The Offset Normal Shape Distribution for Dynamic Shape Analysis

Abstract

This article deals with the statistical analysis of landmark data observed at different temporal instants. Statistical analysis of dynamic shapes is a problem with significant challenges due to the difficulty in providing a description of the shape changes over time, across subjects and over groups of subjects. There are several modeling strategies, which can be used for dynamic shape analysis. Here, we use the exact distribution theory for the shape of planar correlated Gaussian configurations and derive the induced offset-normal shape distribution. Various properties of this distribution are investigated, and some special cases discussed. This work is a natural progression of what has been proposed in Mardia and Dryden, Dryden and Mardia, Mardia and Walder, and Kume and Welling. Supplemental materials for this article are available online.

KEYWORDS:

• EM algorithm
• Offset-normal shape distribution
• Shape analysis
• Spatio-temporal correlations

Supplementary Materials

Supplementary materials associated with Sections 2 to 5 are provided, along with Matlab codes used to perform both the statistical analysis and the simulation studies.

Acknowledgments

The authors thank the Editor, the Associate Editor, and a referee for helpful comments and suggestions, which have significantly improved the quality of the paper. The authors are also very grateful to J. T. Kent for comments on preliminary versions.