Sankhya: The Indian Journal of Statistics

1993, Volume 55, Series A, Pt. 3, 460--480

MULTIVARIATE SHAPE ANALYSIS

By

I. L. DRYDEN,

And

K. V. MARDIA, University of Leeds, U. K

 

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 Bookstien shape variables 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 Procrists tangent space. Standard multivariate analysis can then be performed, for example, Hottelling's $T^2$ test and principal component analysis. We also consider a distribution free approach. Finally, we illustrate the methods with a practical 3D application in Biology.

Subject classification. 62H11

FULL PAPER.

This article in Mathematical Reviews.