LEADER 05458nam 2200697Ia 450 001 9911019301203321 005 20200520144314.0 010 $a9786612307386 010 $a9781282307384 010 $a128230738X 010 $a9780470317006 010 $a0470317000 010 $a9780470317846 010 $a0470317841 035 $a(CKB)1000000000806956 035 $a(EBL)470255 035 $a(SSID)ssj0000342853 035 $a(PQKBManifestationID)11247812 035 $a(PQKBTitleCode)TC0000342853 035 $a(PQKBWorkID)10289453 035 $a(PQKB)11362928 035 $a(MiAaPQ)EBC470255 035 $a(PPN)152549536 035 $a(OCoLC)264615247 035 $a(Perlego)2775086 035 $a(EXLCZ)991000000000806956 100 $a19990105d1999 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aShape and shape theory /$fD.G. Kendall ... [et al.] 210 $aChichester ;$aNew York $cWiley$dc1999 215 $a1 online resource (328 p.) 225 1 $aWiley series in probability and statistics 300 $aDescription based upon print version of record. 311 08$a9780471968238 311 08$a0471968234 320 $aIncludes bibliographical references (p. [293]-297) and index. 327 $aShape 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 ?k1 and ?k2; 1.5 The Fubini-Study metric on ?k2; 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 groups 327 $a2.8 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 shapes 327 $a4.3 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 spaces 327 $aChapter 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 tensor 327 $aChapter 8 Induced Shape-Measures8.1 Geometric preliminaries; 8.2 The shape-measure on ?km induced by k labelled iid isotropic Gaussian distributions on Rm; 8.3 Shape-measures on ?m+1m of Poisson-Delaunay tiles; 8.4 Shape-measures on ?k2 induced by k labelled iid non-isotropic Gaussian distributions on R2; 8.5 Shape-measures on ?k2 induced by complex normal distributions; 8.6 The shape-measure on ?32 induced by three labelled iid uniform distributions in a compact convex set 327 $a8.7 The shape-measure on ?32 induced by three labelled iid uniform distributions in a convex polygon. I: the singular tessellation 330 $aShape and Shape Theory D. G. Kendall Churchill College, University of Cambridge, UK D. Barden Girton College, University of Cambridge, UK T. K. Carne King's College, University of Cambridge, UK H. Le University of Nottingham, UK The statistical theory of shape is a relatively new topic and is generating a great deal of interest and comment by statisticians, engineers and computer scientists. Mathematically, 'shape' is the geometrical information required to describe an object when location, scale and rotational effects are removed. The theory was pioneered by Professor David Kendall to solve p 410 0$aWiley series in probability and statistics. 606 $aShape theory (Topology) 606 $aTopological spaces 615 0$aShape theory (Topology) 615 0$aTopological spaces. 676 $a514/.24 700 $aKendall$b D. G$g(David George),$f1918-2007.$0254288 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911019301203321 996 $aShape and shape theory$94421670 997 $aUNINA