The Offset Normal Shape Distribution for Dynamic Shape Analysis

This paper 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 modelling 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 (1989), Dryden and Mardia (1991), Mardia and Walder (1994) and Kume and Welling (2010).