher G. Small |
| title_fullStr | The Statistical Theory of Shape by Christopher G. Small |
| title_full_unstemmed | The Statistical Theory of Shape by Christopher G. Small |
| title_short | The Statistical Theory of Shape |
| title_sort | the statistical theory of shape |
| topic | Statistics Electronic data processing Statistics, general Computing Methodologies Datenverarbeitung Statistik Differentialgeometrie (DE-588)4012248-7 gnd Shape-Theorie (DE-588)4193842-2 gnd Statistische Analyse (DE-588)4116599-8 gnd Stochastische Geometrie (DE-588)4133202-7 gnd |
| topic_facet | Statistics Electronic data processing Statistics, general Computing Methodologies Datenverarbeitung Statistik Differentialgeometrie Shape-Theorie Statistische Analyse Stochastische Geometrie |
| url | https://doi.org/10.1007/978-1-4612-4032-7 |
| work_keys_str_mv | AT smallchristopherg thestatisticaltheoryofshape |