Directions and projective shapes

Details Directions and projective shapes Directions and projective shapes

2005-08-16

arxiv.org/abs/math/0508280v1

Annals of Statistics 2005, Vol. 33, No. 4, 1666-1699

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053605000000273 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053605000000273

This paper deals with projective shape analysis, which is a study of finite configurations of points modulo projective transformations. The topic has various applications in machine vision. We introduce a convenient projective shape space, as well as an appropriate coordinate system for this shape space. For generic configurations of k points in m dimensions, the resulting projective shape space is identified as a product of k-m-2 copies of axial spaces RP^m. This identification leads to the need for developing multivariate directional and multivariate axial analysis and we propose parametric models, as well as nonparametric methods, for these areas. In particular, we investigate the Frechet extrinsic mean for the multivariate axial case. Asymptotic distributions of the appropriate parametric and nonparametric tests are derived. We illustrate our methodology with examples from machine vision.

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