The Offset Normal Shape Distribution for Dynamic Shape Analysis

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.本文针对不同时刻采集的标志点数据展开统计分析。动态形状的统计分析是极具挑战性的研究课题，难点在于难以刻画跨个体、跨群组且随时间演变的形状变化规律。现有多种可用于动态形状分析的建模方案。本文基于平面关联高斯构型的形状精确分布理论，推导出衍生的偏移正态形状分布（offset-normal shape distribution）。随后，本文对该分布的多项性质展开研究，并探讨了若干特殊情形。本研究是Mardia与Dryden、Dryden与Mardia、Mardia与Walder以及Kume与Welling既往相关工作的自然延伸。本文的补充材料可在线获取。