BIOMETRY / EVOLVE reader 諸氏：
三中信宏（農環研）です。
生物形態測定学の新刊が届きましたので、内容紹介をば。
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I.L. Dryden and K.V. Mardia 1998.
"Statistical shape analysis"
John Wiley & Sons, Chichester, xx+347pp.
ISBN 0-471-95816-6 (hbk.)
US$115.00 (amazon.com), 書店経由で21,000円
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一昨年あたりから新刊予告は出ていたのですが、出版が大幅に遅れたようです。こ
の分野の進展速度を考えれば、それもやむを得ないことと思います。
内容は、一言でいえば、Procrustes測度をもつKendall形状空間とその局所線形化
に関する教科書です。
目次は下記の通りです。セクション項目まで入れたので長くなってしまいました。
--- Table of Contents ---
Preface
Acknowledgements
1 Introduction
1.1 Definition and motivation
1.1.1 Landmarks
1.1.2 Traditional methods
1.1.3 Geometrical methods
1.2 Practical applications
1.2.1 Biology: mouse vertebrae
1.2.2 Biology: gorilla skulls
1.2.3 Medicine: brain MR scans of schizophrenic patients
1.2.4 Image analysis: postcode recognition
1.2.5 Archaeology: alignments of standing stones
1.2.6 Geography: central place theory
1.2.7 Geology: microfossils
1.2.8 Biology: macaque skulls
1.2.9 Biology: sooty mangabeys
1.2.10 Agriculture: fish recognition
1.2.11 Agriculture: robotic harvesting of mushrooms
1.2.12 Genetics: electrophoretic gels
2 Preliminaries: size measures and shape coordinates
2.1 configuration space
2.2 Size
2.3 Some shape coordinate systems
2.3.1 Angles and ratios of lengths
2.3.2 Bookstein coordinates: planar case
2.3.3 Triangle case
2.3.4 Kendall coordinates: planar case
2.3.5 Kendall's spherical coordinates for triangles
2.3.6 Watson's triangle coordinates
3 Preliminaries: planar Procrustes analysis
3.1 Introduction
3.2 Shape distance and Procrustes matching
3.3 Estimation of mean shape
3.4 Shape variability
4 Shape space and distances
4.1 Shape space
4.1.1 Introduction
4.1.2 Filtering translation
4.1.3 Pre-shape
4.1.4 Shape
4.1.5 Size-and-shape: removing location and rotation
4.1.6 Reflection shape
4.1.7 Alternative standardizations
4.1.8 Over-dimensioned case
4.1.9 Planar case
4.2 Distances
4.2.1 Procrustes distances
4.2.2 Alternative distances
4.2.3 Planar case
4.2.4 Triangle case
4.3 Advanced shape coordinate systems
4.3.1 Tangent space coordinates
4.3.2 Kent's polar coordinates
4.3.3 Bookstein coordinates for three dimensional data
4.3.4 Goodall-Mardia QR shape coordinates
4.3.5 Goodall-Mardia polar shape coordinates
5 General Procrustes methods
5.1 Introduction
5.2 Ordinary Procrustes analysis
5.2.1 Full ordinary Procrustes analysis
5.3 Generalized Procrustes analysis
5.3.1 Introduction
5.3.2 Algorithm for higher dimensions
5.4 Variants of Procrustes analysis
5.4.1 Ordinary partial Procrustes
5.4.2 Generalized partial Procrustes
5.4.3 Reflection Procrustes
5.5 Shape variability: principal components analysis
5.5.1 Two dimensional data
5.5.2 Point distribution models
5.5.3 PCA in shape analysis and multivariate analysis
6 Shape models for two dimensional data
6.1 Uniform distribution
6.2 Complex Bingham distribution
6.2.1 The density
6.2.2 The normalizing constant
6.2.3 Properties
6.2.4 Inference
6.2.5 Relationship with the Fisher distribution
6.3 Complex Watson distribution
6.3.1 The density
6.3.2 Calculation of the integrating constant
6.3.3 Inference
6.3.4 Large concentration
6.4 Complex angular central Gaussian distribution
6.5 A rotationally symmetric shape family
6.6 Offset normal shape distributions
6.6.1 Equal mean case in two dimensions
6.6.2 The isotropic case in two dimensions
6.6.3 The triangle case
6.6.4 Approximations: large and small variations
6.6.5 Moments
6.6.6 Isotropy
6.7 Offset normal shape distributions with general covariances
6.7.1 The complex normal case
6.7.2 The equal means case
6.7.3 Properties
6.7.4 Inference for offset normal distributions
6.8 A Bayesian approach
6.9 Practical inference
7 Tangent space inference
7.1 Tangent space inference
7.1.1 One sample Hotelling's T^2 test
7.1.2 Two independent sample Hotelling's T^2 test
7.1.3 Permutation test
7.1.4 Extensions
7.1.5 Dimension reduction in inference
7.2 Inference using Procrustes statistics under isotropy
7.2.1 One sample Goodall's F test
7.2.2 Two independent sample Goodall's F test
7.2.3 One way analysis of variance
7.2.4 Further inference for Procrustes statistics
7.3 Edge superimposition shape coordinates
7.3.1 Bookstein coordinates
7.3.2 Hotelling's T^2 two sample test using Bookstein coordinates
7.3.3 Advantages and disadvantages
7.3.4 Extensions
8 Size-and-shape
8.1 Introduction
8.2 Allometry
8.3 Geometry
8.4 Offset normal size-and-shape distributions
8.4.1 The size-and-shape densuty
8.5 Particular cases
8.5.1 The complex normal case
8.5.2 The equal means case
8.5.3 The isotropic case
8.6 Inference using the offset normal model
8.7 Alternative distributions
8.8 Size-and-shape versus shape
9 Distributions for higher dimensions
9.1 Introduction
9.2 QR decomposition
9.3 Size-and-shape distributions
9.3.1 Coincident means
9.3.2 Collinear means
9.3.3 Planar means
9.3.4 Higher rank case
9.4 Shape densities and Bartlett's decomposition
9.4.1 Coincident case
9.4.2 Collinear case
9.5 Multivariate approach
9.6 Approximations
9.7 A rotationally symmetric shape family
10 Deformations and describing shape change
10.1 Deformations
10.1.1 Introduction
10.1.2 Definition and desirable properties
10.1.3 D"Arcy Thompson's transformation grid
10.2 The Affine deformation
10.2.1 The triangle case: Bookstein's hyperbolic shape space
10.3 Pairs of thin-plate splines
10.3.1 Thin-plate splines
10.3.2 Transformational grids
10.3.3 Principal and partial warp decompositions
10.3.4 Principal component analysis with non-Euclidean metrics
10.3.5 Relative warps
10.4 Alternative approaches and history
10.4.1 Early transformation grids
10.4.2 Finite element analysis
10.4.3 Biorthogonal grids
10.4.4 Other deformations
10.5 Kriging
10.5.1 Universal kriging
10.5.2 Deformations
10.5.3 Intrinsic kriging
10.5.4 Kriging with derivative constraints
10.6 Statistical shape change
10.6.1 Tangent space methods
10.6.2 Growth curve models for triangle shapes
10.6.3 Geometric components of shape change
10.6.4 Paired shape distributions
11 Shape in images
11.1 Introduction
11.2 High-level Bayesian image analysis
11.3 Prior models for objects
11.3.1 Geometric parameter approach
11.3.2 Landmarks: Shape distributions and point distribution models
11.3.3 Graphical templates
11.3.5 Thin-plate splines
11.3.5 Outlines
11.4 Inference
11.5 Multiple objects and occulsions
11.5.1 Classical hough transform
11.5.2 Morphological operations
11.5.3 A Markovian object process
11.6 Warping and image averaging
11.6.1 Warping
11.6.2 Image averaging
11.6.3 Merging images
11.7 Discussion
12 Additional topics
12.1 Consistency
12.2 Distance-based methods
12.2.1 Multidimensional scaling
12.2.2 EDMA
12.2.3 Tests for shape differences
12.2.4 Log-distances and multivariate analysis
12.2.5 Distance methods versus geometrical methods
12.2.6 Euclidean shape tensor analysis
12.2.7 Angular shape analysis
12.3 Incomplete data
12.4 General shape spaces
12.4.1 Definitions
12.4.2 Two object matching
12.4.3 Generalized matching
12.5 Affine shape
12.5.1 Least squares matching: two objects
12.5.2 Least squares matching: multiple objects
12.6 Robust superimposition methods
12.6.1 Resistance to landmark outliers
12.6.2 Object outliaers
12.7 Smoothing
12.7.1 Smoothed matching
12.7.2 Smoothed principal component analysis
12.8 Distribution-free methods
12.9 Unlabelled points
12.9.1 Flat triangle and alignments
12.9.2 Unlabelled shape densities
12.9.3 Further probabilistic issues
12.9.4 Delaunay triangles
12.10 Landmark-free approaches
12.10.1 Curvature
12.11 Postscript
Appendix A: Notation
Appendix B: Software and data
Mouse vertebrae
Gorilla skulls
Handwritten digit 3 data
Other sources
References and author index
Index
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目次から判断して、最近数年の間に出たこの分野の教科書の中ではもっとも包括的
な内容の一冊と思います。
第６章あたりでかなりの「死者」が出るおそれが...。
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** 三中信宏 / MINAKA Nobuhiro / 農環研・計測情報科・調査計画研究室