Bookstein The Measurement of Biological Shape and Shape Change

1978
ISBN: 978-3-642-93093-5
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 24, 191 Seiten, eBook

Reihe: Lecture Notes in Biomathematics

Zielgruppe

Research

Autoren/Hrsg.

Bookstein, F. L.

Inhaltsverzeichnis

One. Introduction: On the Absence of Geometry from Morphometrics.- First Part. The Measurement of Biological Shape.- Two. Shapes and Measures of Shape.- A. Properties of the Euclidean Plane and Euclidean Space.- B. Outlines and Homologous Landmarks.- C. Definitions of Shape, Shape Change, Shape Measurement.- D. Shapes as Data.- Three. Critique of an Applied Field: Conventional Cephalometrics.- A. Landmarks, Curvature, and Growth.- B. Registration.- Four. New Statistical Methods for Shape.- A. Analysis of the Tangent Angle Function.- 1. History.- 2. Sampling from the tangent angle function.- 3. Conic replacement curves and their estimation Fit of a conic to a point — Geometric interpretation — Estimator for a circle — Estimation for the general conic — Computation of the extremum -Linear constraints.- 4. Conic splining Joint conic fitting under constraint -An example — Application — Analysis of parameters.- B. Extension to Three Dimensions: A Sketch.- C. Skeletons Definition — A multivariate statistical method — Bibliographic note.- Second Part. The Measurement of Shape Change Using Biorthogonal Grids.- Five. The Study of Shape Transformation after D’Arcy Thompson.- A. The Original Method.- 1. Thompson’s own work.- 2. Later examples.- 3. Difficulties.- B. Analysis of Growth Gradients.- C. Simulations.- D. Other Morphometric Schemes Vector displacements — Multivariate morphometrics.- Six. The Method of Biorthogonal Grids.- A. Representation of Affine Transformations.- B. General Lines of Growth and Biorthogonal Grids.- C. Summarizing the Grids.- Technical Note 1. Existence and Form of Biorthogonal Grids.- Technical Note 2. Interpolation from Landmark Locations and Arcs The measure of roughness — The vector space and its associated functions — Interpolation from boundary values — Interpolation from boundary values and interior points — Note on computation.- Technical Note 3. Construction of Integral Curves.- Technical Note 4. On Homologous Points.- Seven. Examples of Biorthogonal Analysis.- A. Comparison of Square and Biorthogonal Grids: Thompson’s Diodon Figure.- B. Phylogeny and Ontogeny of Primate Crania.- 1. Functional craniology and craniometrics.- 2. Data for this exercise.- 3. Two types of transformations.- 4. Comparative ontogeny of the apes and man.- Eight. Future Directions for Transformation Analysis.- A. Statistical Methods The symmetric tensor field — Concordance -Linear methods.- B. Computation Other kinds of information about homology -Three dimensions.- C. Likely Applications Computed tomography — Orthodontics — Developmental biology.- Nine. Envoi.- Literature Cited.