Shape changes in the plane for landmark data

• 成果类型: Article
• 署名作者: Prentice, MJ; Mardia, KV
• 署名单位: University of Leeds
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1995
• 页码: 1960-1974
• 关键词: spherical regression; orientation statistics; DIRECTIONAL-DATA; distributions

摘要

This paper deals with the statistical analysis of matched pairs of shapes of configurations of landmarks in the plane. We provide inference procedures on the complex projective plane for a basic measure of shape change in the plane, on observing that shapes of configurations of (k + 1) landmarks in the plane may be represented as points on CPk-1 and that complex rotations are the only maps on CSk-1 which preserve the usual Hermitian inner product. Specifically, if u(1), ..., u(n) are fixed points on CPk-1 represented as CSk-1/U(1), and v(1), ..., v(n) are random points on CPk-1 such that the distribution of v(j) depends only on \\v(j)*Au-j\\(2) for some unknown complex rotation matrix A, then this paper provides asymptotic inference procedures for A. It is demonstrated that shape changes of a kind not detectable as location shifts by standard Euclidean analysis can be found by this frequency domain method. A numerical example is given.