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Multivariate shape analysis. (English) Zbl 0806.62050

Summary: This paper reviews the present state of the art in shape analysis, as well as introducing a few new ideas. The paper begins with a definition of size and then various coordinate systems for shape are considered – the QR decomposition and Bookstein shape variables [F. L. Bookstein, Stat. Sci. 1, 181-242 (1986; Zbl 0614.62144)] in particular. Concepts of distance are reviewed including the Procrustes and Riemannian distances. Gaussian models for configurations are then considered, including perturbation models and principal components models. These models, offset in the size and shape or shape spaces, could then be used for size and shape analysis. However, this approach is complicated and we outline approximations based on tangent spaces – the preshape tangent space and the Procrustes tangent space. Standard multivariate analysis can then be performed, for example Hotelling’s \(T^ 2\) test and principal components analysis. We also consider a distribution free approach. Finally, we illustrate the methods with a practical 3D application in biology.

MSC:

62H99 Multivariate analysis
62H11 Directional data; spatial statistics
62H25 Factor analysis and principal components; correspondence analysis

Citations:

Zbl 0614.62144
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