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Motivated by the problem of nonparametric inference in high level digitalimage analysis, we introduce a general extrinsic approach for data analysis onHilbert manifolds with a focus on means of probability distributions on suchsample spaces. To perform inference on these means, we appeal to the concept ofneighborhood hypotheses from functional data analysis and derive a one-sampletest. We then consider analysis of shapes of contours lying in the plane. Byembedding the corresponding sample space of such shapes, which is a Hilbertmanifold, into a space of Hilbert-Schmidt operators, we can define extrinsicmean shapes of planar contours and their sample analogues. We apply the generalmethods to this problem while considering the computational restrictions facedwhen utilizing digital imaging data. Comparisons of computational cost areprovided to another method for analyzing shapes of contours.

Nonparametric Estimation of Means on Hilbert Manifolds and Extrinsic Analysis of Mean Shapes of Contours