Spatially Regularized Shape Analysis of the Hippocampus Using $P$-Spline Based Shape Regression

Abstract

Shape analysis is increasingly becoming important to study changes in brain structures in relation to clinical neurological outcomes. This is a challenging task due to the high dimensionality of shape representations and the often limited number of available shapes. Current techniques counter the poor ratio between dimensions and sample size by using regularization in shape space, but do not take into account the spatial relations within the shapes. This can lead to models that are biologically implausible and difficult to interpret. We propose to use P-spline based regression, which combines a generalized linear model (GLM) with the coefficients described as B-splines and a penalty term that constrains the regression coefficients to be spatially smooth. Owing to the GLM, this method can naturally predict both continuous and discrete outcomes and can include non-spatial covariates without penalization. We evaluated our method on hippocampus shapes extracted from magnetic resonance (MR) images of 510 non-demented, elderly people. We related the hippocampal shape to age, memory score, and sex. The proposed method retained the good performance of current techniques, such as ridge regression, but produced smoother coefficient fields that are easier to interpret.