Shape distributions for landmark data. (English) Zbl 0686.60017

Mardia, K. V.; Dryden, I. L.

Adv. Appl. Probab. 21, No. 4, 742-755 (1989).

Summary: The paper obtains the exact distribution of F. L. Bookstein’s [Stat. Sci. 1, 181-242 (1986; Zbl 0614.62144)] 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.

MSC:

60D05

Geometric probability and stochastic geometry

Keywords:

distribution on triangles; distribution on quadrilaterals; image analysis; invariant shape measures; model for landmark data

Citations:

Zbl 0614.62144