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Biometrika 2001 88(2):469-485; doi:10.1093/biomet/88.2.469
© 2001 by Biometrika Trust
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Shape, Procrustes tangent projections and bilateral symmetry

J.T. Kent1 and K.V. Mardia1

1 Department of Statistics, University of Leeds, Leeds LS2 9JT, U.Kj.t.kent{at}leeds.ac.ukk.v.mardia{at}leeds.ac.uk

In shape analysis with concentrated data, the Procrustes tangent projection of shapes plays a fundamental role since this projection can be used to convert shape analysis to standard multivariate analysis.In view of its importance, a systematic and rigorous treatment of the Procrustes tangent projection is developed here to facilitate its use in applications.One important application involves an analytical description of bilateral symmetry of objects, together with some related distributional results. An explicit expression for the tangent projection is also derived.

Key Words: Concentrated shape; Hotelling's T2; Object symmetry; Procrustes analysis

Received June 1999. Revised June 2000


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