Population Shape Regression from Random Design Data

摘要

Regression analysis is a powerful tool for the study of changes in a dependent variable as a function of an independent regressor variable, and in particular it is applicable to the study of anatomical growth and shape change. When the underlying process can be modeled by parameters in a Euclidean space, classical regression techniques (Hardle, Applied Nonparametric Regression, 1990; Wand and Jones, Kernel Smoothing, 1995) are applicable and have been studied extensively. However, recent work suggests that attempts to describe anatomical shapes using flat Euclidean spaces undermines our ability to represent natural biological variability (Fletcher et al., IEEE Trans. Med. Imaging 23(8), 995–1005, 2004; Grenander and Miller, Q. Appl. Math. 56(4), 617–694, 1998).