The Statistical Theory of Shape

Shape analysis is an exciting new area of statistics with important applications in biology, computer science, and archeology. This book surveys the two main schools in the area.

Inhalt
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.