Intrinsic inference on the mean geodesic of planar shapes and tree discrimination by leaf growth

Citation
F. Huckemann, Stephan, Intrinsic inference on the mean geodesic of planar shapes and tree discrimination by leaf growth, Annals of statistics , 39(2), 2011, pp. 1098-1124
Journal title
ISSN journal
00905364
Volume
39
Issue
2
Year of publication
2011
Pages
1098 - 1124
Database
ACNP
SICI code
Abstract
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.