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Shape distributions for landmark data

Published online by Cambridge University Press:  01 July 2016

K. V. Mardia  and
I. L. Dryden
K. V. Mardia*
Affiliation:
University of Leeds
I. L. Dryden*
Affiliation:
University of Leeds
*
Postal address for both authors: Department of Statistics, University of Leeds, Leeds LS2 9JT, UK.
Postal address for both authors: Department of Statistics, University of Leeds, Leeds LS2 9JT, UK.
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Abstract

The paper obtains the exact distribution of Bookstein's shape variables under his plausible model for landmark data. We consider its properties including invariances, marginal distributions and the relationship with Kendall's uniform measure. Particular cases for triangles and quadrilaterals are highlighted. A normal approximation to the distribution is obtained, extending Bookstein's result for three landmarks. The adequacy of these approximations is also studied.

Keywords

DISTRIBUTION ON TRIANGLESDISTRIBUTION ON QUADRILATERALSIMAGE ANALYSISINVARIANT SHAPE MEASURESLANDMARKSSHAPE SPACE
Type
Research Article
Information
Advances in Applied Probability , Volume 21 , Issue 4 , December 1989 , pp. 742 - 755
Copyright
Copyright © Applied Probability Trust 1989 

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