Statistical Theory of Shape

AvChristopher G. Small

Inbunden, Engelska, 1996

Del i serien Springer Series in Statistics

1 059 kr

Beställningsvara. Skickas inom 10-15 vardagar. Fri frakt över 249 kr.

Fler format och utgåvor

Häftad

1 062 kr

Beskrivning

The shape of a data set can be defined as the total of all information under translations, rotations, and scale changes to the data. Over the last decade, shape analysis has emerged as a promising new field of statistics with applications to morphometrics, pattern recognition, archaeology, and other disciplines. This book provides a comprehensive coverage of the statistical theory of shape. Both the Kendall and the Bookstein schools of shape analysis are described. It is written for graduate students and researchers in statistics who have some knowledge of multivariate models. An understanding of the basic concepts of differential manifolds is also helpful.

Produktinformation

Utgivningsdatum:1996-08-09
Mått:156 x 234 x 18 mm
Vikt:535 g
Format:Inbunden
Språk:Engelska
Serie:Springer Series in Statistics
Antal sidor:230
Upplaga:1996
Förlag:Springer-Verlag New York Inc.
ISBN:9780387947297

Utforska kategorier

Innehållsförteckning

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.