Author | Small, Christopher G. author |
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Title | The Statistical Theory of Shape [electronic resource] / by Christopher G. Small |
Imprint | New York, NY : Springer New York, 1996 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-4032-7 |
Descript | X, 230 p. online resource |
1 Introduction -- 1.1 Background of Shape Theory -- 1.2 Principles of Allometry -- 1.3 Defining and Comparing Shapes -- 1.4 A Few More Examples -- 1.5 The Problem of Homology -- 1.6 Notes -- 1.7 Problems -- 2 Background Concepts and Definitions -- 2.1 Transformations on Euclidean Space -- 2.2 Differential Geometry -- 2.3 Notes -- 2.4 Problems -- 3 Shape Spaces -- 3.1 The Sphere of Triangle Shapes -- 3.2 Complex Projective Spaces of Shapes -- 3.3 Landmarks in Three and Higher Dimensions -- 3.4 Principal Coordinate Analysis -- 3.5 An Application of Principal Coordinate Analysis -- 3.6 Hyperbolic Geometries for Shapes -- 3.7 Local Analysis of Shape Variation -- 3.8 Notes -- 3.9 Problems -- 4 Some Stochastic Geometry -- 4.1 Probability Theory on Manifolds -- 4.2 The Geometric Measure -- 4.3 Transformations of Statistics -- 4.4 Invariance and Isometries -- 4.5 Normal Statistics on Manifolds -- 4.6 Binomial and Poisson Processes -- 4.7 Poisson Processes in Euclidean Spaces -- 4.8 Notes -- 4.9 Problems -- 5 Distributions of Random Shapes -- 5.1 Landmarks from the Spherical Normal: IID Case -- 5.2 Shape Densities under Affine Transformations -- 5.3 Tools for the Ley Hunter -- 5.4 Independent Uniformly Distributed Landmarks -- 5.5 Landmarks from the Spherical Normal: Non-IID Case -- 5.6 The Poisson-Delaunay Shape Distribution -- 5.7 Notes -- 5.8 Problems -- 6 Some Examples of Shape Analysis -- 6.1 Introduction -- 6.2 Mt. Tom Dinosaur Trackways -- 6.3 Shape Analysis of Post Mold Data -- 6.4 Case Studies: Aldermaston Wharf and South Lodge Camp -- 6.5 Automated Homology -- 6.6 Notes