05458nam 2200697Ia 450 991101930120332120200520144314.097866123073869781282307384128230738X9780470317006047031700097804703178460470317841(CKB)1000000000806956(EBL)470255(SSID)ssj0000342853(PQKBManifestationID)11247812(PQKBTitleCode)TC0000342853(PQKBWorkID)10289453(PQKB)11362928(MiAaPQ)EBC470255(PPN)152549536(OCoLC)264615247(Perlego)2775086(EXLCZ)99100000000080695619990105d1999 uy 0engur|n|---|||||txtccrShape and shape theory /D.G. Kendall ... [et al.]Chichester ;New York Wileyc19991 online resource (328 p.)Wiley series in probability and statisticsDescription based upon print version of record.9780471968238 0471968234 Includes bibliographical references (p. [293]-297) and index.Shape and Shape Theory; Contents; Preface; Chapter 1 Shapes and Shape Spaces; 1.1 Origins; 1.2 Some preliminary observations; 1.3 A matrix representation for the shape of a k-ad; 1.4 'Elementary' shape spaces Σk1 and Σk2; 1.5 The Fubini-Study metric on Σk2; 1.6 The proof of Casson's theorem; Chapter 2 The Global Structure of Shape Spaces; 2.1 The problem; 2.2 When is a space familiar; 2.3 CW complexes; 2.4 A cellular decomposition of the unit sphere; 2.5 The cellular decomposition of shape spaces; 2.6 Inclusions and isometries; 2.7 Simple connectivity and higher homotopy groups2.8 The mapping cone decomposition2.9 Homotopy type and Casson's theorem; Chapter 3 Computing the Homology of Cell Complexes; 3.1 The orientation of certain spaces; 3.2 The orientation of spherical cells; 3.3 The boundary of an oriented cell; 3.4 The chain complex, homology and cohomology groups; 3.5 Reduced homology; 3.6 The homology exact sequence for shape spaces; 3.7 Applications of the exact sequence; 3.8 Topological invariants that distinguish between shape spaces; Chapter 4 A Chain Complex for Shape Spaces; 4.1 The chain complex; 4.2 The space of unoriented shapes4.3 The boundary map in the chain complex4.4 Decomposing the chain complex; 4.5 Homology and cohomology of the spaces; 4.6 Connectivity of shape spaces; 4.7 Limits of shape spaces; Chapter 5 The Homology Groups of Shape Spaces; 5.1 Spaces of shapes in 2-space; 5.2 Spaces of shapes in 3-space; 5.3 Spaces of shapes in 4-space; 5.4 Spaces of unoriented shapes in 2-space; 5.5 Spaces of unoriented shapes in 3-space; 5.6 Spaces of unoriented shapes in 4-space; 5.7 Decomposing the essential complexes; 5.8 Closed formulae for the homology groups; 5.9 Duality in shape spacesChapter 6 Geodesics in Shape Spaces6.1 The action of SO(m) on the pre-shape sphere; 6.2 Viewing the induced Riemannian metric through horizontal geodesics; 6.3 The singular points and the nesting principle; 6.4 The distance between shapes; 6.5 The set of geodesics between two shapes; 6.6 The non-uniqueness of minimal geodesics; 6.7 The cut locus in shape spaces; 6.8 The distances and projections to lower strata; Chapter 7 The Riemannian Structure of Shape Spaces; 7.1 The Riemannian metric; 7.2 The metric re-expressed through natural local vector fields; 7.3 The Riemannian curvature tensorChapter 8 Induced Shape-Measures8.1 Geometric preliminaries; 8.2 The shape-measure on Σkm induced by k labelled iid isotropic Gaussian distributions on Rm; 8.3 Shape-measures on Σm+1m of Poisson-Delaunay tiles; 8.4 Shape-measures on Σk2 induced by k labelled iid non-isotropic Gaussian distributions on R2; 8.5 Shape-measures on Σk2 induced by complex normal distributions; 8.6 The shape-measure on Σ32 induced by three labelled iid uniform distributions in a compact convex set8.7 The shape-measure on Σ32 induced by three labelled iid uniform distributions in a convex polygon. I: the singular tessellationShape 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 The statistical theory of shape is a relatively new topic and is generating a great deal of interest and comment by statisticians, engineers and computer scientists. Mathematically, 'shape' is the geometrical information required to describe an object when location, scale and rotational effects are removed. The theory was pioneered by Professor David Kendall to solve pWiley series in probability and statistics.Shape theory (Topology)Topological spacesShape theory (Topology)Topological spaces.514/.24Kendall D. G(David George),1918-2007.254288MiAaPQMiAaPQMiAaPQBOOK9911019301203321Shape and shape theory4421670UNINA