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April 2011 Intrinsic inference on the mean geodesic of planar shapes and tree discrimination by leaf growth
Stephan F. Huckemann
Ann. Statist. 39(2): 1098-1124 (April 2011). DOI: 10.1214/10-AOS862


For planar landmark based shapes, taking into account the non-Euclidean geometry of the shape space, a statistical test for a common mean first geodesic principal component (GPC) is devised which rests on one of two asymptotic scenarios. For both scenarios, strong consistency and central limit theorems are established, along with an algorithm for the computation of a Ziezold mean geodesic. In application, this allows to verify the geodesic hypothesis for leaf growth of Canadian black poplars and to discriminate genetically different trees by observations of leaf shape growth over brief time intervals. With a test based on Procrustes tangent space coordinates, not involving the shape space’s curvature, neither can be achieved.


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Stephan F. Huckemann. "Intrinsic inference on the mean geodesic of planar shapes and tree discrimination by leaf growth." Ann. Statist. 39 (2) 1098 - 1124, April 2011.


Published: April 2011
First available in Project Euclid: 9 May 2011

zbMATH: 1216.62084
MathSciNet: MR2816349
Digital Object Identifier: 10.1214/10-AOS862

Primary: 62G20
Secondary: 53C22 , 62H30

Keywords: asymptotic inference , central limit theorem , forest biometry , geodesic and parallel hypothesis , Geodesic principal components , shape analysis , strong consistency , Ziezold mean

Rights: Copyright © 2011 Institute of Mathematical Statistics


Vol.39 • No. 2 • April 2011
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